MAGISTERARBEIT. Titel der Magisterarbeit. "Spatial competition in Polish elections" Verfasserin: Monika Turyna

MAGISTERARBEIT Ttel der Magsterarbet "Spatal competton n Polsh electons" Verfassern: Monka Turyna angestrebter akademscher Grad Magstra der Sozal- und Wrtschaftswssenschaften (Mag. rer. soc. oec) Wen, Im Jun 2008 Studenkennzahl It. Studenblatt: A 066 913 Studenrchtung It. Studenblatt: Magsterstudum Volkswrtschaftslehre Betreuer: O. Unv.-Prof. Dr. Denns Mueller

Abstract The followng work presents a comprehensve analyss of the Polsh parlamentary electons n 2007 from the publc choce perspectve. Poland s a very young modern democracy and ts young age determnes the shape of research t s a subject of. The classcal poltcal scence lterature s qute broad, but there are almost no nterdscplnary works, such as dealng wth the publc choce theory or economcs. The above facts consttute the man motvaton for wrtng ths work. We fnd t partcularly nterestng, verfyng whether t s possble to apply modern economc technques for the case of a country, whch seems stll be developng n terms of legal rules concernng the electon as well as the actual shape of the poltcal scene. The am of ths work s to apply spatal competton approach and publc choce research on coaltonal barganng to the case of Polsh parlamentary electons. It s to be verfed n a frst place, whether a multparty probablstc model can be used to model the poltcal scene and results of the electon. Factor analyss dentfed two dmensons mportant for the poltcs n Poland. One s the typcal economc dmenson whereas the other dmenson represents Catholc Church values and the vew of the role of the church n publc lfe. The spatal competton takes place n the space spanned over these two dmensons. Two models are estmated, a pure probablstc and a jont model. The pure probablstc model turns out to be superor for the case of Poland. Predcted probabltes correspond qute well wth the actual results for the two smaller partes PSL and SLD, but the model fals to predct vote shares for PO and PIS. The problem of abstenton s beleved to be the man reason for ths phenomenon. The estmated coeffcent equals -.3546574 for the pure spatal model and for ths value of the coeffcent no convergent equlbrum shall be observed. For the case of PO and PIS the Downsan hypothess seems to be justfed, whereas for SLD and PSL strategc behavor s the most probable. Second part of the emprcal study deals wth coaltonal behavor. For the case of Poland we observe that the heart s the area wthn the three medan lnes crossng the deal ponts of PO, PSL and SLD. We may predct that the government that forms shall nclude at least one of these partes. Snce a coalton of PO and PSL s currently rulng, the noton seems to predct the stuaton well. The dmenson-by-dmenson model also seems to ft well n to the coaltonal barganng process n Poland. Wth some exceptons, most of the 1

mnstres representng economc and relgous dmenson are occuped by members of partes predcted by the theory. Zusammenfassung De folgende Arbet legt ene wetgespannte Analyse der polnschen Parlamentswahlen 2007 aus Scht der Publc Choce Theore an. Polen st ene sehr junge Demokrate und sen gernges Alter defnert den Forschungsgegenzustand. De klasssche poltkwssenschaftlche Lteratur st umfangrech aber es mangelt an fächerübergrefenden Werken, de sch mt der Wrtschafts- oder Publc Choce Theore befassen. Der oben genannte Tatsache st als der Hauptanlass, dese Arbet zu schreben. Wr fnden es besonders nteressant zu überprüfen, ob es möglch st, moderne ökonomsche Forschungsmethoden m Falle enes Staats anzuwenden, dessen Rechtsgrundsatz und poltsche Szene noch ncht völlg entwckelt snd. Zweck deser Arbet st es, Modelle der Raumkonkurrenz und der Koaltonsverhandlungen m Falle der polnschen Parlamentswahlen anzuwenden. Es wrd zuerst überprüft, ob en probablstsches Mehrparteenmodell engesetzt werden kann um damt de Ergebnsse der Parlamentswahlen modelleren. Mttels Faktorenanalyse wurden de zwe wchtgsten Dmensonen der polnschen poltschen Bühne bestmmt. De erste Dmenson st de typsche ökonomsche Dmenson, während de zwete Dmenson de katholsche Weltanschauung und de Rolle der katholschen Krche m öffentlchen Leben darstellt. De Raumkonkurrenz wrd m Raum abgehalten, der zwschen den zwe obengenanten Dmensonen ausgespannt st. Zwe Modelle werden engesetzt, das ren probablstsche Modell und das gemensame Modell. Im Falle Polens erwest sch das rene Modell als das bessere. De erhalten Wahrschenlchketen entsprechen den tatsächlchen Wahlergebnssen für de zwe kleneren Parteen PSL und SLD, aber das Modell st für de zwe anderen Parteen PO und PIS erfolglos. Das Problem der Stmmenthaltung wrd wohl der Grund deser Erschenung sen. Der erhaltene Koeffzent entsprcht -.3546574 n dem renen Modell und für desen Wert des Koeffzents sollte ken konvergentes Glechgewcht festgestellt werden. Im Falle der großen Parteen PO und PIS erschent de Downs Hypothese begründet, während m Falle der anderen Parteen en strategsches Verhalten höchstwahrschenlch st. Der zwete Tel der emprschen Forschung beschäftgt sch mt Koaltonsverhandlungen. Im Falle Polens st zu beobachten, dass das Herz m Berech legt, der zwschen dre Medanlnen ausgespannt st, de de Idealpunkte der dre Parteen PSL, 2

SLD und PO überschneden. Wr prognostzeren, dass der neu gebldete Mnsterrat wengstens ene von desen Parteen nkluderen sollte. Da de Koalton von PO und PSL derzet regert, schent das Herz de aktuellen Umstände rchtg zu prognostzeren. De Dmenson-nach-dmenson-methode passt ebenfalls gut zur Begründung des Ablaufs der Koaltonsverhandlungen m Falle der polnschen Parlamentwahlen. mt engen Ausnahmen werden de mesten Mnsteren von den durch de Theore vorhergesagten Partemtgledern geletet. 3

Table of contents Introducton 5 Chapter 1. Determnstc votng 9 Part 1. Two-party competton n a one-dmensonal polcy space 9 Part 2. Two-party competton n a mult-dmensonal polcy space 15 Part 3. Mult-party equlbrum 21 Chapter 2. Probablstc votng 32 Chapter 3. Coaltonal models 45 Part 1. Tradtonal theores 45 Part 2. Multdmensonal theores 50 Chapter 4. Spatal competton and coalton formaton n 2007 electon 59 Part 1. The consttutonal system n Poland 59 Part 2. Model of pre-electon competton 65 Part 3. The coaltonal behavor 86 Conclusons 92 Bblography 97 4

Introducton Poland s a very young modern democracy. The frst partally free electon took place n 1989, when just 35% of the seats n Sejm and all the seats n the Senate were assured to be freely elected. The frst entrely free electon was conducted n 1991. Up untl 2007 only 7 parlamentary electons have taken place. Accordng to most poltcal scence scholars, Polsh parlamentarsm s stll developng and therefore t s volatle and subject to major shfts or even crses. Furthermore, hstorcal events play a major role n determnng the shape of the poltcal competton and ts dfferng deologes. Due to these factors t s partcularly nterestng to analyze Poland s development as a democracy, snce n dong so we are able to wtness a process that n most Western democraces took place decades ago, whle at the same tme evaluate t usng modern research technques. There s also a wde feld for comparson wth more mature democratc European countres. The young age of the Poland s democracy also determnes the shape of research around t. The classcal poltcal scence lterature avalable s qute broad, but there are almost no nterdscplnary works dealng wth the publc choce theory or economcs. In fact, t was mpossble to fnd any paper applyng publc choce theory to the poltcal stuaton n Poland. It appears that there s no lterature as yet concernng spatal competton n Poland. Sosnowska (2000) represents a rare example of a game-theoretcal approach appled to predct the formaton of Polsh parlamentary coaltons n 1997. The above factors consttute my man motvatons n wrtng ths work. My am was to verfy whether t s possble to apply modern economc technques to the case of a country lke Poland, whch seems stll be developng n terms of legal rules concernng the electon as well as n terms of the actual shape of the poltcal scene. In partcular I wanted to explore f 5

Poland s poltcal structures -- whch are wdely derved from other countres and whch use mported consttutonal solutons -- would develop n a manner smlar to other countres hstorcal development. Moreover, t s often argued that Polsh poltcans are not yet professonal, as they do not use modern publc relatons research and furthermore a poltcal culture n general s not yet fully establshed. My use of a Downsan approach can to some extent verfy ths hypothess. A second motvaton for my research was the fact that there s lttle or no lterature on ths topc. Known applcatons of the publc choce theory nclude Great Brtan, the Netherlands and Israel, but t has so far not been appled to any countres n Central or Eastern Europe. The am of ths paper s to begn to fll ths gap and apply contemporary publc choce research to an nterestng new case. The goal of ths work s to prove whether the theory of spatal competton s sutable for explanng parlamentary electons n Poland. Specfcally, two major spatal competton ssues and some auxlary hypotheses are analyzed. Frstly, I explore whether a mult-party probablstc model can be used to model the Polsh poltcal scene, n partcular to model the results of the 2007 electon. Two models are evaluated, consstng of a pure probablstc and a jont model. The pure probablstc model turns out to be superor n Poland s case. However, nether of these models takes nto account the non-spatal characterstcs of the competng partes and t s argued that for at least some canddates non-spatal characterstcs should further researched. In addton, I tested how many spatal dmensons characterze the poltcal competton. Two dmensons are proven to be suffcent to model Poland s poltcal scene: an economc dmenson and a relgous dmenson. The second part of the emprcal study concentrates on the post-electon behavor of the partes, as well as on the coaltonal barganng that took place and ther mpact on the post-electon postonng. It s predcted 6

that for some partes, strategc behavor may play a strong role n choosng ther manfested deal pont, whereas for the other partes the pure Downsan approach adequately explans ther observed poston. A fnal goal was to dentfy whether a Nash equlbrum could be found for Poland s poltcal spectrum, and f so, to show f t s convergent or non-convergent and f the major Polsh partes are stuated close to the Nash equlbrum or f the opposte s true. The study of the Polsh 2007 parlamentary electons was accomplshed wth the use of data obtaned from the Publc Opnon Research Center (CBOS). The research was conducted n 2007 and ncludes 1385 ndvdual observatons, each contanng nformaton about respondents opnons on key poltcal and economc ssues and ther poltcal preferences, as well as some characterstcs of the respondents. The author gathered data on poltcal partes va drect responses from party representatves to questons about ther stance on poltcal and economc ssues. Where necessary, nformaton was completed wth the use of publshed party manfestos. The emprcal research ncludes data transformaton wth the use of factor analyss, n order to obtan spatal postons of the partes and voters deal ponts. Subsequently estmated postons are used to calculate spatal dstance, whch s then mplemented as an explanatory varable n a multnomal probt explanng the choce of each competng party. The followng work s dvded nto fve parts. Chapter 1 descrbes the development of the spatal theory of votng, begnnng wth the Hotellng theory and ts elaboraton by Downs and other authors. More contemporary determnstc votng models are also examned. In Chapter 2 the probablstc votng theory s presented. Ths ncludes two party competton models as well as mult-party competton n a mult-dmensonal polcy space. Chapter 3 deals wth coaltonal models that descrbe how the partes behave once they obtan seats n 7

the parlament and how the cabnet forms. These observatons also nclude the mpact of the post-electon cabnet formaton on the pre-electon competton between partes. Chapter 4 comprses a broad analyss of the parlamentary electon n 2007 n Poland. Frst, an overvew of the Polsh poltcal scene s presented, and a short hstory of ts development snce 1989 s gven. Some crucal consttutonal ssues concernng electons, cabnet formaton and the relatons between the legslatve and executve bodes are also presented. The second part of Chapter 4 comprses data analyss and transformaton, whch leads to a constructon of a spatal competton model. The results of these two models of spatal competton, a pure one and another ncludng ndvdual characterstcs, are presented and thoroughly analyzed. Part 3 of Chapter 4 compares poltcal theory wth the actual post-electon coaltonal behavor of Polsh partes. The last part of ths work comprses my conclusons, where I dscuss whether convergent equlbrums can be found for Poland and whether post-electon barganng s consstent wth the noton of the poltcal heart. 8

Chapter 1. Determnstc votng Part 1. Two-party competton n a one-dmensonal polcy space. A useful economc apparatus for the analyss of poltcal partes deologcal postonng was frst developed by Harold Hotellng (1929) and subsequently by Arthur Smthes (1949). Hotellng developed a spatal competton model n whch two grocery stores compete for customers along a gven street. He also suggested that an approprate poltcal parallel for ths model would nvolve the competton of two partes or canddates for the votes of voters durng an electon. One dmenson was assumed for the possble set of locatons (polcy outcomes). Accordng to Hotellng s model, ndvdual voters (consumers) ether comprse a fnte set M [ 1,2,..., m] wth a generc voter (consumer), or are descrbed by a contnuous, twce dfferentable dstrbuton functon F (y) on [0;1]. Each has preferences over the alternatves [0;1] representable by symmetrc, dfferentable, sngle-peaked utlty functon u (y). When M s an nfnte set, F(y) s the dstrbuton of voters deals (Shepsle, 1991). The orgnal Hotellng work specfcally assumes a unform dstrbuton of voters. Addtonally, nelastc demand and zero transacton costs were assumed n ths model, assumptons that were relaxed n later works. Each voter (consumer) votes for a party (buys from a compettor) closest to hs deal pont, as measured by Eucldean dstance. Hotellng concludes that under a unform dstrbuton both sellers wll eventually converge toward the centre of a dstrbuton n order to maxmze ther number of customers and ths result consttutes equlbrum. In the context of competton for votes, ths means that n a two-party system wth a unform dstrbuton of voters vews on a one-dmensonal deologcal ssue 9

the two compettors (ether partes or ndvduals) would nevtably adopt the same platform. In other words the wnnng outcome would be a medan poston outcome, a result consstent wth the medan voter theorem as stated below. Medan voter theorem (sngle dmensonal ssue): If x s a sngle dmensonal ssue, and all voters have sngle-peaked preferences defned over x, than x m, the medan poston, cannot lose under majorty rule. (Black, 1958) Ths pont consttutes a Condorcet wnner, a pont that cannot be beaten by any other pont n any parwse votng. Those who have extended Hotellng's deas have done so by relaxng one or both of the assumptons stated earler. Arthur Smthes and other economsts dspensed wth the assumpton of nelastc demand. Smthes assumed nstead that demand depends on prce and that sales at any gven pont of the market wll vary accordng to how much delvery prces are rased by transportaton costs. For ths reason two competng frms wll be under pressure not only to move closer together to n order to mprove sales n ther "compettve regon", they wll also be under pressure to move farther apart to mprove sales n ther respectve "hnterlands." When these two opposte forces reach equlbrum the competng frms could well be some dstance apart. Contnung the sde dscusson of poltcs, Smthes argued that electoral "demand" s also elastc, snce a voter who feels that both partes are too far from hs deologcal poston can smply stay away from the polls. (Stokes, 1963). If so, two phenomena may occur: alenaton and ndfference. Indfference: Voter votes ff U P ) U ( P ) for some 0 ( 1 2 10

Alenaton: Voter votes ff there exst some 0, such that U ( P*) U ( P ), for j 1,2 The j and are voter-specfc constants that determne whether they vote or not. Ths means that once partes get too close to each other, or too dstant from a voter s deal pont t may not be worthwhle for the voter to go and vote. Downs has retaned Smthes' assumpton of elastc demand and has further modfed the Hotellng model by dspensng wth the assumpton that the publc s evenly dstrbuted over a one-dmensonal space. In fact Downs has done much more than ths. Hs book An Economc Theory of Democracy (1957) consttutes a major theoretcal background for many aspects of party postonng theory, deologes, asymmetrc nformaton and other aspects of votng. Downs analyzed dverse dstrbutons over the one-dmensonal left-rght poltcal scale 1. Frst I shall analyze what happens n two-party systems when voters are dstrbuted normally along the deologcal scale. Partes wll nevtably move towards the centre of a dstrbuton and even a possble loss of extremsts wll not deter ther movement towards each other, because there are so few voters to be lost at the margns compared wth the number to be ganed n the mddle. If the probablty that a voter does not vote s an ncreasng functon of the closeness of two canddates postons, a movement towards the centre of any symmetrc dstrbuton has a symmetrcal effect on the two canddates vote totals. The equlbrum s stll located at the medan. If the probablty that a voter does not vote depends postvely on a canddate s dstance from the voter s s deals, the canddate s pulled toward 1 Also known as conservatve lberal n Amercan nomenclature and as conservatve lberal socal lberal n Europe. 11

the mode of the dstrbuton. If the dstrbuton s symmetrcal and un-modal, the mean and mode wll concde and agan the medan voter outcome wll occur (Mueller, 2003). The medan voter result may be upset f the dstrbuton s asymmetrc or polymodal. Under asymmetrc dstrbuton (fg. 1) the optmal poston s the mode f voters become alenated (Comanor, 1976). D M Fgure 1.1 Optmal canddate locaton f the dstrbuton s asymmetrc. Pont D n the fgure represents the mode, and pont M the medan of the dstrbuton. A canddate may gan votes by movng toward the mode poston f voter alenaton occurs. However, Comanor concludes that the deologcal dfference would usually be so small that t could be neglected. If we alter the dstrbuton to a bmodal one (fg. 2), the competton for votes does not necessarly create movement towards the medan. 12

D 1 D 2 Fgure 1.2 Optmal canddate locatons n a polymodal dstrbuton. Downs argues that under ths type of bmodal dstrbuton, a possble loss at the tals s not s not compensated by a gan n the medan part of the dstrbuton, therefore compettors would reman at opposte poles n terms of ther deology. A two-party system need not lead to convergence on moderaton as predcted by Hotellng and Smthes. However voter alenaton may be so weak that t does not necessarly push the two canddates towards the modes. In ths case the equlbrum may stll be placed n the medan, or a stable set of strateges may not n fact exst. (Davs et al., 1970) Downs concludes that the possblty that partes wll be kept from convergng n a two-party system depends on the refusal of extremst and ndfferent voters to support ether party f they became too smlar, or too dstant from the voters deal pont. But abstenton s rratonal n an deal world where nformaton s costless and complete and the act of votng does not use up scarce resources (Downs, 1957). As long as there was an nfntesmal dfference between the two compettors, extremst voters would be forced to vote for ether of the two partes, no matter how dstasteful the party s polces seemed compared to ther deal pont government. 13

Moreover, f the move towards the modes was strong enough, whchever party won would attempt to mplement radcal polces, n opposton to the other party s deology. Ths means that government polcy would be hghly unstable, and democracy would lkely produce chaos. The orgnal Hotellng model concludes that there s no stable equlbrum wth two or more grocery stores. However, Downs states that poltcal partes cannot move deologcally past each other, snce they would lose ntegrty. Thus, deologcal movement s restrcted at most to progress up to the nearest party on ether sde (Downs, 1957). Moreover, there are a lmted number of partes that can be supported. At ths pont the economc and poltcal parallel begns to dverge. The behavor of real world poltcal partes s not determned by economc condtons alone, and ths causes the electoral spatal models to gve dfferent results than mght be seen n purely economc scenaros. Accordng to Downs, ths means that a stable equlbrum can exst under a unform or mult-modal dstrbuton as long as the partes are concerned wth keepng ther ntegrty and good reputaton. The equlbrum number of partes depends on the shape of the dstrbuton of voters and the nature of the lmt on ntroducng new partes. Ths lmt s determned by the electoral rule beng used. Under the frst-past-the-post system t s lkely that a two-party system wll eventually occur, snce partes that repeatedly lose would tend to merge untl the survvors had a reasonable chance of wnnng a majorty. Under a proportonal representaton system, the lmt s determned by the mnmum number of votes that a party needs to obtan n order to enter the legslature, where subsequently they can form a coalton. One has to bear n mnd, however that t s not necessarly true n every stuaton. 14

Part 2. Two-party competton n a mult-dmensonal polcy space. Plott (1967) descrbes the set of assumptons necessary to provde equlbrum when votng on a mult-dmensonal ssue under majorty rule. He develops multple sets of assumptons where there s no constrant on the possble moton as well as where the possble set of outcomes s lmted e.g. by a budget constrant. In ths context moton means * * * a small change n varables ( dx, dx,..., dx ) from the status quo (e.g. X n Eucldean n - space, E n 1 2 n ). In ths case ndvdual would vote n favor of the ssue (vote for ) f the moton over X ncreases hs utlty, therefore f: U x 1 dx * 1 U x 2 dx * 2 U... x n dx * n 0 That s, votes for moton b k whenever U bk where 0 U s the gradent vector for ndvdual s utlty functon. The group of voters (1,2,,m), each havng assocated gradent vectors U a, a,..., a ) would vote for a moton f Ab 0 where ( 1 2 n a. A.. am 11 1...... a a 1n mn Plott s assumptons necessary for the equlbrum to exst can be summarzed as follows: 15

1. The exstence of an unconstraned equlbrum requres that ndfferent ndvduals do not vote "yes." 2. Any equlbrum must be a pont of maxmum utlty for at least one ndvdual. 3. The remanng (even number of) rows of A can be dvded nto pars for whch there exsts a strctly postve soluton to y y j a a 1 1 a a 2 j2...... a a n jn 0, y,y j 0 The last condton means that all ndvduals for whom the pont s not a maxmum can be dvded nto pars whose nterests are dametrcally opposed. The above condtons are necessary and suffcent for a pure-strategy Nash equlbrum to exst. The most mportant problem here s that there s nothng nherent n utlty theory that would assure the exstence of equlbrum. In fact, equlbrum could only be reached by a hghly mprobable accdent. (Plott, 1967). The above analyss as well as the results obtaned by Kramer (1973) and McKelvey and Schofeld (1986) generally fnd that unless some specfc and hghly mprobable condtons are fulflled a pure strategy Nash equlbrum wll not exst when an ssue s more than one-dmensonal. Here, the strand of research begun by Hotellng hts an obstacle that hnders ts ablty to explan the deologcal postonng of poltcal partes n the real world. Subsequent authors provde results that ether assure the exstence of an equlbrum wthn mxed strateges; develop the orgnal model n a way that allows for exstence of a core; or that try to fnd a set of results other than a core that could partally serve as a soluton for emprcal concerns. Ths last strategy ncludes solutons lke the uncovered set, whch I wll dscuss shortly, or a poltcal heart, dscussed n Chapter 3. 16

Kramer and McKelvey have demonstrated two ways n whch the ntutons generated by the model can wthstand the apparent knfe-edge character of ts equlbrum results. Kramer (1977) has shown that, under a stylzed dynamc, two competng canddates should move ther platforms toward a "mnmax set," centrally located among the voter deal ponts. Whle the platforms may leave the mnmax set once havng reached t, they wll mmedately begn to approach t agan. Moreover, as the number of voters becomes larger, the mnmax set shrnks to a pont and that pont s the medan f one exsts (Calvert, 1985). The uncovered set, on the other hand, has been appled to dverse nsttutonal settngs by several authors. McKelvey and Ordeshook (1976) defne an "admssblty relaton" that s qute smlar to the coverng relaton, and they go on to show the connecton between the admssble set and the outcomes resultng from two-canddate competton. Fshburn (1977) defnes and nvestgates the normatve propertes of a set based on a domnance-lke relaton. Rchelson (1980) shows the connecton between Fshburn's set and the uncovered set, and ntroduces a choce set based on a more natural defnton of domnance. Shepsle and Wengast (1984) have appled and extended Mller's results to show how the coverng relaton can be used to set lmts on agenda-reachable outcomes n multdmensonal choce spaces. (McKelvey 1986) McKelvey (1986) studes the ssue of coverng and domnance relatons n a settng more relevant for the case of party competton n a multdmensonal space. He assumes that there are a fnte number of N voters, a convex set X m of alternatves, N a weak order and R X X representng s preferences. Thus, each R s reflexve, complete, and transtve. We let P and I denote the asymmetrc and symmetrc parts of R, respectvely (McKelvey 1986). It s moreover assumed that each ndvdual s preferences can be represented by a contnuous utlty functon, and that preferences are strct quas-concave and 17

compact ( R s compact). Addtonally, he makes assumptons about wnnng coaltons. A set of wnnng coaltons W s sad to be monotonc and proper, and also strong. P(X) and R(X) are socal preferences. Weak domnance D X X relaton s defned; For any x, y X, xdy P( x) P( y) R( x) R( y) The coverng relaton, denoted C X X s defned; For all x, y X, xcy xdy xpy The uncovered set s defned as the maxmal elements of the coverng relaton. Formally, for any bnary relaton Q X X and set A X, the maxmal elements of the relaton Q n A (f Q s asymmetrc) are defned: M( Q, A) { x A y A,~ yqx} Then the uncovered set s defned: UC( X A) M( C, A) McKelvey models two-canddate competton as a two-person, zero-sum game, wth the canddates as players, who compete for the votes of the electorate through the polcy postons they adopt. Thus, canddate strateges consst of the announcement of a polcy poston that they wll adopt f elected, and then voters are assumed to vote for the canddate whose polcy poston they prefer. Two theorems conclude the above dscusson on the mportance of the uncovered set for party competton: (a) All admssble strateges (and hence all ultmately admssble strateges) for the game are ncluded n UC (X). m (b) If : X s a mxed strategy equlbrum for the game, then the support for, supp( ) must satsfy supp( ) UC( X ) 18

(For proofs, please see McKelvey 1986) To summarze, t s clear that the uncovered set may provde a useful generalzaton of the core when a specfc core does not exst. It s useful n dverse nsttutonal settngs, n partcular n a two-party mult-dmensonal competton. It contans the support set of any mxed strategy equlbrum to the two-canddate competton game. Moreover, the uncovered set shrnks to a medan once the dstrbuton of deal ponts becomes symmetrcal. Another strand of research on the two-party competton when ssues are of more than one dmenson modfes the orgnal model, addng addtonal elements that ether change the nsttutonal settng, or add non-downsan assumptons about the characterstcs of the canddates nterests. Calvert (1985) analyzes what mpact some sgnfcant changes n the model s assumptons have on the robustness of equlbrum, namely, when canddates are not only nterested n wnnng offce, but are also nterested n polcy they could thereafter mplement. He argues that, n the real world, canddates may also be genunely nterested n polcy outcomes for two reasons. In the frst place, a canddate may have actual personal preferences; and secondly he may be constraned by prevous poltcal agreements. In both cases a canddate may be wllng or forced to gve up some of hs votes n order to acheve a desred polcy. Calvert makes some partcularly specfc assumptons, but he argues that some of hs results can potentally be generalzed. The dstrbuton of voters preferences s assumed to be symmetrcal. Each voter has a contnuous, bounded utlty functon whose ndfference curves are spheres centered at a voter s deal pont, wth utlty decreasng monotoncally wth Eucldean dstance away from a voter s deal pont (Calvert 1985). The man concluson s that convergence to the medan s stll present, as s the stuaton when both canddates choose 19

the same platform, located at the medan of the dstrbuton. However, as already mentoned, these conclusons are based on very strct assumptons. Another attempt to develop the tradtonal model was by ntroducng valence ssues, meanng ssues on whch all voters adopt the same poston. Examples of these ssues mght be poltcal corrupton, economc growth etc. Ansolabehere and Snyder (2000) fnd that f the two canddates score on valence ssues dffer, than equlbrums can exst even when the condtons for a Condorcet wnner do not hold. Clearly, f one canddate has a substantal lead n a valence ssue, he wll wn regardless of other canddates postons. The basc assumptons are standard: voters have preferences wthn an n-dmensonal ssue space and a valence ssue whch are Eucldean. Therefore, utlty decreases once the canddate moves away from the voter's deal pont. Canddates move smultaneously and care only about holdng offce. Several results are obtaned. Frst, the equlbrum places no restrctons on the strategy of the canddate wth the lower valence score. However, f a canddate does not have a strong lead, he needs to place hs polcy near the yolk. The yolk s defned as the smallest ball n n that ntersects all medan hyperplanes (McKelvey 1986). Here t must be sad that the condtons for equlbrum hold only f canddates care about maxmzng the probablty of wnnng, and not about maxmzng ther share of votes. Therefore, f we ntroduce some voter s uncertanty or we assocate a stronger mandate wth a hgher vote-share, then equlbrums wll not exst. Concludng ths secton t can be sad that, for the above analyss to have a constructve effect on determnng real-world partes postons, some strct condtons have to be met. These nclude: that only two partes compete and that they do not fear the entry of a thrd, that canddates are concerned only wth maxmzng ther share of the vote, that voters are fully cognzant of the canddates platforms as well as ther own preferences, that 20

canddates are nformed about voters preferences and so forth. Whether ths s true n realty s an emprcal rather than theoretcal queston, and depends very much on a partcular socetal composton, poltcal culture, electoral nsttutons and so forth. Part. 3. Mult-party equlbrum Whereas the pluralty system typcally produces two-party competton, proportonal representaton s meant to produce a set of partes n the legslature that are representatves of the preferences of the electorate. Typcally the effectve number of partes that enter the legslature under the PR system s greater than two. Under the pluralty system, obtanng a hgher number of votes than an opponent assures that a party wns and may ntroduce ther polcy. Under PR, the party that obtans the hghest number of votes does not necessarly ntroduce ther stated polcy, unless they receve more than 50% of the vote. Voters who take part n these electons need to take ths fact nto account when decdng whch party to gve ther vote to. Partes behavor also needs to nvolve both cooperatve and compettve features. On the one hand, partes must compete wth each other n front of the electorate to gan parlamentary seats. On the other hand t s crucal to the modelng of mult-party competton to explore the cooperatve aspect of the coalton game by analyzng the relatonshp between partes manfestos and the polcy outcomes of the coaltons they form. As a result t s partcularly dffcult to analyze mult-party competton. Lterature dealng wth ths ssue s scarce. As already mentoned, Downs (1957) states that equlbrum s possble wth more than two partes competng. However, ths s not a formal analyss, but rather an ntutve analyss. Namely, Downs fnds that under proportonal representaton, a 21

party that wns only a small percentage of the total vote may stll place some of ts members n the government. Thus the mnmum amount of support necessary to keep a party gong s much smaller than that needed n a pluralty system. Nevertheless, each party must stll obtan a certan mnmum number of votes n order to elect members of the legslature who mght then enter a coalton. For ths reason a gven dstrbuton of voters can support only a lmted number of partes. Therefore the condtons necessary for equlbrum do exst (Downs, 1957). Nevertheless, the phenomenon that the pluralty system produces two-canddate competton, called the Duverger s law, does not always take place. If the country s dvded nto electoral dstrcts, among whch voter preferences are not unformly dstrbuted, then there are deologcal centers and the logc of Duverger s law does not hold. I wll start my analyss wth the mult-canddate pluralty case. Eaton and Lpsey (1975) provde a model of spatal economc competton among frms that can be appled to electoral stuatons. The model apples drectly to pluralty rule wth vote maxmzaton. Voters are assumed to vote sncerely for the canddate spatally closest to ther deals; full spatal moblty and zero conjectural varaton for each competng agent s also assumed. Call the set of voters wth deal ponts closest to electoral agent the electoral support of, and partton ths support nto left-hand support and rght-hand support. The necessary and suffcent condtons for equlbrum when voter dstrbuton s unform are that (Shepsle 1991): (1) No electoral agent s support s smaller than any other agent s half-support (2) Perpheral agents are pared; Cox (1987) establshed the property that no locaton can be occuped by more than two agents. For non-unform voter dstrbutons, the necessary and suffcent condtons for equlbrum, n addton to (1) and (2) are: 22

(3) If s an unpared electoral agent, then f B ) f ( B ) where B L and B R are the ( L R boundares between ts electoral support and that of -1 and +1 respectvely. (4) If s pared then f B ) f ( B ) where B SS and B LS are the short-sde and long-sde ( SS LS boundares, respectvely, of s support. (please see Shepsle 1991) If a dstrbuton s polymodal, then there are condtons for equlbrum. Lettng r be the number of modes, the number of agents must be less or equal to twce r, thus namely that: n 2r. Cox (1987) fnds an addtonal nterestng property of a vote-maxmzng equlbrum, Theorem: In pluralty electons wth n 3 vote-maxmzng electoral agents, any Nash equlbrum x x, x,..., x ) must have [0, Q 1 ] [ Q,1] for some agents. ( 1 2 n x 4 3 4 ( Q, ) s the nterquartle range. Cox s theorem states that f a Nash equlbrum s 1 Q3 4 4 to exst n a mult-canddate competton, t must nvolve extremst canddates that le outsde the nter-quartle deologcal range. Cox therefore concludes that n contrast to a two-party case, canddates would not converge towards the centre n a mult-canddate pluralty system. Cox also analyzes other objectve functons that could characterze the competng agents. Instead of maxmzng votes, an agent could maxmze hs pluralty, meanng he ams to wden the margn between hm and hs closest opponent. Cox (1987) reports results on the necessary and suffcent condtons for a Nash equlbrum, whenever canddates have dfferent objectves. However, as argued by Shepsle (1991) wnnng n a pluralty-rule contest requres that an agent receve more votes than any other agent. A canddate s margn of vctory need not be maxmzed; t need only be greater than the other canddates. In pluralty- 23

rule contests, rank maxmzaton seems more lkely. Denzau, Kats and Slutsky (1985) report ther results on the condtons needed for a Nash equlbrum n a rank maxmzng contest. The above results dealt wth the mult-party pluralty systems. The stuaton under a PR system s entrely dfferent. Greenberg and Weber (1985) provded a formal analyss of the smple mult-party model wth vote-maxmzng canddates. They create a model of a proportonal representaton competton wth a unform quota system. Ths means that each canddate has to obtan a mnmum number of votes, not a mnmum fracton of the total vote. The quota system has been used n the electons to the Rechstag n Wemar Republc, and t s somewhat smlar to the d Hondt method, to the extent that the d Hondt system determnes the quota so as to obtan a fxed number of representatves and t s not set arbtrarly. Cox (1991) proves that under some crcumstances the two systems are equvalent. The formal model s as follows. We assume that there s a fnte socety consstng of n voters, s a fnte set of alternatves and m s a postve nteger not exceedng n. Indvduals preferences are complete, transtve and sngle-peaked. Greenberg and Weber prove that there wll always be an m-equlbrum;.e. an equlbrum n whch for the subset of alternatves A, the support of each alternatve conssts of at least m ndvduals (thus each elected canddate receves at least m votes), whereas no other alternatve s supported by m voters. Secondly, they fnd that not every m-equlbrum s consecutve. Voter support s called consecutve f for any three ndvduals,j,k wth <j<k whenever, k S( a; N, A) mples that j S( a; N, A) In other words, f and k prefer alternatve a to any other alternatve n A so wll others whose peaks le between peaks of and k. The second result s somewhat surprsng, and makes the analyss of the potental mult-party equlbrums even more complcated, especally when we ntroduce ssues wth more than one-dmenson. 24

Greenberg and Weber conclude that the above results may partally contrbute to the dscusson on proportonal representaton, but they are aware of the shortcomngs of ther analyss. Frstly, they assume that only sncere votng takes place. and secondly they make the problematc assumpton of vote maxmzaton under unform quota. Ths assumpton s especally doubtful n the case of a system smlar to a unform quota system such as the wdely used d Hondt method. On the other hand, Greenberg and Shepsle (1987) present a mult-seat contest, n whch a fxed number K of seats s at stake. A canddate s elected once he fnshes n the top K number of vote-getters. Here, success s based on performance. The ssue space s onedmensonal, voters have symmetrcal sngle-peaked preferences and they vote sncerely. Furthermore, no pont n the [0;1] ssue space can be occuped by more than one canddate. As already dscussed, n ths type of contest canddates do not need to maxmze ther votes. In Greenberg and Shepsle s model, canddates are not vote-maxmzers. Instead a canddate need only ensure that he gets no fewer votes than K-1 other canddates. Greenberg and Shepsle defne a K-equlbrum as set A of K locatons n [0;1] wth the property that the support for a canddate located at any one of these deologcal ponts exceeds the support ganed by a canddate centered at any other locaton. Therefore, at any pont n A the canddate wns, because he cannot be dsplaced by a prospectve entrant who s based at some locaton outsde A (Shepsle 1991). More formally, let S ( a; A), be the support for a gven other canddates at the ponts n A, be the set of voters closer to a than to any other pont n A. For a voter dstrbuton F(x) on [0;1], the measure of support for a s gven by: s ( a; A) F[( a a )/ 2] F[( a a )/ 2] 25

where a and K-equlbrum s a set A such that (1) A =K a are the locatons of a s rght and left neghbors, respectvely, n A. A (2) s( b; A b) s( a; Ab) for all a n A and all b not n A. The man result by Greenberg and Shepsle s the mpossblty theorem: Theorem: For every gven K 2, there are socetes satsfyng the structure descrbed above for whch there s no K-equlbrum. They clam that for any two locatons n [0;1] there wll always be a thrd locaton at whch the voter support wll exceed that of at least one of the exstng locatons, and thus the entrant wll fnsh among the top vote-getters. On the other hand, the theorem does not state that the K-equlbra never exst, therefore the entry of more canddates s not dsequlbratng. It only states that equlbrums do not exst for some voters preferences. Another characterstc of the K-equlbrum s that n equlbrum the entry of new partes s deterred. Fnally, Schofeld (1994) presents a general model of n-party competton n whch partes are nterested n the perqustes from holdng offce, as well as n polcy concerns. Ths general set-up comprses some elements of prevously descrbed works, namely the Cox s attempts to generalze the two-party model under electoral rsk (1984) as well as models of multparty competton by Eaton-Lpsey (1975) and Baron (1991). As prevously noted, the model deals wth the crucal feature of multparty competton, namely the fact that partes need to both compete and cooperate n order to be able to mplement ther desred polces. Durng the frst stage they declare manfestos n order to obtan votes and seats; n the second stage these manfestos become bndng when coaltons are beng formed. 26

The model s as follows. For a poltcal scenaro nvolvng the set N { 1,..., n} of partes, on a compact, convex set W W of outcomes, each party has a true preference correspondence P : W W, where for a W, P (a) s a convex set of outcomes strctly preferred to a. W may nclude both polcy and prvate outcomes. It s assumed that P can be represented by a strctly pseudo-concave utlty functonu : W, u s dfferentable and has a unque crtcal pont at whch utlty s maxmzed. Let W ~ be the space of Borel probablty measures on W, endowed wth the topology of weak convergence (see Fudenberg and Trole, 1991). W ~ ~ contans the space W 0 of all fnte lotteres over W, where a fnte lottery s a collecton { a, p( )} of outcomes a j W and j a j J probabltes p a ) satsfyng p a ) 1. Indvdual preferences are extended over W ~ ( j ( j ~ ~ gvng P : W ~ W. P ~ s represented by a von Neumann-Morgenstern utlty functon ~ ~ U : W on W 0 defned as: U ({ a j, p( a j )}) p( a j ) u ( a j ). j Each party has a strategy space Z q that s compact and convex. Each strategy profle of party choces N ~ z ( z 1,..., z ) Z Z gves an outcome nw 0. (Schofeld n N 1994). As already noted, ths general model can be vewed as generalzng prevous works on mult-party competton. The above cted model by Eaton and Lpsey (1975) consders an n- party competton, based on the electoral functon e N : Z N where N s a compact smplex n N. e (z) s party s share of the vote, gven the strategy vector z, and party utlty s determned by ts vote share. Dasgputa and Maskn (1986) showed that a mxed 27

strategy Nash equlbrum would exst under condtons that restrct dscontnutes n a jont strategy space. In Schofeld (1994) each party chooses a strategy z Z and each Z =Z, a fxed polcy space. Agan, as n Eaton and Lpsey t s assumed that there s a contnuous electoral N functon e: Z, whch for each profle N N z Z gves the vector of electoral strength e( z) ( e1 ( z),..., e ( z)) satsfynge ( z) 1. n N For a three-party competton Schofeld fnds that a mxed strategy equlbrum always exsts, and under some assumptons a stable pure strategy Nash equlbrum can be found. Hs theory s as follows: Theorem: If Z s compact, convex then for each vector of blss ponts o= N { o1, o2, o3} Z and scheme { ( ):, j {1,2,3}, j} of prvate benefts, there exsts a mxed strategy Nash j equlbrum. For each N o Z, there exsts * 0 * such that whenever j for each j n then there exsts a stable pure strategy Nash equlbrum. The proof can be found n Schofeld (1994). A pure strategy Nash equlbrum exsts whenever prvate benefts from formng a coalton are suffcently hgh. Moreover, specfc confguratons of blss ponts gve rse to unque, stable pure strategy Nash equlbrum. Two addtonal theorems proven by Schofeld provde some nterestng conclusons about the nature of equlbrums. Defnng that: (1) Three ponts z, z, z } are -bounded n lnearty f: mn, j { j k { z j z j k z k } k 28

(2) Three ponts z, z, z } are -bounded n symmetry f: { j k max z z z z across all permutatons of,j,k, j, k k j k Theorem: If prvate benefts are zero, there exsts * 0 such that f the blss ponts are - bounded n lnearty, for any *, there exsts a unque, stable Nash equlbrum whch s * * * convergent. That s { z, z, } le all wthn the convex hull of o, o, }. Moreover, the 1 2 z3 Nash strateges are also -bounded n lnearty. { 1 2 o3 Theorem: If prvate benefts are zero and Z s the dsc, then there exsts * 0 such that f the blss ponts are -bounded n symmetry, for *, then there exsts a unque stable pure strategy Nash equlbrum z * n the nteror of Z whch satsfes z * z * j o o j b j ( ) 1. In the case 0 b ( ) 2 for each par {,j}. j The frst theorem suggests the exstence of a convergent Nash equlbrum f blss ponts are close to lnear. Ths s ntutve snce the lnearty n a way decreases the dmenson of a polcy space, so that the result s parallel to the one obtaned by Dasgputa and Maskn (1986). The closer the ponts are to co-lnearty, the hgher the coeffcent wll be of the medan party. The second theorem mples that the equlbrum s dvergent f the blss ponts are close to symmetry or symmetrcally placed. Note that equlbrum postons le outsde the Pareto set of the partes, namely the convex hull of o, o, }. It s also worth notng that n a { 1 2 o3 29

* symmetrc case expectaton ( E / Z)( f ( z )) from the jont strategy s precsely the center of the dstrbuton of blss ponts /3( o o ). 1 1 2 o3 Fnally for the three-party case Schofeld reports the effects of perqustes from holdng offce. Theorem: If prvate benefts are non-zero and constant then for each o, o, } whch s - { 1 2 o3 bounded n symmetry, there exsts a unque, stable Nash equlbrum z * whch satsfes z * z b (, ) o o where b (, ) decreases as o ncreases (for each ). * j j j j The above theorem fnds that f blss ponts are close to symmetry and prvate benefts are suffcently hgh, then there s a stable convergent Nash equlbrum whch s unquely defned by the parameters o, o, o, }. Moreover the equlbrum les wthn the Pareto set { 1 2 3 for poltcal partes. For an n-party set-up Schofeld fnds that for each and profle { o : N} there s a mxed strategy Nash equlbrum. He also theorzes that smlar characterstcs of equlbrums could be found for a case wth n canddates under smlar structural assumptons. However, we need to bear n mnd Plott (1967) and Kramer (1973) s fndngs, whch generally deny the exstence of pure strategy Nash equlbrums n a mult-dmensonal set-up. Concludng the work by Schofeld we fnd that the results are ntutve. In the onedmensonal case, the model shows convergence towards the medan poston. In the twodmensonal case dvergence occurs. However, f prvate benefts of the same order of magntude as polcy payoffs are ntroduced, than a weak form of convergence s observed. Only f prvate benefts completely domnate polcy nterest would Downsan convergence to 30

a sngle polcy pont generally occur. Ths result seems to confrm the prevous research. If polcy nterest s a strong motvaton for the canddates, t would be hard for them to form a pure strategy equlbrum, and f they dd, ths equlbrum would le outsde the Pareto set. Concludng ths dscusson of determnstc votng models, t should be sad that ths knd of research dd not fnd much success n emprcal research. One reason for ths state of affars s that n general, theoretcal results do not correspond to what s observed n realworld poltcs. It s possble that theoretcal papers lack some mportant assumptons about poltcan s behavor, or just smply do not take nto account country-specfc, hstorcally determned effects. Secondly, ths type of theoretcal framework s dffcult to model, especally n a more than one-dmensonal set-up. Although early emprcal lterature ncorporates the medan voter theorem, most contemporary emprcal papers ncorporate models that assume canddates uncertanty about voter s actons, namely probablstc votng models. These wll be dscussed n the next chapter. 31

Chapter 2. Probablstc votng The man concluson from determnstc models of votng s that unless some very restrctve assumptons about voters preferences and partes nterests are fulflled, an equlbrum wll not exst n a more than one-dmensonal polcy space. Therefore, a new strand of spatal theory research has arsen. Instead of assumng that voters would defntely vote for a canddate whose poston s closest (e.g. n Eucldean norm) to a voter s deal pont, theorsts assume that the probablty of a voter gvng ther ballot to a partcular party ncreases when the dstance between the voter s deal pont and a canddate s platform decreases. Ths approach s consstent wth the ratonal choce theory, where the randomness of voters choces can arse from unobserved features of the model. It s also consstent wth the assumpton that voters nformaton about canddates platforms can be hghly lmted n realworld electons. One s frst mpresson s that ths set-up deals wth the dscontnuty assocated wth determnstc votng. Under a determnstc set-up, the probablty that a voter wll gve hs vote to a canddate equals zero untl a certan pont, and then t becomes one. (Fg. 2.1) 32

X 1 V Fgure 2.1 Voter s V response to the moves of Canddate 2 In a determnstc framework, the stuaton n fgure 2.1 would nvolve a dscontnuty. Imagne there s a second party that could adopt poston X 2. V represents the deal pont of a voter, wth crcular ndfference curves. If a second canddate adopts a polcy outsde the vsble ndfference curve (e.g. n the dashed part of the lne whch descrbes the dstance) the second canddate s probablty of wnnng equals zero. However, f the second party adopts a polcy closer to pont V than the other canddate ths probablty changes rapdly to equal 1. Ths sort of voters behavor also requres that voters be perfectly nformed about partes platforms, snce a slght change mples an entrely dfferent outcome. Ths sort of behavor s not observed n realty. Probablstc votng assumes a more smooth dstrbuton of canddates chances to receve a vote. Probablstc votng models enhance the possblty of equlbrum, partcularly n cases where the random component of voter decson-makng s suffcently strong (Enelow and Hnch, 1989). Due to ths, there s more lterature dealng wth party competton of more than two partes under a probablstc set-up. Most of the papers fnd that equlbrums exst n 33

scenaros wth more than two competng partes. Uncertanty models are more common n emprcal papers, for reasons that have already been dscussed. In the followng paragraphs I wll descrbe the survey of probablstc models conducted by Coughln (1990). He gathered the results of several works on two-party competton n a probablstc set-up, and descrbed and compared the results usng unfed notaton. The followng assumptons are common to most of the analyzed papers. If partculars dffer t s noted. Suppose there are two canddates c=1,2 who compete for a poltcal offce. A nonempty set S, assumed a subset of an Eucldean space l E s a strategy set for both canddates. c S s the strategy of canddate c. There s a set of N elgble voters, each denoted as N. For each ndvdual voter there are two probablstc votng functons 1 2 P : S S [0,1] and P : S S [0,1 ] such that for each c {1,2 } and, )S S the ( 1 2 c correspondng number P 1, ) s a condtonal probablty that wll vote for canddate ( 1 c, gven that c=1 chooses 1 and c=2 chooses 2. The expected vote for canddate c s c c denoted EV 1, ). The expected pluralty for canddate c s denoted Pl 1, ). It s ( 2 ( 2 assumed that canddates maxmze ther pluralty. However, n some papers t s assumed that not pluralty, but rather the expected vote wll be maxmzed. But f we assume that voters abstan only when they are ndfferent, these two assumptons are equvalent. Some papers consder what happens when canddates maxmze pluralty, as well as what happens under the alternatve assumpton that each canddate maxmzes hs probablty of wnnng. Under the general assumptons dentfed by Aranson, Hnch and Ordeshook (1973) (see also Duggan, 2000) these two assumptons are agan equvalent (Coughln, 1990). 34

A work by Hnch (1977) ntates the strand of research on probablstc, twocanddate models. In hs paper he re-examned the one-dmensonal Hotellng-Downs model showng that, under mnmal uncertanty about voters choces, the medan result no longer holds. If we assume that N={1,2,3}, 2 P, ) I P (, ) and 1 ( 1 2 1 2 P, ) P ( x x ) where P : 1 ( 1 2 2 1 (a) s dfferentable (b) yp '( y) 0 (c) P '( y) 0 n some range of ts arguments (d) P ( 0) 1/ 2 x are voters deal ponts, then a strategy (m,m) s feasble for each canddate, but t s not an equlbrum (Hnch 1977). Hnch ponts out that examples can be found where no equlbrum exsts, and he also provdes cases where equlbrum s always assured. Ths smple example shows that ntroducng uncertanty to the model changes ts features n an unexpectedly dramatc way. On the other hand, Banks and Duggan (2005) prove that although addng uncertanty caused the medan poston to no longer consttute a pure strategy Nash equlbrum, they concluded that the pure (and mxed) strategy Nash equlbrums must be close to the medan. These results wll be dscussed n more detal n the further part of ths secton. A subsequent paper by Hnch (1988) dentfes the condtons for mult-dmensonal electon models where f an equlbrum exsts, then t must be at the mean. The detaled constructon of the model can be found n Hnch (1988) and Coughln (1990). Hnch proves 35

that equlbrum must be placed at the mean of the dstrbuton. Ths result s not supported by the subsequent research of Banks and Duggan (2005) whose fndngs contradct hs theorems. Another form of ntroducng uncertanty about voters choces can be found n the bnary Luce model whch uses the model of expectatons frst developed by Luce (1959). For the partcular purpose of electon models, ths means that the canddates use a bnary Luce model for the ndvdual voters selecton probabltes f, for each N there exsts a postve, real-valued scalng functon f (x) on S, whch s such that P (, ) 1 1 2 f ( 1) f ( ) f ( ) 1 2 2 f ( 2) P ( 1, 2). (Coughln 1990) f ( ) f ( ) 1 2 The scalng functons are assumed to be concave and dfferentable. It s also assumed that: (a) the canddates common strategy space S s non-empty, compact and convex (b) the set of voters N s fnte. Ntzan and Coughln (1981) establshed that, when the canddates use the bnary Luce model for the ndvdual voters selecton probabltes and the above assumptons are satsfed, then the followng result holds true: Theorem: * ( * 1, 2)S S s an equlbrum ff both * * 1 and 2 maxmze n W ( x) log( U ( x)) over S. 1 Kaneko and Nakamura (1979) addtonally establshed that f (a) there s a clear alternatve all ndvduals x 0 S whch represents one of the worst alternatves for 36

(b) we set U ( x 0 ) 0 and SU ( x) 0 x then the objectve functon specfed above s a Nash socal welfare functon. Therefore, workng under the above assumptons an equlbrum strategy for a canddate maxmzes the Nash socal welfare functon. Coughln and Ntzan (1981) also establsh that under these assumptons there s always an equlbrum and f at least one voter has as a strctly concave utlty functon, then the equlbrum s unque. Enelow and Hnch (1982) analyze an electon takng nto account non-spatal canddate characterstcs,.e. features that canddates cannot alter durng the electon are consdered. Ther analyss provdes new suffcent condtons for the exstence of an electoral equlbrum. Enelow and Hnch assumed that the common strategy set S s such that [ 0,1] S where postons can be nterpreted as spendng levels for a sngle publc ssue. For each E ndvdual voter N there s an deal pont, x( ) S, that enters nto hs evaluaton of a canddate s strategy (Coughln 1990). Enelow and Hnch assume that voters can be dvded nto two groups 1 and 2 each havng respectvely n 1 and n 2 voters and each 1 has the deal pont x ( ) 0 whereas for 2, x ( ) 1. Each voter formulates the nonspatal characterstcs of a canddate n numercal terms denoted respectvely c 1 and c 2. Voters also place a partcular weght of mportance on a canddate s strategy relatve to ther non-polcy features denoted by a. Enelow and Hnch assume that for each N and 1, 2 S 2 1f ( 2 x( )) ( 1 x( )) P ( 1, 2) 0 otherwse 2 1 37

where c 2 c 1 2. Analogously, for P ( 1, 2) wth 2 replacng 1 and vce-versa on the a a rght-hand sde. It s assumed that canddates beleve that (a) the dstrbuton of across the group 1 s normal wth mean 0 and varance 2 1 (b) the dstrbuton of across the group 2 s normal wth mean 0 and varance 2 2 Therefore the canddates are uncertan about the non-polcy value for a partcular voter, but know the dstrbuton for each group. Addtonally let ~ x n 1 n2 1, whch s a weghted mean deal pont (f varances are equal the pont s n 2 2 1 an un-weghted mean deal pont) 2 2 Theorem: If 2 (1 ~ 2 x and 2 [1 (1 ~ ) 2 ] then 1 ) (1) an equlbrum exsts 2 x (2) ( * * * 1, 2) s an equlbrum f and only f ~ x * 1 2 The concluson s that for a suffcently hgh varance of the non-polcy feature, an equlbrum exsts and s located at the weghted mean deal pont. Ths result corresponds the one obtaned by Hnch (1978) whch was dscussed earler. Ths concluson s partcularly mportant because t means that any mnorty has an mpact on the equlbrum, therefore there s no tyranny of the majorty. Ths result underlnes the dfference between votng n a drect democracy as opposed to n a representatve democracy. In the latter, voters vote for both polcy and non-polcy ssues characterzng the canddates and f the uncertanty about non-polcy ssues s hgh enough, the equlbrum exsts and s not located wthn the deal ponts of a majorty group, but n the weghted mean of the whole dstrbuton of voters. 38

Lnbeck and Webull (1987) developed a model of balanced-budget re-dstrbuton between soco-economc groups as a result of electoral competton between two poltcal partes. In ths model, partes are uncertan about the voter s preferences wth regards to deologcal consderatons and poltcal non-polcy features. If there are more than two groups the strategy set s mult-dmensonal, and uncertanty n the model s crucal n order to provde an equlbrum. Lnbeck and Webull assume that the set of voters N s fxed and every voter N has a fxed ncome. The canddates have a common partton { 1,..., m} of the electorate. Strateges avalable to the canddates are vectors s ) m ( s 1,..., s m E of possble transfers to the members of partcular groups. Addtonally t s assumed that canddates choose a balanced-budget redstrbuton. Thus: S { s E m : m 1 n s 0 s 0, N, } Ln, Enelow and Dorussen (1999) present an extenson of a two-party competton model of Enelow and Hnch (1989). In the model M 2 canddates compete for the votes of N voters n a compact, convex subset X of a k-dmensonal polcy space k (Ln, Enelow and Dorussen, 1999). Canddates select a pont n the polcy space n order to maxmze ther obtanable number of votes, assumng the others wll do lkewse. Under ths assumpton the set of ponts chosen by the canddates consttutes a Nash equlbrum by defnton, snce every player chooses the best polcy gven the locaton of opponents. Voters vote for the canddate they prefer and ths preference s probablstc. Uj[] denotes the voter s utlty from canddate j. Ths utlty depends on the dstance between the voter s deal pont and a polcy pont chosen by a canddate. Poston of canddate j s denoted by 39

cj [ Xj1, Xj2,..., Xjk ]' And the deal pont of voter s denoted by v[] X [ ], X [ ],..., X [ ]]'. [ 1 2 k The dstance between the two ponts s denoted by Dj[] and s assumed to be contnuous, twce dfferentable functon of cj. Utlty as usual s a functon of the dstance between a voter s deal pont and a chosen polcy pont: the shorter the dstance, the greater the utlty. Ths set-up also comprses a probablstc component, whch represents voters uncertanty about a canddate s poston or other characterstcs that could nfluence the voter s choce. Voters evaluaton of a canddate conssts of an error term. The dea of voters uncertanty about partes postons goes back to Downs, who notes that n real-world poltcs voters are usually badly nformed about canddates postons and need strong deologcal sgnals to be able to dstngush between competng players. In the model by Ln, Enelow and Dorussen (1999) total utlty, ncludng the error term equals Uj[ ] Ej Dj[ ] Ej d for j 1,...,M (0, ). 2 j Voters are assumed to vote sncerely for two man reasons. Frstly t s dffcult to model sophstcated votng, and secondly sophstcated votng would requre voters to have a deep knowledge of canddates postons to the pont that they would be able to antcpate the results of an electon, and ths would contradct the uncertanty assumpton. In other words under a probablstc set-up t seems more logcal to assume that voters vote sncerely, snce they do not have suffcent knowledge about a canddate s polcy ponts to do anythng else. A voter votes for Canddate 1 f hs utlty from 1 s hgher than that of other canddates, therefore f U 1[ ] Uj[ ] ( E1 Ej) ( D1[ ] Dj[ ]) 0. Substtutng 40

Ej1 E1 Ej and Dj1[ ] Dj[ ] D1[ ] we obtan that voter votes for canddate 1 f, and only f, Ej1 Dj1[ ]. Let e1 [ E21, E31... EM1]', Σ1 be the ( M 1) ( M 1) varance-covarance matrx of e1 and d1[] [ D21[ ], D31[ ]... DM1[ ]]'. F the cumulatve densty functon of e1 - s assumed to be contnuous and twce dfferentable. The probablty that voter votes for Canddate 1 s therefore equal P1[ ] F( d1[] ; Σ1). The expected number of votes for Canddate 1 from a populaton of N voters equals N EV1 F( d1[] ; Σ1) and for any other canddate j t s equal EVj 1 F( d j[] ; Σj). 1 The maxmzaton of the number of expected votes obtaned by a gven canddate requres solvng a frst order condton: N EVj cj N 1 Dj[ ] g( dj[] ; Σj) 0, where g ( dj[] ; Σj) s the sum of all elements n the cj F( dj[] ; Σj) gradent vector. Second order condtons for a statonary pont can be found n dj[] Ln, Enelow and Dorussen 1999. A suffcent condton for the exstence of a global equlbrum s concavty of EVj on compact, convex set X, whch s fulflled whenever 2 Dj[ ] Dj[ ] ( x' x)/( x' ) cjcj' cj h( dj[] ; Σj) g( dj[] ; Σj) where h ( dj[] ; Σj) s a sum of all elements of a hessan matrx 2 F( dj[] ; Σj). It can be observed that the sze of a rght-hand sde of ths equaton dj[] dj[] ' reduces wth the ncreasng varance of j - Σj; therefore, ncreasng the uncertanty of voters s a stablzng factor n mult-canddate electons. Wth hgher uncertanty, t s easer to satsfy the suffcent condtons for equlbrum. De Palma, Hong and Thsse (1990) also 41

prove that as M ncreases t takes greater uncertanty to provde equlbrum n a onedmensonal case. Adams (1999) presents a general model of probablstc ssue votng. Voters are located n an n-dmensonal ssue space and vote for partes belongng to the set R. Each party { A, B,..., M} R proposes a platform k k, k,..., k }. The set of platforms that the partes { 1 2 n select { a, b,..., m} s denoted by L; the cardnalty of L equals the cardnalty of R. Voters evaluaton of each party s gven a real-valued functon e( x, k). Each voter s characterzed wth an ndvdual salence parameter s, whch vares the mportance voters attach to partes platforms, relatve to voters non-ssue-related motvatons. Key assumptons about the probablty are as follows: (1) Each party K beleves that for each voter : F[ se( x, k)] P ( K, R, s) where F s a postve, real-valued functon on F[ se( x, j)] j L (2) When voters attach no mportance to partes platforms.e. they are only motvated by non ssue-related consderatons, then the salence parameter s equals zero (3) F s a strctly monotone, ncreasng and contnuously dfferentable functon n ts argument. It means that the probablty that votes for K ncreases when he evaluates a party s platform more postvely (Adams, 1999) It should be noted that from (2) t follows that, f voters attach no mportance to partes platforms, then the probablty of wnnng for each party equals: P ( K, R, s) F[0e( x, k)] F[0e( x, j)] jl F[0] 1 F[0] R jl Adams consders two dfferent party motvatons: ether to choose a platform that wll maxmze ther expected vote share, or to maxmze ther expected vote margns over 42

competng opponents. Both optons are workable, and serve to explan real-world poltcs. Whether partes wll choose to maxmze ther vote shares or ther margn over other compettors s an emprcal queston and hghly depends on a partcular electoral system, and the current poltcal stuaton. Maxmzng a margn over a compettor would be more plausble under pluralty rule, but n a proportonal representaton system, the poltcal stuaton would determne the concrete behavor of canddates. The central theorem presented n Adams (1999) deals wth the problem of the exstence of equlbrums. An addtonal assumpton s made that there s a unque most popular platform M such that for all K R V E ( k) e( x, k) s maxmzed when k=m. V Theorem: For any voter dstrbuton, exsts such that 0 s mples that for each party K R : a) K s expected vote share ( K, s) ncreases monotoncally wth (k) VR b) K s expected vote margn M ( K, L, s) ( K, s) ( L, s) over any rval VR VR VR E V canddate L R, ncreases monotoncally wth E V (k) (Adams, 1999) What follows s that for 0 s M s a domnant strategy for each vote- or rank- maxmzng party, regardless of the platforms proposed by rval partes, whenever s s suffcently small.e. when voters attach suffcent mportance to non-polcy ssues. When all partes engage n vote- or rank- maxmzng then M represents an equlbrum n domnant strateges. The result s ntutvely understandable. What s mportant s that Adam s theorem allows for a stuaton where not all partes are vote- or rank- maxmzers. It s partcularly mportant for emprcal research snce n real-world poltcs partes (especally extremst ones) are often motvated by concerns other than vote-maxmzaton. The theorem s lmted, 43

however, to stuatons where M s unque; whenever M cannot be determned unquely, then partes choces may depend on the behavor of rvals. 44

Chapter 3. Coaltonal models The two prevous chapters dealt wth models of party postonng needed n order to maxmze the obtaned pluralty or the probablty of wnnng the electon. However, none of these takes nto account the stuaton once the electon s over and there s a need to set a government that can mplement polces desred by ts members. Buldng a cabnet that conssts of members of the parlament s common to most mult-party democraces. In fact, t s exactly ths element of the democratc process that normally causes the nstabltes of cabnets n parlamentary democraces. For example, t may turn out that partes postons, once set n equlbrum accordng to the one of probablstc models descrbed n chapter 2, may afterwards be unable to form a cabnet f forced to commt to ther prevously set postons. Therefore, partes n mult-party envronment need to take nto account the necessty of coalton formaton after the electon. Part 1. Tradtonal theores The tradtonal models of coalton formaton go back to von Neumann and Morgenstern (1953). The authors argue that the coalton that would form s the mnmal wnnng coalton. Mnmal wnnng coaltons are characterzed by the fact that f any of the members defect, the coalton loses ts wnnng status and t no longer controls that majorty of seats n the legslature. Therefore, all members of the coalton are necessary n order for the coalton to be a wnnng one. Ths theory assumes that partes are purely Downsan and therefore only care about holdng offce and the perqustes connected wth t, and have no nterest n the deologcal dstance between the members of a coalton. Not only s ths 45

theory based on unrealstc assumptons, but ts predctve power proved neffectve for use n emprcal research. Moreover, t was argued that the theory s not effcent n the sense that the set of possble coaltons predcted s overlarge. An attempt to reduce the predcton-set was made by Rker (1962), who argued that only a fracton of the possble mnmal wnnng coaltons wll form. A mnmum wnnng coalton s a mnmal wnnng coalton consstng of just enough members to gve the coalton the mnmum weght needed (Rker, 1962). Another way to reduce the predctve set was proposed by Leerson (1968) n the barganng poston theory. Leerson argues that only a coalton wth the smallest number of actors wll form. The theory s based on the assumpton that t s easer to form a coalton wth a smaller number of partes, because barganng s less problematc. The three theores outlned above all predct that governments of a specfc sze wll form. However, they neglect to address the deologcal postons of partes. Moreover, they do not predct the exstence of mnorty governments. One of the frst attempts to nclude polcy postons n theores of coalton formaton was made by Axelrod (1970), who ntroduces the term mnmal connected wnnng coalton. The mnmal connected wnnng coalton theory says that coaltons wll form that are deologcally connected along a polcy dmenson (Axelrod, 1970). For a coalton to be connected partes must be adjacent to each other on a polcy dmenson. Stll, ths theory does not account for an absolute deologcal dstance between the partes, only ther relatve postons. The frst researcher to note that the most mportant ssues n polcy formaton are polcy consderatons was De Swaan (1973), who presents the polcy dstance theory, also called closed mnmal range theory. Ths s a verson of mnmal connected wnnng theory that accounts for, not only the orderng of partes, but also ther actual postons. The closed 46

mnmal range coalton s a mnmal connected wnnng coalton wth the smallest deologcal range. Austen-Smth and Banks (1988) authored a crucal work for coalton theory research whch attempted to connect the theory of electoral competton before the electon wth the behavor of partes after the electon, when cabnet formaton takes place. The model s smplfed to three partes and just one polcy dmenson, but t stll dentfes mportant equlbrum features that could be generalzed. The formal model goes as follows. There are three partes, and, where,, that compete n a onedmensonal polcy space P R for the votes of a fnte set of ndvduals N. It s assumed that P and N n > 15 and odd. The followng scheme of events takes place: at tme t=-2 the partes smultaneously announce polcy postons n P: p p, p, p } and at tme { t=-1 the voters vote, each castng a sngle ballot for one of the partes. Each of the partes requres a fxed quota of votes n order to enter the parlament. From t=1 the partes attempt to form a government that wll collectvely choose the desred polcy y P and the dstrbuton of portfolos among the members, whch s characterzed as choosng a dstrbuton of a fxed amount G of transferable benefts across the partes: ( G ) { g, g, g }: gk 0k and gk G (Austen-Smth and Banks, 1988). The k process of formng a cabnet goes as follows: at tme t=1 the party wth the largest fracton of seats makes a proposal to form a coalton and dstrbute the perqustes. The members of the proposed coalton can ether accept or declne the proposton. If the offer s accepted by a suffcent number of partners, then the members form a cabnet; f t s declned at tme t=2 then the second largest party makes a proposal and the scheme repeats. Fnally f the 47

government s not formed after t=3, than a caretaker government s formed, whch makes equtable polcy and benefts decsons. The strategy of each party conssts of three elements: an electoral poston p k P, a proposal D( w) P( G) where D(w) denotes the set of wnnng coaltons and a k response strategy rk : Dk ( w) P ( G) T {0,1 } specfyng whether party k accepts (1) or rejects (0) a proposal that ncludes k n a coalton, where ths response may be a functon of tme [t=1,2,3]. A strategy for voter s a functon : P P P ( ) whch specfes the probablty that wll vote for a partcular party gven ther polcy postons. Voters are assumed to be purely polcy-orented and ther preferences are characterzed by quadratc utlty functons over the polcy space P. In fact, general results hold for any symmetrcal, convex utlty relaton. It s also assumed that voters deal ponts are symmetrcally dstrbuted around the medan voter s deal pont. Partes polcy preferences are a functon of the dfference between ther electoral postons and the fnal polcy outcome. The reason for that s based on the ablty of voters to make ther decsons condtonal on the past performance of partes.e. on the degree of commtment of partes to ther polcy statements n the formaton of government. Therefore even f the partes are only concerned wth wnnng electons and collectng benefts, they must take nto account the dfference between ther electoral poston and the fnal outcome snce voters may adopt retrospectve strateges. The followng proposton brefly descrbes the equlbrum outcome n the legslatve stage (the formal statement can be found n Austen-Smth and Banks (1988)) Proposton: Let party k offer the proposal at t=1, party h at t=2 and party j at tme t=3. * (1) If k has a majorty n the legslature, then y pk, g k G * (2) If k does not have a majorty, then C { k, j}, * y les between p and p and k kj 48

max g g * k * j ( p G g * j k, g p * h kj ) 0 2 f y * p kj and 0 otherwse (Austen-Smth and Banks, 1988) Therefore, n equlbrum there wll be ether one party that obtans the majorty, or two partes that form a cabnet between the party wth the hghest fracton of the vote and the one wth the lowest. The model generates a unque coalton predcton, where the coalton s mnmum wnnng but not of mnmum sze and not necessarly connected. The votng equlbrum n the frst stage of the electoral scheme s descrbed brefly n the followng proposton. Proposton: A votng equlbrum * ( p ) s well defned for all p P P P. It s such that at least one party s penalzed (n terms of votes) f, relatve to the dstrbuton of voter preferences (1) Any two partes are too close (2) No party s centrally located (3) Partes are too wdely dspersed. The above condtons ensure that n equlbrum, partes wll be located symmetrcally around the medan of the voter dstrbuton. What s most nterestng here s that n equlbrum some voters do not vote sncerely. Moreover, f the voters are lmted to votng sncerely, then equlbrum becomes mpossble. The last outcome s partcularly nterestng n the context of the concepton that a proportonal representaton system leads to formng the legslature, n whch preferences of voters are relatvely well represented, and the varety of ther nterests are covered. The above results suggest that ths concept s mstaken when voter s strategc behavor s n play. 49

Part 2. Multdmensonal theores Laver and Shepsle (1996) present a portfolo allocaton model. It s based on some mportant assumptons, namely that: (1) Poltcans are Downsan (2) Each dmenson of polcy s governed by a partcular portfolo (3) There s mnsteral dscreton, meanng that the mnster of a department has consderable dscreton to act on hs or her own, ndependently of the other members of the cabnet. As descrbed by Laver and Shepsle (1996) the cabnet formaton process n most of the parlamentary democraces can be descrbed by the followng three stage scheme. In stage I a legslatve party s selected, whch then proposes a partcular cabnet, descrbed n terms of a partcular allocaton of cabnet portfolos between member partes. If the proposal s smply a contnuaton of the exstng status quo than the proposal s repeated wth some other party selected. If the proposal dffers, then the process advances to stage II. The partes who have been allocated a portfolo n the proposton may veto t and refuse to partcpate. If they do so the process goes back to stage I, f not t advances to stage III. In the last stage the proposed cabnet s put to a parlamentary vote. If t gans majorty support then t replaces the status quo. If t does not gan support then the procedure goes back to stage I and the status quo remans unchanged. It must be noted here that n most parlamentary democraces ths process s restrcted to a fnte number of repettons after whch f no consensus s obtaned a new electon takes place. Further repettons of stage I sometmes gve the rght to make the government proposal to some other body e.g. the presdent. 50

Laver and Shepsle (1996) present a model of mult-dmensonal cabnet formaton. The basc assumptons are as follows. There s a set of legslatve partes, each wth a certan weght and polcy poston. Each party weght s expressed as the share of ts seats n the legslature. The polcy poston of each party s expressed n terms of the polcy t wshes to mplement on each key polcy dmenson. Seat shares and polcy postons are assumed to be common knowledge among all relevant actors. The stuaton descrbed can be seen as a lattce presented n fgure 3.1. Polcy dmenson 2 AC BC C A BA CA AB B CB Polcy dmenson 1 Fgure 3.1 A lattce of polcy postons There s a set of government departments and mnstres, each responsble for the development and mplementaton of publc polcy n a partcular area correspondng to a partcular polcy dmenson. One or more departments may be responsble to a sngle mnster. Fnally, t s assumed that the government formaton process descrbed earler takes 51

place. Proposals nclude the specfcaton of whch partners wll hold cabnet portfolos wth jursdcton over the varous key polcy dmensons. Two preference relatons need to be determned, one over polces and another over cabnets. The set of polces preferred by a majorty to polcy x s known as the polcy wnset of x, labeled W * ( x ). The set of cabnets preferred by a majorty to cabnet X s known as the lattce wnset of X denoted W(X). To see whether a partcular cabnet s n equlbrum we need to frst determne f there are any cabnets n ts lattce wnset that are preferred to t. Fgure 3.2 presents the lattce wnset of a coalton BA. Polcy dmenson 2 AC BC C A BA CA AB B CB Polcy dmenson 1 Fgure 3.2 The wnset of BA cabnet The yellow-shaded area s a polcy wnset for a cabnet consstng of partes B and A. Ths cabnet gves the portfolo assocated wth dmenson 1 to party B, and that of polcy 52

dmenson 2 to party A. Every pont nsde the area s preferred by some majorty to a polcy mplemented by a cabnet BA. Note however, that the lattce wnset W(BA) s empty, whle there s no cabnet that s forecast to mplement a polcy that wll be preferred by a certan majorty. By assumpton any two of the three partes n fgure 3.2 comprse a majorty and what follows s that party A s a medan legslator n dmenson 2, whereas party B s n a medan poston n dmenson 1. The forecasted polcy output of ths cabnet s the dmensonby-dmenson medan n the polcy space (DDM) and thus t s known as a DDM cabnet. Kadane (1972) shows that any pont n a contnuous polcy space that s at an equlbrum - meanng that ts wnset s empty - must be the DDM. (Laver and Shepsle 1996). In fgure 3.2 there s no alternatve government n the wnset of BA. Consequently BA s preferred by some legslatve majorty to all the alternatve cabnets. If BA s the status quo, then any alternatve wll be blocked by a legslatve majorty. Proposton: The DDM cabnet s an equlbrum government f there s no alternatve government n ts wnset. The DDM cabnets may be not the only equlbrum governments. An example s presented n fgure 3.3 n whch the shaded area denotes how partes A and C feel about a mnorty government n whch both dmensons are occuped by party B. 53

Polcy dmenson 2 AC BC C A BA CA AB B CB Polcy dmenson 1 Fgure 3.3. The wnset of B cabnet We see that two alternatve governments BA and BC le wthn the wnset of a government B. However, both these governments consst of party B as a member, therefore both could be vetoed by B. Party B s called strong, snce every alternatve government requres ts assent. Generalzng from ths, f a strong party has an deal pont that has an empty wnset, ths party s called very strong. If a very strong party takes all key portfolos n a cabnet, t s by defnton an equlbrum cabnet. Ths very strong party must have ts deal pont at DDM. Alternatvely, a party may have an deal pont wth a non-empty wnset, but s strong because the party partcpates n, and thus can veto, every cabnet n ths wnset. Ths sort of party s called merely strong. Generally stuatons may also exst n whch there s no strong party and there can be at most only one strong party (for a proof please see Laver and Shepsle 1996). 54

The exstence of any strong party has a major mpact on government formaton. Ths ncludes both very strong and merely strong partes. Proposton: When a strong party exsts, t s a member of every equlbrum cabnet. It follows that t s mpossble to create an equlbrum government wthout the partcpaton of an exstng strong party. Ths means that the exstence and dentfcaton of a strong party s a very mportant strategc feature of any government formaton. Furthermore, the deal pont of a strong party has a huge mpact on the stuaton, snce whether t s or s not strong hghly depends on other partes confguraton. Small changes n postons or weghts may lead to strong perturbatons and dsequlbrum n government foundaton process. Fnally Laver and Shepsle dentfy another equlbrum stuaton nvolvng merely strong partes. Proposton: When there s an empty-wnset DDM, no cabnet n the wnset of the strongparty deal s n equlbrum f t s less preferred by the strong party than the DDM. (Proof n Laver and Shepsle 1996) Ths means that even when a merely strong party cannot credbly veto some proposals, or must lft ts vetoes va poltcal barganng, the equlbrum wll never be less desrable for t than a DDM cabnet wth an empty wnset. In other words, to the extent that a merely strong party can use ts vetoes, t wll be able to use them to gan results that t prefers at least as much as a DDM cabnet wth an empty wnset. The latter results suggest that strong partes must have deal ponts that are n some sense central. By defnton the deal pont of a very strong party s at the dmenson-bydmenson medan. In the case of a merely strong party, when the DDM government s majorty preferred to all others, the merely strong party must be at the medan poston of at least one dmenson of polcy, n order to be able to veto the DDM cabnet. We may therefore 55

conclude that partes have ncentves to place themselves n the central postons along at least one polcy dmenson. These results somewhat contradct the earler dscussed models of probablstc votng, n whch dvergent equlbrums can sometmes be found. The results obtaned by Laver and Shepsle suggest gong back agan to medan voter results. However, n ths case, partes do not take at all nto consderaton deal ponts of voters, but only the confguraton of other partes postons. It s not hard to magne that ths sort of behavor may lead to cyclng and a general lack of equlbrum n whch a chaotc sequence of proposals and counter-proposals wll be observed. Usng ths model, we would end up havng electons every half a year or so but n realty, as already noted, the sequence of proposals s usually consttutonally restrcted. The ratonal foresght approach suggests that the creaton of an equlbrum cabnet ncludes the antcpaton of all the possble key factors that mght destablze t. Ths means that an equlbrum cabnet ought not to be destablzed by any antcpated events. In other words t s more lkely only to lose stablty n the face of unexpected events. Shocks that occur are able to destablze the cabnet by changng parameters n a way that could not be foreseen before cabnet formaton. These changes n poltcal envronment nclude changes n polcy dmensons as well as party postons, weghts of partes and so on. One example of ths mght be f a party formng a majorty sngle-party cabnet splt as a result of some nternal crss, whch would create a stuaton wth no majorty party. Defectons, by-electon defeats and so on produce smlar outcomes, so that a majorty party does not have enough margn over a requred majorty. Another type of shock that mght destablze an equlbrum cabnet s the emergence of a new ssue. Ths may ental the creaton of a completely new polcy dmenson due to foregn or nternal events. It may result n perturbaton of party postons on exstng polcy 56

dmensons, changng nter-party dstances and therefore the locaton of ndfference curves defnng wnsets underpnnng the strategc bass for a partcular equlbrum government. (Laver and Shepsle 1996) A thrd type of shock concerns partes perceptons of each other. Even under a perfectly symmetrcal and nformed formaton of cabnet, ts ntegrty depends strongly on the ablty of a merely strong party to wn standoffs aganst the other partes. Other types of shocks may also be present and have an mpact on the cabnet formaton process, such as party weghts, ther deal ponts and so forth. Schofeld (1993) presents a model coalton barganng based on the already ntroduced concept of the poltcal heart. The work by Schofeld agan stresses the typcal stuaton n mult-party poltcs, n whch partes need to face compettve and cooperatve features smultaneously. It s therefore approprate to assume that partes are nterested n the fnal polcy outcome (ether because they receve utlty from the desred polcy, or as assumed by Austen-Smth and Banks (1988) because ther polcy s evaluated by retrospectve voters). Unlke Austen-Smth and Banks (1988) Schofeld assumes that true polcy preferences of the partes are prvate, but each party s concerned wth polcy.e. ts utlty functon takes the form u : W R. In partcular Eucldean preferences are assumed, therefore u 1 2 x) x x where x s the blss pont of party and x s the fnal outcome. 2 ( The set of partes N { 1,...,,..., n} s exogenously determned. Partes make declaratons ( manfestos ) z W on a bass of whch seat allocaton s determned e( z) ( e1 ( z),... e ( z)) where e (z) s a fracton of seats of a party. Each party n 57

acts as f the declared polcy reflected ther true polcy preferences. 1 u' ( x) 2 x z 2 denotes the nduced utlty functon for party. A coalton M that controls the majorty of seats n the legslature s a wnnng one. D (z) s the famly of wnnng coaltons defned by z. Let W(M) be the compromse set of coalton M (namely, the convex hull of the declared postons of the members of M) (Schofeld, 1993). The core CH( D( z)) s the ntersecton across all W(M) for M n D(z). CY(D(z)) cycle set s the closed set bounded by medan lnes.e. the lnes on each sde of whch, le the majortes. It has the property that f a pont d les outsde t, than there exst a pont g whch s preferred to d by a majorty coalton. Fnally, the poltcal heart s defned as the unon of the core and the cycle set: H( D( z)) CH( D( z)) CY( D( z)). It has the followng propertes: (1) If the core s non-empty, the heart s the core (2) It s lower hem-contnuous (3) It s non-empty and Paretan. 58

Chapter 4. Spatal competton and coalton formaton n the 2007 Polsh electon Part 1. The consttutonal system n Poland Poland s ruled by a parlamentary system of government. The basc formulaton of ths type of governng system was frst ntroduced by the French Thrd Republc consttuton n 1875. The bascs of the system n whch the executve branch s desgnated by the head of state and at the same tme must be supported by the parlament are present, but the Polsh parlamentary system reveals some partcular characterstcs whch make t a bt dfferent from the standard model and are well worth descrbng before further analyss. Poland s hstory and ts parlamentaransm have both played a role n shapng these characterstcs. The current governng system n Poland was formed by the consttuton of 1997. Ths replaced the temporary amendments put nto place n 1992, whch were desgned to transform Poland from a sngle- to a mult-party system and from socalsm nto a free market economy. It s based on a bcameral parlament the Natonal Assembly, whose term of offce equals 4 years. The lower chamber s called the Sejm, whereas the upper chamber s the Senate. The consttuton stpulates the possbltes for extendng a term of offce n case of an emergency state, and also detals the possbltes for shortenng t n certan specfc stuatons. One such stuaton s f two-thrds of the Sejm elect to dssolve parlament (f ths happens, then Senate s automatcally dsbanded). A second stuaton that can lead to parlamentary dssoluton arses f parlament does not submt the Budgetary Act for approval by the presdent wthn a partcular tme. The last enumerated stuaton s the most mportant for the purposes of ths work. Parlament may be dsbanded f t s unable to form a government or to gve a vote of confdence to the government proposed by the Presdent. In the latter case, the 59

consttuton foresees and does not permt the possblty of endless coalton barganng that could prevent a government from ever formng. The electons to Sejm can be descrbed by fve characterstcs: they are unversal suffrage, proportonal, equal, drect and anonymous (that s, they are conducted by a secret ballot). Deputes are elected n 41 electoral dstrcts, 7 to 19 members from a closed lst n each. The total number of members equals 460. A d Hondt formula s currently used to dvde the seats. In 1991 the Hare-Nemeyer formula was used, and n 2001 the modfed Sant- Laguë method. The latter way of transformng the number of votes nto seats s more proportonal and t allows for a close rato of votes to seats receved, whereas the d Hondt method encourages larger partes to obtan more seats. Furthermore, the system sets a partcularly hgh threshold of votes needed for seats: 5% for partes and 8% for coaltons. One reason for ths set-up mght be the fragmentaton of the Polsh poltcal scene 2, whch though dmnshng stll appears to determne the shape of Polsh governments. Ths partcular characterstc of Polsh parlamentaransm seems to have a bg nfluence on electon results. In the upper chamber, senators are chosen n unversal suffrage, drect and proportonal electons under relatve majorty rule n 40 electoral dstrcts, up to a total of 100 members. It should be noted that although the parlament s bcameral, the rghts of the Senate are very weak. Among the enttlements relevant to ths paper, one needs to only to note that the Senate may reject or amend the blls passed by the Sejm but any rejecton or amendment may stll be overruled by an absolute majorty vote n the Sejm. In ths sense, the role of the Senate n formng legslatve acts s mnor and focuses manly on correctng mstakes n blls enacted by the lower chamber. 2 In the frst free electon n 1991, 29 dfferent partes receved seats. 11 of these partes receved just one vote. 60

The presdent of Poland s elected n a unversal suffrage, drect, equal and anonymous electon. Ths gves the presdent an unusually strong mandate not often encountered n other parlamentary systems across Europe. Among the enttlements of the presdent, one may dstngush between prerogatves and actons that requre a countersgn of a competent mnster. Among the presdental prerogatves t s mportant to cte both the rght of legal ntatve and the rght to veto blls proposed by the parlament, whch can be overruled by a 3/5 majorty of Sejm members. The presdent s strong publc mandate and veto ablty can and does lead to stuatons where a smple or even absolute majorty may be nsuffcent to pass a bll, especally n a cohabtaton stuaton, n whch the presdent (though formally s/he cannot be a member of any party) for all ntents and purposes represents the vews of the opposton. The presdent may also convene a referendum after obtanng the assent of the Senate. One must bear these presdental enttlements n mnd n order to properly analyze coalton barganng n Poland. The presdent desgnates the executve n a form of a cabnet, but the cabnet must enjoy the confdence of the Sejm. One consttutonal excepton to ths rule s when the Sejm chooses mnsters, and the members are afterwards apponted by the presdent. The latter stuaton occurs f the Prme Mnster desgnated by the presdent s unable to form a government that would receve a vote of confdence from the Sejm by absolute majorty n the presence of at least half of the representatves. If the second procedure also fals, the rght of the ndcaton of a Prme Mnster goes back to the presdent, and the frst step s repeated; however, a smple majorty of votes s suffcent to acheve a vote of confdence. If after ths procedure t s stll mpossble to form a cabnet, new electons must be convened. The coaltonal barganng process has been thus restrcted n order to ensure a contnuty of governance. Among ts rghts the cabnet also holds the rght of ntatve. 61

Formaton of the poltcal scene n Poland Before further analyss, t s mportant to understand how certan hstorcal events have mpacted specfc aspects of Polsh poltcs. Trade unons had a crucal hstorcal nfluence on governance, especally wth regards to the Soldarty movement n Poland s transton from a sngle-party authortaran regme to a democratc system. Ths stuaton, mproper from a democratc pont of vew, s now overruled by the consttuton, whch says (Art. 100 1) that Canddates for Deputes and Senators may be nomnated by poltcal partes or voters, a contraro not by the trade unons. Another mportant feature of Polsh poltcs s a dstncton between the left and the rght. Left-wng partes are for the most part aganst the nvolvement of the Catholc Church n Polsh poltcs, and they do not queston the accomplshments of the People s Republc of Poland (ths was the offcal name of the country from 1952 to 1989, when t was ruled by the communst Polsh Unted Workers Party). On the other hand, the rght-wng partes, usually connected wth the Soldarty movement, refer to natonal tradtons, support the Catholc Church s nvolvement n poltcs, and dscard the accomplshments of the prevous regme. Though the descrbed dvson has become weaker, t stll more or less dctates the shape of Polsh poltcs. However, n the 2007 and 2005 electons the poltcal competton focused on two rght-wng, post-soldarty partes and the left or post-communsts played a rather mnor role. Current major poltcal partes Four of the poltcal partes n contemporary Poland were able to obtan seats n the current parlament. In ths secton I wll brefly descrbe ther hstory and deology. 62

The Cvc Platform (Platforma Obywatelska) The Cvc Platform was founded n 2001. It manly conssts of lberal ex-members of the Soldarty Electoral Acton party (Akcja Wyborcza Soldarność) and Unon for Freedom party (Una Wolnośc) whch from 1997 to 2001. The Cvc Platform s a Chrstan-democratc and lberal-conservatve poltcal party, combnng lberal stances on the economy wth conservatve stances on socal and ethcal ssues, ncludng opposton to aborton, gay marrage and euthanasa. Among ther man proposals flat tax, fast prvatzaton, decentralzaton and labor law lberalzaton shall be cted n ths study. The party s atttude towards the European Unon s moderately enthusastc. In the European Parlament ths party s part of the European Democrats. The Polsh People's Party (Polske Stronnctwo Ludowe) Founded n 1990,t s consdered an agraran centrst party. The name of the party has a century-old hstory and t was one of the most mportant partes n the 1920-1939 perod. However, these days the members of the new Polsh People's Party come manly from the ex-communst Unted People s Party whch was strongly assocated wth the old regme. Because of ths, pror to 2003 ts program was rather left-wng wth a focus on agrcultural ssues. However, after quttng ther coalton wth the Democratc Left Allance Party they have moved towards the centre of the poltcal scene. It cannot be forgotten that rural areas are one of the man benefcares of Poland s accesson to the European Unon. In the European Parlament ths party s a member of European Democrats. Law and Justce (Prawo Sprawedlwość) - Ths party was establshed n 2001 by the Kaczyńsk brothers; Lech, the current Presdent of Poland, and Jarosław, the current party presdent. Most of the present party members were assocated wth the conservatve and socalst parts of the Soldarty Electoral Acton Party. It has bult ts poltcal strength mostly through leadng a crusade aganst poltcal corrupton. (Prevously, Lech Kaczyńsk was the 63

Charmen of the Natonal Control Chamber as well as the Mnster of Justce). The party s consdered to be socal-natonal-conservatve. Ther platform ncludes support for state nterventon n the economy, centralzaton, restrctng monetary polcy ndependence, enforcng stronger penaltes for crmnals, and fnally consttutonal reform n order to strengthen the role of the Presdent. Its atttude to the European Unon s rather skeptcal. In the European Parlament they are a member of the Unon for Europe of the Natons. Democratc Left Allance (Sojusz Lewcy Demokratycznej) A socal democratc party. Intally t was a drect descendant of the communst Polsh Unted Workers Party the rulng party from 1948 to 1989. The name was used for a coalton of left-wng partes from 1991 to 1999. It was formally establshed as a sngle party on Aprl 15, 1999. In late 2006, t joned the Left and Democratc Partes, an allance of centre-left socal lberal partes. In the early 90 s they abandoned ther back-to-communsm message and swtched to supportng socal democracy. Ths party represents a modern socal-democratc program modeled on the Labour Party or SDP. In 2001-2003 the then-governng Prme Mnster along wth the party s charman Leszek Mller mplemented market-orented reforms whch together wth numerous corrupton scandals runed the party s popular mage. However, t has a staunch group of supporters whch can be estmated as comprsng 10% of elgble voters. The party s enthusastc about the European Unon. In the European Parlament ths party s a member of the Party of European Socalsts. 64

Part 2. Model of pre-electon competton Data The data here was obtaned from Publc Opnon Research Center (CBOS Centrum Badana Opn Społecznej). The research was conducted n 2007 and ncludes 1385 ndvdual observatons. After excludng observatons lackng data, and these n whch respondents dd not plan to vote n the electon, the sample was reduced to 483 observatons. Respondents were asked questons about ther economc and poltcal concerns; ther electoral preferences and they answered questons about ther own characterstcs. In order to map the deologcal preferences of the voters, seven questons were asked, each elctng an opnon about an mportant socal or economc matter. Respondents were asked to place ther answers on a scale between 1 and 7. The questons are n Table 4.1. 65

Table 4.1 Questons about poltcal and economc ssues A B C D E F G H I 1) Crme should be fought toughly, even f t hnders cvl rghts 7) Crme should be fought n a way that does not hnder cvl rghts 1) Unemployment s harmful to the economy and should be stopped 7) A lttle unemployment can be proftable for the economy 1) The Catholc Church should be separate from the state and should not nfluence poltcs 7) The Catholc Church should have a major nfluence on poltcs 1) Publc fgures should provde statements as to whether they collaborated wth the People s Republc of Poland securty apparatus 7) Publc fgures should not have to provde statements as to whether they collaborated wth the People s Republc of Poland securty apparatus 1) Only select publc companes should be prvatzed 7) As many as possble publc companes should be quckly prvatzed 1) The state should provde hgh levels of publc servces, such as health care and educaton 7) Ctzens should be responsble for provdng themselves wth educaton, healthcare etc. 1) Rcher people should pay hgher fracton of ther ncome n taxes 7) Everyone should pay the same tax rate, regardless of ncome. 1) Aborton should be absolutely forbdden 7) Aborton should be allowed wthout restrcton. 1) Poland should am towards the hghest possble degree of ntegraton nto the European Unon 7) Poland should keep a hgh degree of autonomy wthn the European Unon The answers to the above questons were then rescaled n such a way that they le wthn a (-1;1) scale. On a bass of the answers, a factor analyss was conducted to fnd the man factors that le behnd the gven answers. As expected there was a strong soco-poltcal factor that descrbes the atttude of the responder towards the church. Table 4.2 presents the loadngs of each answer. 66

Table 4.2 Loadngs of answers Factor 1 Factor 2 A 0.252 0.225 B 0.447 C 0.107-0.614 D 0.223 0.245 E 0.409 F 0.579 G 0.478 H 0.224 0.459 I -0.291 SS loadngs 1.105 0.799 Proporton Var 0.123 0.089 Cumulatve Var 0.123 0.212 2 - Test* p-value=0.0517 The factors where obtaned usng maxmum lkelhood estmaton wth Varmax rotaton method; obtaned wth R 2.4.1 * H0: two factors are suffcent It may be noted that the frst factor may be assocated wth the economc state control vs. economc lberalsm scale, wth a hgh mpact of responses to questons B, E, F and G. The second factor descrbes respondents world-vew as conservatve or lberal. In the second factor, we fnd a partcularly hgh mpact of responses to questons C and H, questons that descrbed the vews of the respondent on the role of church and aborton. Apart from the economc dmenson, these world-vew questons turned out to be, as predcted, the man deologcal ssue and the decdng factor n shapng Polsh poltcs. For a deeper analyss of the latter statement a regresson was conducted whch nvestgated the mpact of each deologcal factor on how the each voter places ther vews on the left vs. rght scale (1 denotng left-wng, 7 rght-wng outlook). 67

Table 4.3 Impact of factors on left/rght self-percepton. Source SS df MS Number of obs = 483 -------------+------------------------------ F( 2, 480) = 4.83 Model 197.681911 2 98.8409557 Prob > F = 0.0084 Resdual 9823.99511 480 20.4666565 R-squared = 0.0197 -------------+------------------------------ Adj R-squared = 0.0156 Total 10021.677 482 20.791861 Root MSE = 4.524 ------------------------------------------------------------------------------ left_rght Coef. Std. Err. t P> t [95% Conf. Interval] -------------+---------------------------------------------------------------- factor1 -.3578391.1584206-2.26 0.024 -.6691226 -.0465555 factor2 -.3451811.1496859-2.31 0.022 -.6393017 -.0510606 _cons 4.745342.2058495 23.05 0.000 4.340864 5.149819 ------------------------------------------------------------------------------ Obtaned wth Intercooled Stata 9.1 Both factors have hghly sgnfcant mpact on the respondents self-percepton. Lberal economc vews cause voters to place themselves as left-wng. Smlarly, approval of separatng church from state, and support for aborton avalablty also places respondents as left-wng. Poltcal partes In the 2007 electon, four partes were able to gan seats n the parlament. The names, abbrevatons, votes obtaned and seats obtaned are presented n the table 4.4. Ths paper does not nclude the German Mnorty Party whch has obtaned one or two seats n the parlament snce 1991, and who gan the great majorty of ther votes n the south-western part of Poland. As the natonal mnorty representatve t s excluded from passng the threshold. Tradtonally, the German Mnorty supports the government regardless of ts poltcal stance. 68

Table 4.4 Partes n the parlament Name Abbrevaton Votes n % Seats Platforma Obywatelska (The Cvc Platform) PO 41.51 209 Polske Stronnctwo Ludowe (Polsh People's Party) PSL 8.91 31 Prawo Sprawedlwość (Law and Justce) PIS 32.11 166 Sojusz Lewcy Demokratycznej (Democratc Left Allance) (In parlament as a coalton wth mnor partners) SLD 13.15 53 Mnejszość Nemecka (German Mnorty) MN 0.20 (8.81 n Opole electoral dstrct) 1 As mentoned earler, the same set of questons on poltcal and economc ssues was also presented to party leaders. In cases where no answer was obtaned from a party, the mssng values were estmated on a bass of partes manfestos. Ths work only ncludes partes that were able to receve seats n Sejm n the electon of 2007. Here, an nterestng observaton can be made about voters percepton of partes postons n comparson wth the vews held by actual party representatves. Table 4.5 shows comparson of partes percepton about the nne ssues conducted by CBOS on a sample of voters (dfferent from the one used n ths work). Table 4.5 Comparson of partes postons percepton and the actual postons. PO PSL PIS SLD Percepton Poston Percepton Poston Percepton Poston Percepton Poston A 3,84 7 3,61 7 3,12 1 4,03 7 B 3,08 5 2,75 2 2,82 1 3,27 3 C 3,12 1 3,61 2 3,63 7 2,00 1 D 2,79 2 3,40 2 2,34 1 5,34 1 E 3,99 2 3,09 3 3,37 2 4,58 1 F 3,47 3 3,35 1 2,66 1 3,52 1 G 3,75 7 4,10 1 2,94 1 3,65 1 H 1,98 3 1,64 2 1,41 1 4,00 7 I 3,47 1 4,21 2 4,17 7 3,27 1 69

From the above table, one may observe that most of the partes are consdered to be far more moderate than they actually are. Voters do not perceve partes vews as extreme, but nstead tend to place them n the centre of the deologcal scale. The case of the SLD s partcularly nterestng. SLD party authortes place themselves as a tradtonal soco-lberal party wth a lberal world-vew, supportng the separaton of church and state and optng for a hgh state control over the economy. However, voters perceve them to be the most economcally lberal party of the four analyzed, probably due to the prevously mentoned market reforms they ntated n 2001-2003. Ths suggests that voters do not perceve any of the partes as beng tradtonally left-wng. The above results also suggest that we may expect a hgh varance of ths percepton of party postons n any further research, snce the rate of error seems to be ncredbly hgh. Factor analyss was adopted to obtan values for partes deologcal postons. These wll be used n the constructon of the spatal model n the next secton.. Densty and spatal placement of partes On a bass of factor loadng, deologcal scores were obtaned for each voter. These were combned to gve an deal pont for each voter on two polcy dmensons. The frst dmenson s called Economc and the second Relgous. The lower value of the economc dmenson ndcates support for a hgher level of nterventonsm n the economy. Low levels along the relgous dmenson suggest support for secularsm, whereas hgh values mean support for a hgh degree of nvolvement for Catholc values n publc lfe. Based on ths, a two-dmenson kernel densty, wth an axs-algned bvarate normal kernel estmaton of voters postons was conducted. The graph llustratng the estmated densty to two factors s presented n fgure 4.1 70

Fgure 4.1 Densty of voters postons. Fgure prepared usng the lattce package wth R 2.4.1 The majorty of voters are concentrated n the quarter of the deologcal space representng the left-wng economc vews, therefore supportng hgh state control over the economy and a conservatve world-vew. The latter result suggests that Catholc values are wdely held, and that voters expect the church to play a strong role n poltcal lfe. At frst glance, the partes postons adopted n table 4.4 suggest that partes ft nto these popular opnons qute well. The scorngs for each party serve as the deal ponts for partes postons and are used n further analyss. Fgure 4.2 presents partes postons estmated on a bass of factor analyss n comparson wth the densty of voters postons. 71

Fgure 4.2. Voters and partes postons Fgure prepared usng the lattce package wth R 2.4.1 From fgure 4.2 t can be observed that all the partes are qute well postoned n the deologcal space. The peak of the dstrbuton s occuped by the PSL, whch places tself n the medan of the economc dmenson. The party on the left of the relgosty scale s the SLD, whereas the other three compettors are placed n the more conservatve part of ths deologcal space. The SLD need not compete wth other partes for the relgous left-wng orented voters and should capture the votes of all electors located at the bottom-left corner of the dstrbuton. The other three partes are almost collnear along the relgosty scale, and they compete prmarly n one dmenson the economc one. 72

The model The profle of voters deal ponts ( x ) and the profle of party postons ( j ) jk are N combned to obtan the dstance (n ths case a Eucldean norm was calculated) of each voter from every party, producng an array jk ( j ) N. The votng ntentons of the electors are represented wth a matrx K ( y j ) N n whch j y =1 f voter voted for party j n the 1997 electon and 0 otherwse. Probablty matrx j representng probablty that votes for j must be calculated (the realzaton of whch s obtaned by maxmum lkelhood estmaton). The pure spatal theory of electoral competton assumes: 2 2 Pr( u u for all1 j) Pr( ( :1 ) (see Schofeld et al. 1998) j j 1 1 j 1 j j Models of bnary choces usually deal wth characterstcs that vary by ndvduals but not by alternatves. An advantage of measurng the characterstcs that vary by alternatves s that we may then determne the effect of addng an alternatve usng ts characterstcs. The followng model specfcaton allows for both types of characterstcs. The general specfcaton s as follows: u j a X j j j where: u j - utlty of voter from party j a - vector of characterstcs unque to voter X j - Vctor of characterstcs specfc to party j wth respect to voter. ~ N( μ, Σ) - errors are allowed to be correlated across canddates. j 73

The alternatve specfc multnomal probt adopted n the research allows for correlated errors as well as for the heteroscedastcty of error varances. The major advantage of the multnomal probt model s relaxng the IIA (the Independence of Irrelevant Alternatves) assumpton, whch could be problematc f the alternatves were close together. Ths general specfcaton allows for estmatng both the pure spatal model and the model wth ndvdual characterstcs. Frst the pure spatal model was estmated. Stata 9.1 fts multnomal probt models (MNP) usng a maxmum smulated lkelhood (MSL) mplemented by the Geweke- Hajvasslou-Keane (GHK) algorthm n order to compute the multdmensonal ntegral. Results of the estmaton are presented n table 4.6. We observe that the sample vote shares ft qute well wth the actual electon results, expect n the case of PIS, for whch the actual result turned out to be much worse than n the presented sample. Possble reasons for ths fact are analyzed n the followng subsectons. 74

Table 4.6. Pure spatal model results 95% CI Parameter Posteror mean SD Lower Upper Spatal dstance -.3546574.0669118 -.485802 -.2235128 Log smulated-lkelhood = -463.2318 Predcted vote share PO.3862066.0070562.3723419.4000714 PSL.0897353.00289.0840568.0954138 PIS.3996703.0065921.3867162.4126245 SLD.1354893.0029335.1297258.1412528 Sample vote share PO 39.64 PSL 8.59 PIS 39.14 SLD 12.6 Actual vote share PO 41.51 PSL 8.91 PIS 32.11 SLD 13.15 Obtaned wth Intercooled Stata 9.1 On a bass of the pure spatal estmates t was possble to predct vote probabltes for each party based on the economc and relgous vews of the voters. Fgures 4.3, 4.4, 4.5 and 4.6 present the probabltes for the PO and PIS partes. We may observe that probablty of votng for the Cvc Platform party ncreases along wth ncreasng economc lberalsm, up to over 0.5 for those n support for the mnmal nterventonsm. The probablty remans constant along the second spatal dmenson - relgosty - for each of the three partes: PO, PSL and PIS. In fact, these three canddate partes are almost collnear n ths dmenson. The relgous dmenson should nfluence the probablty of votes gong to the SLD. The votng probabltes fgures do not exhbt such a 75

relaton. However as I wll observe n the jont model, the relgous self-mage of the voter s sgnfcant. Possble reasons for ths wll be dscussed n the next secton. 76

Fgure 4.3 Estmates of voter probabltes for the Cvc Platform party (PO) Fgure 4.4 Estmates of voter probabltes for the Polsh People's Party (PSL) 77

Fgure 4.5 Estmates of voter probabltes for the Law and Justce party (PIS) 78

Fgure 4.6 Estmates of voter probabltes for the Democratc Left Allance party (SLD) Fgures prepared usng the lattce package wth R 2.4.1 The probablty of votng for the Polsh People s party (PSL) reaches ts maxmum of 0.086 at the mean of the dstrbuton of voters along the economc dmenson. Therefore we may say that the PSL consttutes a typcal center party, n terms of economc vews. In the case of the Law and Justce party (PIS) the probablty of votng ncreases along wth support for state control up to the maxmal value of 0.6. A possble reason for ths s that the PIS s consdered a populst party, and therefore ams to be perceved as provdng a hgh amount of socal benefts. The probablty of votng for the Democratc Left Allance party (SLD) also ncreases n the economc dmenson; therefore left-wng orented voters would typcally vote for ths party. However, the specfcty of the Polsh poltcal scene causes a lack of competton between PIS and SLD. SLD s perceved as post-communst, no matter what ther actual values are, whereas the PIS s typcally assocated wth tradtonal values and conservatsm. The two partes are placed on far opposte ends of the relgosty scale. However, what s partcularly mportant for the case of SLD s that ther probablty reaches a local maxmum on the lberal end of the economc scale. The latter fact may be assocated wth the mspercepton of the party poston descrbed n table 4.5 Predcted vote shares were obtaned as an expected value of ndvdual probabltes. The predcted vote shares correspond qute well to real outcomes for the cases of PSL and SLD. For PIS and PO the results dffer substantally from the actual outcomes. The analyss of the latter phenomenon s presented n the next subsectons. 79

Tables 4.8 and 4.9 present results obtaned from the jont model. In addton to the spatal dstance, ndvdual characterstcs such as educaton level, relgosty, sze of town of resdence and dsposable ncome act as ndependent varables. 80

Table 4.7 Independent case varables Name dst Spatal dstance Mejsc Sze of town categorcal varable Educ Educaton categorcal varable Dochod Income Wara Relgosty categorcal varable 1) country 6) cty over 500.000 nhabtants 1) ncomplete prmary educaton 11) hgher educaton (Master s degree) dsposable ncome per capta n the household 1) deeply relgous 4) not relgous Table 4.8 The jont model results Alternatve-specfc multnomal probt Number of obs = 1584 Case varable: label Number of cases = 396 Alternatve varable: parte Alts per case: mn = 4 avg = 4.0 max = 4 Integraton sequence: Hammersley Integraton ponts: 200 Wald ch2(13) = 818.99 Log smulated-lkelhood = -428.05799 Prob > ch2 = 0.0000 ------------------------------------------------------------------------------ choce Coef. Std. Err. z P> z [95% Conf. Interval] -------------+---------------------------------------------------------------- party dst -.4028812.0284324-14.17 0.000 -.4586076 -.3471548 -------------+---------------------------------------------------------------- PIS (base alternatve) -------------+---------------------------------------------------------------- PO mejs.0908009.0115508 7.86 0.000.0681618.11344 dochod -7.06e-06.0000213-0.33 0.740 -.0000488.0000347 wara.0593645.0785482 0.76 0.450 -.0945871.2133161 educ.0367887.0083464 4.41 0.000.02043.0531473 _cons -1.091558.2400008-4.55 0.000-1.561951 -.621165 -------------+---------------------------------------------------------------- PSL mejs -1.019483.3127687-3.26 0.001-1.632499 -.4064679 dochod -.0009103.0005607-1.62 0.104 -.0020092.0001886 wara 1.15987 1.268426 0.91 0.360-1.326199 3.64594 educ.1508094.1604894 0.94 0.347 -.1637441.4653629 _cons -6.01845 2.642121-2.28 0.023-11.19691 -.839988 -------------+---------------------------------------------------------------- SLD mejs.0697914.0159276 4.38 0.000.038574.1010089 dochod -.000209.0000336-6.23 0.000 -.0002747 -.0001432 wara.6357459.167271 3.80 0.000.3079006.9635911 educ.016352.0104738 1.56 0.118 -.0041762.0368803 _cons -4.549912.7774798-5.85 0.000-6.073744-3.026079 -------------+---------------------------------------------------------------- 81

Predcted vote share Mean SD 95% CI Lower Upper PO.3854222.0081261.3694553.4013891 PSL.0882957.0026948.0830008.0935907 PIS.4047057.0088689.3872791.4221322 SLD.1217155.002128.1175342.1258968 Sample vote share PO 39.64 PSL 8.59 PIS 39.14 SLD 12.6 Actual vote share PO 41.51 PSL 8.91 PIS 32.11 SLD Obtaned wth Intercooled Stata 9.1 13.15 Table 4.9 Margnal effects Alternatves Varable PIS PO PSL SLD Spatal dstance PIS -.08334.103998.003453.030016 PO.080109 -.110849.006788 1.e-194 PSL.003231.006852 -.010241.000168 SLD 1.2e-12 2.e-194 3.e-195 -.030184 Case varables mejs -.009879.042321 -.027444.005654 dochod 8.7e-06.000014 -.000023 -.000015 wara -.021106 -.003392.028483.047147 educ -.008525 Obtaned wth Intercooled Stata 9.1.007557.003214.001162 The jont model descrbes the shape of Polsh poltcs well. For the two major partes the hghest change n votng probablty can be assocated wth the spatal dstance and less wth other characterstcs. Out of all the canddates, the spatal dstance coeffcent s hghest for these two partes. The two factors that dstngush between the electorate of the PO and the PIS are town sze and educaton, whereas ncome and relgosty do not mpact the choce between these two canddates. The electorate of the PO conssts of nhabtants of bgger ctes 82

wth relatvely hgher educaton n comparson wth those votng for PIS. These two factors seem to determne the opnons of voters n the analyzed dmensons, snce the spatal dstance term has partcularly strong margnal effect for PO and PIS. The major problem wth both the pure spatal and the jont model s the fact that nether one correctly predcts the votng probabltes for the two major partes (results for the other two are satsfactory). Even ntroducng ndvdual characterstcs nto the jont model does not help to resolve ths ssue. Accordng to the theoretcal predctons, the PIS should receve almost eght percent of votes less than t actually had, whereas the predcted vote probablty for the PO s lower than ther actual result. Non-spatal characterstcs of the two partes seem to play a role. A major one that can help explan the presented result s the fact that 2007 electon was a pre-term electon after two years of a coalton formed by the PIS and two mnor partes (who dd not receve seats n the parlament after 2007) that eventually resgned as a result of not beng able to successfully govern. The strong mpresson of decreptude assocated wth the PIS after ths may have resulted n far lower result than that suggested by the spatal poston of the party, who actually seem to be best ftted to the deal ponts of the voters. In the case of the PSL, the only sgnfcant ndvdual characterstc s the town sze, whch had a negatve effect on ther vote probablty. Ths s due to fact that PSL s tradtonally consdered an agraran party that only represents the nterests of farmers; therefore, non-spatal characterstcs that were not reflected n ths study seems to be mportant for predctng the overall result. The margnal effect on spatal dstance s sgnfcant for all alternatves, except for SLD. For the case of SLD we observe very strong negatve mpact of the relgosty varable, reflectng the fact that t s the only party assocated wth secular values. Also ncome and 83

town sze have a strong mpact on the votng probablty for SLD: t ncreases along wth the town sze and decreases wth ncome. The spatal varable does not have a strong mpact on the probablty, agan confrmng that electorate of ths party does not necessarly decde on the bass of the actual party s poston, but on ts non-spatal characterstcs, n ths case ts assocaton wth post-communsm. Table 4.10 Informaton crtera LL AIC BIC Bayes Factor Pure spatal model -463.2318 729.6472 740.3826 exp(35)>10 15 Jont model -428.05799 898.116 1010.838 Log-smulated lkelhood ncreases for the jont model from -463 to -428. Bayes factor suggests the choce of the jont model, but ths measure does not account for the lost degrees of freedom. On the other hand, both nformaton crtera fnd the pure spatal model superor n predctng the votng probabltes for each of the four Polsh partes. Ths s qute ntutve when we observe that votng probabltes reman almost the same, and that the log-lkelhood ncreases only slghtly for the two models, whereas the lost of degrees of freedom for the second model s qute substantal. The problem of abstenton Voter turn-out n the electon of 2007 barely exceeded 50% (equaled 53.88%). In Poland s case, the most probable explanaton for ths s alenaton. Accordng to a 2007 CBOS study, only 33% of Poles beleve that among the competng partes there s one that represents ther opnons well(cbos Report BS/73/2007). The frst mpresson that strkes one s that, accordng to the estmated voter postons (seen n fgure 4.2) three of the partes; that s, the PO, the PSL and the PIS, place themselves n good postons that cover the area 84

wth the hghest densty of voters, so that one mght thnk that ths would preclude voter abstenton. On the other hand, f we recall the mspercepton of partes postons presented n table 4.5, ths phenomenon can be understood. Fgure 4.7 shows how the actual partes postons dffer from the publc s percepton. Fgure 4.7 Partes postons and ther publc percepton Fgure prepared usng the lattce package wth R 2.4.1 The man problem connected wth voter abstenton s how t actually nfluences the results of the electon. We observed that the probabltes obtaned from the spatal model for the two man partes dffer substantally from the real ones. If abstenton had on average the same effect for every party, ths would not cause the results to dffer between the whole populaton and the sample that actually voted. However, n Poland s case ths s not true. 85