P and V(p w,y) V(p,y) for at least one-half the measure of

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1 Majorit Choice of an Incoe argeted Educational Voucher 1 Dennis Epple, ichard oano, and Sinan Sarpca Online Appendix A. epresentative Deocrac Model with a Continuu of pes. his part of the appendix is largel an adaptation of Proposition 2 and Corollar 1 in Besle and Coate (1997) to the case of a continuu of tpes. heir central assuption is that the polic preference of ever population eber is known and, if a population eber is elected, then that polic will be ipleented. heir Corollar 1 states roughl that existence of a Condorcet winner aong preferred polic vectors in the population iplies single candidate equilibriu exists for sufficientl low cost of becoing a candidate, with the individual having the Condorcet winning polic vector the candidate (and winner). Besle and Coate (BC) assue an integer nuber of voters, an of who can be a candidate. Our odel assues a continuu of voters and thus potential candidates, indexed b endowed incoe, with continuous distribution F() and densit f(), the latter positive on the support of. We ake analogous assuptions about preferences and equilibriu as do BC. We next suarize those assuptions and introduce a bit ore notation, and then report the results of interest. We provide an additional result about uniqueness of equilibriu, but under a strong odification to BC s odel. A population eber has indirect utilit function V = V(p,), where p is a polic vector. In the voucher-odel application, a voucher, incoe tax rate, eligibilit threshold, and per student level of public expenditure arise in equilibriu, but the polic vector in the indirect utilit function V is tri-variate as one variable is eliinated b the governent balanced-budget requireent. Let p*() denote the preferred polic choice of voter, which we assue is unique. Let P * * * denote the set of p* values; i.e., P {p () f() 0}. he results regard the case where there is a Condorcet winner p w : p w is a Condorcet winner if voters for all * p P. p P and V(p w,) V(p,) for at least one-half the easure of w * Let w satisf p w = p*( w ). Incoe w a or a not be unique though it is unique in the voucher application. However, we have ultiple voters with incoe w, consistent with the notion that f() is positive. Let Y w denote the set of w values. Equilibriu assues voters first decide whether to becoe candidates, followed b voting. An voter can becoe a candidate at 0 cost, and voters choose to be candidates or not siultaneousl. Given the slate of candidates, assued non-ept at the oent, voters siultaneousl and costlessl vote b voting for one candidate, though an voter can abstain. If a voter is indifferent between candidates and votes, then the voter randoizes with equal probabilities aong the. he candidate receiving the highest easure of votes is the winner and that candidate s preferred polic is ipleented. If there is a tie aong the highest vote getters, then a winner is selected aong the with equal probabilities. If no candidate enters the race or if a positive easure of votes fails to aterialize, then a relativel lous polic p 0 is 1 Part A of this appendix tracks closel part of the on-line appendix for Epple and oano (2014). 1

2 ipleented, which is worse for everone than a positive easure of policies assued that voters never choose a weakl doinated strateg when voting. * pp. 2 It is also wo preliinar results are: esult 1: If two candidates enter fro the set whose policies are preferred to p 0, then a candidate that is ajorit preferred will win. esult 2: If one candidate enters fro the set whose policies are preferred to p 0, then that candidate is elected. esult 1 is iplied b the assuption that voters never choose a weakl doinated strateg. Given that it is costless to vote, a voter is never worse off and soeties better off voting for their preferred candidate if there are just two candidates fro this set. 3 As well, sincere voting is iplied with two candidates. esult 1 and the sincerit iplication are results in BC. esult 2 follows since everone prefers the election of an candidate fro this set to the lous default outcoe. It is not an equilibriu for a zero easure of voters to vote. he ain result is as follows: esult 3: Assuing a Condorcet winner aong preferred policies: (i) a single candidate equilibriu having a candidate w exists, with that candidate elected; and (ii) a single candidate equilibriu ust have a w elected. Proof of esult 3: (i) If onl a w becoes a candidate, then that candidate will be elected b esult 2. 4 A w becoing a singleton candidate is an equilibriu, since, b esult 1, an Y would not be elected and then gains nothing b also entering; nor would another w entering w gain since his preferred polic arises anwa. (ii) It is not an equilibriu for an Y to be the onl entrant, since, b esult 1, a w would enter and win the election. We ephasize that esult 3 is a siple adaptation of BC s Corollar 1. We can odif the BC odel to generate uniqueness of equilibriu with equilibriu polic p w. Assue two parties that siultaneousl offer their part s candidac to an voter. Onl part candidates run. Once the slate is set, voters siultaneousl vote as above. Preferences are as above, in particular part affiliation of a candidate does not affect preferences. Such a political process ight arise if running for election is prohibitivel costl for a non- w 2 he notion is that a lack of leadership if no one is elected results in a worse polic than that advocated preferred b soe potentiall elected households (though this assuption is becoing increasingl difficult to defend). Note, too, that BC assued, if onl one candidate enters, that candidate is autoaticall the winner (as that candidate could vote for hiself if no one else votes). Since we require a positive easure of votes to win given the continuu, we ust odif the assuption a bit. 3 If the two candidates are equall preferred b everone, then everone still votes in equilibriu to avoid the possibilit that no one votes and the lous default polic arises. 4 he w candidate ust have a polic in the set ajorit preferred to p 0, since p w is ajorit preferred in P *. 2

3 affiliated candidate, while the part bears all running costs fro exogenous funds for their affiliated candidate. A part wants to win the election. Under these assuptions and assuing a Condorcet winner: esult 4: 5 Equilibriu has each part offer their candidac to a w, at least one accepts the offer, and the resulting polic is p w. Obviousl, the parties offer a candidac to a w. At least one accepts the candidac offer to avoid the default polic if neither runs. Whether one or both potential candidates run, voting equilibriu obviousl iplies that p w is ipleented. B. Propositions with Strongl eligious Households. We refer to the strongl religious as just religious, and the other households as non-religious. We assue the sae incoe distributions for both tpes, and that the proportion of religious tpes equals. Both tpes have the sae utilit function (as in the text) if public school is attended. If private school is attended, school qualit for religious tpes equals q, with 1, where q is per student expenditure in the private school attended. As in the text, the initial analsis here concerns equilibriu effects with religious households assuing the superintendent chooses public school. Note that such a superintendent ight be religious; the preferred polic choice of a religious and non-religious household is the sae if public school is attended. We first establish the analogues of Proposition1-c. Let (t,z,g) denote the iniu incoe of a religious households that would choose private school given (t,z,g), with z either equal to 0 or v, assuing eligibilit for the voucher in the latter case. It is obvious that (t,z,g) (t, z,g) for all relevant policies. he coparative statics in (1) in the text hold for (t,z,g) just like for (t,z,g). Just to avoid tediu, we assue policies and an incoe distribution such that religious tpes will attend both public and private schools, i.e., in (t,v,g) (t,0,g) ax, where the second inequalit is iplied b the coparative statics. he elected superintendent will continue to choose (v,) to iniize the tax rate given his preferred choice of g (i.e., the analogue of Proposition 1b obviousl holds). We can state the proble as iniizing t given ty = B(,v,g,t), for given g and where B is equilibriu public expenditure. hus, B ust be iniized over (,v). We show the equivalent of Proposition 1- cii using this strealined approach. (As with no religious tpes, it is convenient to prove part cii before part ci. he odified proposition is: Proposition 1-cii. argeting: Assue equilibriu has a superintendent that chooses public school and let g * denote the superintendent s choice of g. If v > 0 is strictl optial (i.e., 5 Jackson, Mathevet, and Mattes (2007) provide a siilar result. See their Propositions 1 and 2. 3

4 soeone uses the voucher), then depending on paraeters. * equals either * (t,0,g ) or * (t,0,g ),which value Proof of Proposition 1-cii. o econoize on notation, we just write g for g * in this proof. First we argue that v < g is optial. If v = g, then the superintendent saves nothing b providing an private school students the voucher, ipling v = 0 is also optial (a contradiction). o show the reaining results, we ust consider two cases, delineated b whether (t,0,g ) or (t,v,g ). Case 1: (t,0,g) (t, v,g). In this case, it ust be that: in ax (t,v,g) (t,v,g) (t,0,g) (t,v,g). he latter values delineate 5 ranges within which can fall, and over which B(,v,g,t) differs. We show that B is iniized over at either (t,0,g) or (t,0,g). o show this, we write out B for each range and copute its derivate with respect to. We have: ange 1: [, (t,v,g)]. Here no one gets a voucher and in B (t,v,g) (t,v,g) g f ()d (1 )f ()d. in in ange 2: B/ 0. hus, ( (t,v,g), (t,v,g)]. Here B v (t,v,g) (t,0,g) (t,0,g) f ()d g f ()d f ()d (1 )f ()d (t,v,g ) in in B/ (vg) f( ) 0, the inequalit since we know v < g. hus, ange 3: ( (t,v,g), (t,0,g)]. Here B v f ()d (1 )f ()d (t,v,g) (t,v,g) (t,v,g) (t,0,g) (t,v,g) (t,0,g) g f ()d f ()d (1 )f ()d (1 )f ()d. in in B/ (vg)f( ) 0. hus, ange 4: ( (t,0,g), (t,0,g)]. Here B v f ()d (1 )f ()d (t,v,g) (t,v,g) hus, (t,v,g) (t,0,g) (t,v,g) (t,0,g) g f ()d (1 )f ()d (1 )f ()d (1 )f ()d. in in B/ [v (1 )g]f( ), the sign of which depends on the relative value of v and (1 )g. ange 5: ( (t,0,g), ax ]. B v f ()d (1 )f ()d g f ()d (1 )f ()d. (t,v,g) (t,v,g) (t,v,g) (t,v,g) in in Here, 4

5 B/ vf( ) 0. Noting that B is continuous, using the derivatives of B in the 5 ranges it is iplied that if v g(1 ), then the iniu is at (t,0,g); and if vg(1 ), then the iniu is at (t,0,g). (If v g(1 ), then an between and including the two threshold is optial, but this will not arise genericall.) Case 2: (t,0,g) (t,v,g). In this case, it ust be that: in (t,v,g) (t,0,g) (t, v,g) (t,0,g) ax. Again, there are five ranges into which ight fall, and we proceed as in Case 1. ange 1: [, (t,v,g)]. Here no one gets a voucher and in B (t,v,g) (t,v,g) g f ()d (1 )f ()d. in in ange 2: B/ 0. hus, ( (t, v,g), (t,0,g)]. Here B v (t,v,g) (t,0,g) (t,0,g) f ()d g f ()d f ()d (1 )f ()d (t,v,g ) in in B/ (vg) f( ) 0, the inequalit since we know v < g. hus, ange 3: ( (t,0,g), (t,v,g)]. Here B v f ()d g f ()d (1 )f ()d. (t,v,g) (t,0,g) (t,v,g ) in in B/ vf( ) 0. hus, ange 4: ( (t,v,g), (t,0,g)]. Here B v f ()d (1 )f ()d (t,v,g) (t,v,g) hus, (t,v,g) (t,0,g) (t,v,g) g f ()d (1 )f ()d (1 )f ()d. in in B/ [v (1 )g]f( ), the sign of which depends on the relative value of v and (1 )g. ange 5: ( (t,0,g), ax ]. B v f ()d (1 )f ()d g f ()d (1 )f ()d. (t,v,g) (t,v,g) (t,v,g) (t,v,g) in in Here, B/ vf( ) 0. Noting that B is continuous, using the derivatives of B in the 5 ranges it is iplied that if v g(1 ), then the iniu is at (t,0,g); and if vg(1 ), then there are two local inia at (t,0,g) and (t,0,g). Either of the latter ight be optial depending on paraeters. hus, we have shown that one of copleting the proof. (t,0,g) or (t,0,g) is optial in an case, 5

6 We now show the analogue of Proposition 1-ci, beginning with a stateent of it (though its stateent is exactl as for the case with no religious tpes). Proposition 1-ci. Assuing equilibriu has a superintendent that chooses public school, a * voucher v ( 0,g ) is optial. Proof of Proposition 1-ci Again, we drop the * fro g. We have alread shown v < g is optial assuing v > 0. hus, we show v = 0 is not optial, specificall b showing B can be decreased with a positive v. In the vicinit of v = 0 (with non-negative v), onl Case 2 in the Proof of Proposition 1-ci can arise; i.e., it ust be that ( t,0,g ) ( t,v,g ), this since (t,0,g ) (t,0,g ). Suppose that the superintendent sets ( t,v,g ). We show that B is decreasing in v in the vicinit of v = 0 with the latter choice, ipling a positive v is optial, since the alternative potential optiizing choice of (fro Proposition 1-cii) would ipl lower et B if such a is optial. hen: ( t,0,g ) ( t,v,g ) ( t,0,g ) B v f ( )d g f ( )d ( 1 ) f ( )d. ( t,v,g ) in in respect to v: Differentiating with ( t,0,g ) ( t,0,g ) B / v f ( )d v [ f ( )d ] / v g [ ( t,v,g ) / v ] f ( ( t,v,g )). ( t,v,g ) ( t,v,g ) he first two ters in the latter approach 0 as v approaches 0, while the last ter is negative since (t,v,g ) / v 0. Next we develop the analogue of Proposition 1-ciii regarding voting coalitions in equilibriu with the elected superintendent choosing public school. First note that those choosing public school in equilibriu with the sae incoe have the sae local polic and thus voting preferences whether religious or not. However, because religious tpes have stronger preference to attend private school, the sets of incoe tpes that choose public school generall differs. Let f pub () denote the population densit of nonreligious tpes that attend public school and f pub () the sae for religious tpes. f pub () equals (1 )f() if public school is chosen b non-religious household with incoe and 0 otherwise. f pub () equals f() if public school is chosen b religious household with incoe and 0 otherwise. he ranges of incoe where public school is chosen var with paraeters and are iplicit in the Proof of Proposition 1-ci. hose that choose private school and receive no voucher prefer lower t (and care not about g and v) whether religious or not. hese incoe sets can differ, too, but we need not provide notation for this. he sign of (4) in the text again deterines the local voting preferences of those that choose private school and receive a voucher. he equilibriu incoe sets for which this is positive or negative will in general differ between religious and non-religious tpes, both because Uq will differ and because those that choose private school (and get a voucher) can differ. Let Y + denote the nonreligious incoe set that obtain a voucher and for which U v > 0 and let Y + the analogous set of religious households. Proposition 1-ciii. Assuing equilibriu has a superintendent that chooses public school, w pub pub ust satisf: (i) [ f ( ) f ( )]d ( 1 ) f ( )d f ( )d.5; w Y and Y 6

7 (ii) Households in (i) other than w prefer a candidate with arginall higher incoe and the reaining households prefer a candidate with arginall lower incoe. he proof is exactl as for Proposition 1-ciii and is oitted. he specifics of the voting coalitions are of interest, but var with polic characteristics as noted above. An exaple is that in Figure 3 in the text. Proposition 2 in the text describes the set of potential optia for all candidates, which is necessar to confir existence of equilibriu. o provide the analogue of Proposition 2 when there are religious tpes, the following lea is useful. Lea 1. An elected superintendent with incoe s that would choose private school and set v = g > 0, would choose Max [, ( t,0,g )]. s Proof of Lea 1. Given v = g, the superintendent s objective is to iniize the tax rate while aking sure to be eligible hiself for the voucher. Miniizing the tax rate corresponds to axiizing the easure of households that attend private school with no voucher since the public cost of all those who take a voucher or attend private school with a voucher is the sae. Onl religious tpes with ( t,0,g ) and non-religious tpes with ( t,0,g ) will attend private school with no voucher. Given the own-eligibilit constraint and that, the choice of then axiizes the easure of households that attend private school with no voucher. If, then the superintendent aintains his own eligibilit and axiizes the s easure of households that attend private school with no voucher with an [, ], but s then chooses due to the benevolence assuption (A8) because this allows ore households to get a voucher and subsidize it rather than attend public school. With Lea 1 in hand, the analogue of Proposition 2 is ver siilar. Proposition 2: A household that chooses the polic vector and itself chooses public school follows the polic described in Propositions 1-ci and 1-cii A household that chooses the polic vector and itself chooses private school either: (i) chooses t=g=v=0 with optial private consuption; or (ii) sets v = g > 0, with = Max [, ( t,0,g ], t satisfing: (B.1) Max[, ] Max[, ] f ( )d ( 1 ) f ( )d ty, in in Max v,t,,g U ( v ) and with v solving: Assuing a household s.t. Max[, (t,0,g )];( B.1); and v g. choosing private school faces a strictl quasi-concave optiization proble, polic tpe (i) [(ii)] is optial if > [<] Y/F(). he proof parallels that of Proposition 2 and is oitted, though we ake a few coents. In addition to the difference in the eligibilit threshold as copared to the case with no religious tpes (Lea 1), the budget constraint for a superintendent that chooses polic (i) is odified to 7

8 account for the alternative schooling choices of religious and non-religious tpes. A difference that is not apparent fro coparing the two versions of the proposition is that the threshold incoe where an elected superintendent is indifferent to choosing public school and private school, each with the superintendent setting polic, is lower for religious than non-religious households. his is ver intuitive and seen in the exaple developed in the text. 6 What is perhaps surprising is that the incoe level where an elected superintendent choosing private school transitions to the 0-tax polic does not differ between religious and non-religious tpes, i.e., satisfies = Y/F(). he intuition is that the decision as to whether to eplo taxes to fund private consuption is purel a fiscal one, dependent on incoe but not on the deand for private consuption. C. Coputational Progra Suar. Overview: We first suarize the coputational strateg for the case when there onl nonreligious households. We then explain how the strateg is extended to incorporate preferences of religious households. he progra calculates a feasible set of polic alternatives, S, that includes the ost-preferred polic of each citizen. he set of ost preferred policies, s, is then selected fro S. his is the set of citizen-candidate proposals. he Condorcet winner, if an, is then obtained b finding the polic fro s that defeats all other policies in s in pairwise voting. As detailed in Section 2, a citizen candidate s polic proposal is a tuple coprised of the tax rate, voucher, expenditure per student in public school, and highest incoe eligible for the voucher: t,v,g,. he approach of the progra is to consider a polic triple (t,v,g) while exploiting Proposition 1 of Section 3 to deterine. Fro Proposition 1, a citizen candidate who proposes a positive voucher will propose a targeted voucher with the incoe-eligibilit liit set equal to the incoe of the individual indifferent between public and private when not receiving a voucher: =(t,0,g). It is also useful in the describing the coputations to refer to the incoe, denoted a in the progra, of the lowest-incoe individual indifferent who will take up the voucher. his is the individual eligible for the voucher who is indifferent between public school with no voucher and private school with the voucher: a = (t,v,g). As deonstrated in Section 3, there are three possible regie tpes: 1. (t,v,g) with g>v 0 2. (t,v,v) with v>0 3. (0,0,0) An individual who would attend public school under his/her ost-preferred polic will propose a egie 1 polic. An individual who would attend private school with a voucher under his/her 6 he arguent is this. For given incoe, the optial polic choice and utilit level for religious and non-religious tpes are the sae conditional on choosing public school. However, for given incoe and optial polic choices utilit is higher for religious tpes than non-religious tpes if private school is chosen. he latter is iplied b the fact that religious tpes value private schooling ore and would therefore have higher utilit even if choosing the sae polic values as is optial for a non-religious tpe in private school. hus, the range of incoe where the private alternative is preferred b an elected superintendent ust be wider. 8

9 ost-preferred polic will propose a egie 2 polic. In egies 1 and 2, the incoe eligibilit liit,, is deterined b Proposition 1 as described above. An individual who would attend private school without a voucher under his/her ost-preferred polic will propose the egie 3 polic, with =in. Citizen Candidates: Discretize the incoe distribution b selecting an equall spaced grid of values of incoes spanning the support of the incoe distribution [in,ax]. Denote these incoes j for j=1,,j,. his is the set of citizen-candidates in the odel. In the progra, the space between points on this grid is $1,000. Feasible Policies: We next describe the strateg for calculating the set S that will contain s as a proper subset. Let a citizen-candidate with incoe j be naed j. egie 1: Calculate the (t,v,g) allocation ost preferred b j assuing j attends public school (even if j does not prefer public school under his ost-preferred polic). Do this calculation for each j for j=1,,j,. Let (tj,vj,gj) be j s polic fro this calculation. his calculation also provides the incoes,a,j = (tj,vj,gj) and,j = (tj,0,gj). hese incoe boundaries are used in the calculation of votes. Hence, for each j, the progra saves the row vector (tj,vj,gj, a,j,,j). hese row vectors are stacked verticall to obtain a atrix of diension JX5. Calculation of (tj,vj,gj) for j for egie 1 proceeds as follows. he citizen-candidate choosing a ost-preferred egie 1 polic faces the following constraints: 1) Governent budget constraint. 2) Boundar-indifference condition for a,j 3) First-order condition for private school expenditure, ea,j if a,j attends private school 4) Boundar-indifference condition for,j 5) First-order condition for e,j if,j attends private school he coputational approach entails solving a sste of 17 nonlinear siultaneous equations. he five constraints iplicitl express five variables as functions of g and v: t(g, v), ea(g, v), a(g, v), e(g, v), (g, v). Differentiate each of the five constraints with respect to g to obtain the derivatives of the preceding five functions with respect to g. Differentiate each of the five constraints with respect to v to obtain the derivatives of the preceding five functions with respect to v. ogether, this ields 15 equations for the constraints and their derivatives. he two additional equations are the first-order conditions for the citizen-candidate s ost-preferred g and v. hese are obtained b differentiating the citizen-candidate s utilit function with respect to g and with respect to v. (Note that the derivative of the citizen-candidate s utilit function ields dt(g,v))/dv=0.) For each citizen candidate, j, this sste of 17 nonlinear siultaneous equations is solved. egie 2: All feasible policies satisfing v=g are calculated regardless of whether the are preferred polic of an candidate. he coputations proceed siilarl to those for egie 1, b solving a sste of nonlinear siultaneous equations while invoking the g=v constraint. his calculation also provides the incoe, a,j, of the individual indifferent between attending public school with spending gj = vj and attending private school with a voucher vj. For each j, the 9

10 progra saves the row vector (tj,vj,vj,a,j,,j). hese are stacked verticall to obtain a atrix of diension Jx5. egie 3: For regie three, there is a single polic (0,0,0). Hence this polic ields the vector (0,0,0,in,in) where in is the lower bound of the support of the incoe distribution. he set S: he union of the above three sets of policies ields set S. In the progra, the union of these policies is obtained b verticall stacking the above to obtain a atrix of diension (2J+1)x5. Let K=2J +1. Hence, S has diension Kx5. Proposals: Calculate the utilit of candidate j for each ever polic in S. he polic that axiizes the utilit of j is then the proposal of candidate j. his calculation for each candidate j then ields the set of polic proposals s. Voting: A rando saple (e.g., 100,000) of incoes is drawn fro the incoe distribution. hese are voters. A guess is ade of the incoe of the winning candidate, and this incoe is the contender, c, against which others are paired. he proposal of c is voted against the proposal of the lowest-incoe individual, 1, and the fraction of voters favoring the proposal of c is calculated. If the fraction exceeds.5, the proposal of c is voted against the proposal of the nexthighest incoe, 2. If the proposal of c is not defeated b an alternative, c this step of the coputations is copleted. If the proposal of c is defeated b the proposal of soe candidate, sa, i, then i becoes the new contender, i.e. c=i. he proposal of the new c is voted successivel against the proposal of i+1, i+2, etc until either c defeats all reaining alternatives or c is replaced b a new contender. his process continues until the reigning c is paired against all proposals through that of J. Winning this series of votes is a necessar condition to be a Condorcet winner. Let w denote the incoe of this winner. he proposal of w is then paired against ever other proposal. If w defeats all alternatives, then w is the Condorcet winner. If the proposal of soe other candidate defeats w, there is no Condorcet winner, and no citizen-candidate equilibriu exists. eligious Candidates: When there are both religious and non-religious tpes, there are again the sae three regie tpes. Now, however, the sste of nonlinear equations for egie 1 ust take account of the fact that there are different incoe thresholds for take-up of the voucher, i.e., (t,v,g) differs between religious and non-religious tpes. Siilarl, the incoe thresholds for attending of private school when not eligible for a voucher also differ. In addition, the ostpreferred egie 1 polic alternative for a given j differs between religious and non-religious tpes. Hence, the nuber of equations that need to be solved to obtain an eleent of S for egie 1 is roughl double that for the case with onl non-religious tpes. In addition, this sste of equations needs to be solved twice as an ties to obtain the ost preferred polic for each j for each religious tpe. Siilar generalization is required to solve for eleents of S for egie 2. In total, S then contains (4*J+1) eleents. he eleents of s then are then chosen, each eleent being a ost-preferred alternative of either a religious or a non-religious individual on the grid of incoes. Voting to select the winner, if an, proceeds as before with utilit for the eleents of s differing b incoe and b religious tpe. eferences 10

11 Besle, ioth and Stephen Coate, An Econoic Model of epresentative Deocrac, Quarterl Journal of Econoics, 112, Februar 1997, Epple, Dennis and ichard oano, On the Political Econo of Educational Vouchers, Journal of Public Econoics, 120, Deceber 2014, Jackson, Matthew, Laurent Mathevet, and Kle Mattes, Noination Processes and Polic Outcoes, Quarterl Journal of Political Science, 2, 2007,