Stategic Timing of Ballot Initiatives: vidence fom Wisconsin School Refeenda Mac Meedith Stanfod Gaduate School of Business Political conomics Field Pape Last Updated: 11/15/04 ABSTRACT: One impotant consideation when studying diect democacy is the ules on agenda establishment. In thei seminal seies of aticles, Rome and Rosenthal 1978, 1979 identified the ability of a budget maximizing monopolist efeendum agenda-sette to extact a geate amount of expenditue than desied by the median vote. While in Rome and Rosenthal s models, the agenda sette execised contol only ove the amount of the efeendum, this pape focuses on the ability of an agenda-sette to gain favoable outcomes though the stategic timing of elections. Since diffeent subsets of the electoate may tunout to vote fo an initiative o a efeendum given the emaining composition of the ballot, elections scheduled fo diffeent times may poduce diffeent median votes. As a esult, an agenda sette with the powe to schedule the election may attempt to schedule the election at a time that poduces a median vote closest to thei ideal point. This pape pesents a fomal model of stategically timing of school efeenda. The emainde of the pape then empiically tests the fomal model using a dataset of school distict efeendum in Wisconsin fom 1990-003. The esults show some evidence of stategic timing, though they ae not paticulaly obust.
I. Intoduction: In the United States many policy decisions ae made by a vote of an electoate at lage. Appoximately half of the states in the United States have povisions fo some fom of citizen-initiated diect legislation Matsusaka, 1995. In addition, many states and municipalities make tax and expenditue decisions though efeendum. Thee is a geat deal of heteogeneity in the ules specifying how and when these initiatives and efeenda each votes. Fo example, states geneally equie the numbe of signatues in suppot of a citizen initiative to exceed some pecentage of the votes paticipating in the most ecent gubenatoial election. This equiement vaies fom two pecent in Noth Dakota to fifteen pecent in Wyoming Matsusaka, 1995. Califonia s poposition 13 and Massachusetts poposition 1 ½ demonstate the enomous potential policy influence of diect democacy. As a esult, it is impotant to undestand how the pesence of diect democacy, and the ules suounding its administation, affects economic and political outcomes. The ules on agenda establishment have been of histoical inteest in the study of diect democacy. In thei seminal seies of aticles, Rome and Rosenthal 1978, 1979 identified the ability of a budget maximizing monopolist efeendum agenda-sette to extact a geate amount of expenditue than desied by the median vote. In the Rome and Rosenthal models, the budget maximizing monopolist agenda-sette execised powe by contolling the amount of the efeendum. In some cicumstances, howeve, thee may be additional souces of agenda contol. This pape focuses on the ability of an agenda-sette to gain favoable outcomes though the stategic timing of elections. Since
diffeent subsets of the electoate tunout to vote fo an initiative o a efeendum given the emaining composition of the ballot Rubinfeld, 1980; Smith 001; Tolbet, Gummel, and Smith, 001, elections scheduled fo diffeent times may poduce diffeent median votes. As a esult, an agenda sette with the powe to schedule the election may attempt to schedule the election at a time that poduces a median vote closest to thei ideal point. The emainde of the pape poceeds as follows. Section II povides a bief eview of the pevious liteatue on diect democacy. A fomal model of stategically scheduling elections is developed in section III. Section IV pesents empiical tests of the pedictions made in section III. The emainde of the pape then applies data to the empiical pedictions. The dataset, which coves school distict efeenda in Wisconsin fom 1990 to 003, is descibed in section V. Results fom the empiical tests ae pesented in section VI. Section VII concludes. II. Pevious Liteatue: A numbe of ecent papes have looked at the elationship between the pesence of citizen-initiated diect legislation and govenment expenditues. Zax 1989 finds that states and municipalities in the United States that pemitted diect initiatives fo statutoy puposes had highe govenment expenditues than non-initiative states and municipalities. In contast, Matsusaka 1995 finds that state expenditues and tax evenues ae appoximately fou and eight pecent lowe espectively in those states that
pemit diect legislation. Similaly, Feld and Matsusaka 003 estimate that Swiss cantons that equie mandatoy efeendum fo new spending had 19% less spending than compaable cantons without mandatoy efeendum. Besley and Case 003 also find a negative coelation between the pesence of initiative and measues of govenment spending and taxation, though they geneally find that this elationship is not statistically significant. Less liteatue has been poduced on the effects of efeendum on govenmental expenditue. Much of the existing liteatue has focused on how the demogaphics of an electoate affect expenditue outcomes in municipalities that face a common state efeendum pocess. Fo example, Rome, Rosenthal, and Munley 199 and Stevens and Mason 1996 test how the composition of the electoate affects school efeendum poposals and outcomes in New Yok and Oegon espectively. A numbe of othe papes, like Begstom, Rubinfeld, and Shapio 198, Rubinfeld 1977, and Tedin, Matland, and Weihe 001, have studied how individual s chaacteistics affect thei voting behavio on an expenditue efeendum. In only a few papes in the ecent liteatue on diect democacy is thee any discussion of agenda setting. Feld and Matsusaka 003, Gebe 1996, and Matsusaka 1995 all empiically test how the size of the signatue equiement fo diect initiatives affects govenmental expenditues. All thee papes find a positive elationship between the numbe of signatues equied to intoduce a diect initiative and govenment expenditue. Balsdon, Bunne, and Rueben 003 and Rome, Rosenthal, and Munley 199 test whethe school budget efeenda poposed by school boads ae consistent with the budget-maximization model of Rome and Rosenthal 1978, 1979. Baldson,
Bunne, and Rueben find that school boads act like isk-avese budget maximizing agenda-settes. Rome, Rosenthal, and Munley conclude that lage school disticts tend to act like budget maximizes, while small school disticts seem to popose efeendum moe in line with the pefeences of the median vote. Two pevious papes, Dunne, Reed, and Wilbanks 1997 and Pequet, Coats, and Yen 1996 discuss the ability of agenda-settes to contol the timing of elections. Dunne, Reed, and Wilbanks collect school bond data fom 0 states whee school boads have the powe to schedule the date of efeendum on school bonds. They test whethe the scheduling of school bonds fo non-geneal elections is independent of whethe the school boad was elected in a non-geneal election. The authos find that school boads that wee elected in non-geneal elections wee moe likely to schedule bond issues fo a non-geneal election. This is pesented as evidence of the stategic scheduling of elections. Pequet, Coats, and Yen study tunout in local school boad popety tax elections in Louisiana. They find that the popotion of votes against a school-tax poposition is significantly and positively elated to tunout, and that tunout is significantly and positively elated to the numbe of othe additional issues on the ballot. While both Dunne, Reed, and Wilbanks 1997 and Pequet, Coats, and Yen 1996 discuss the possibility of the stategic timing of elections, in neithe pape do the authos diectly test this hypothesis. Dunne, Reed, and Wilbanks esult that school boads that ae elected in non-geneal election ae moe likely to popose school efeendum in a special election could aise simply as a esult of unobseved community pefeence ove the numbe of elections. Pequet, Coats, and Yen s esults only show that thee may be an advantage fo school boads to popose school efeendum in special
elections. They povide no evidence that school boads stategically do so. This pape fills this void in the liteatue by fomally modeling and testing the stategic timing of school efeendum elections. III. Theoetical Model: Let N be the finite set of an odd numbe of votes in a school distict. Assume that i N that pefeences fo the amount of public school expenditue R + fo the distict can be epesented by the following utility function : U =, i 1 i i whee is i's unique ideal expenditue on schooling. Let m N be the individual with the median ideal expenditue, and define m individual m s ideal expenditue. The level of is detemined though a one-shot efeendum pocess. A efeendum is appoved if it eceives at least as many yes votes and it eceives no votes. Let epesent the evesion level of expenditue if a efeendum is not poposed o a poposed efeendum does not pass. It is assumed that m >. A vote favos the efeendum if U U, and othewise opposes it. The entie electoate, howeve, does not necessaily tunout fo the election. When faced with a efeendum fo an expenditue of, a vote tuns out to vote iff: p B C 0 Rike and Odenshook, j j + j j j 1968, whee B j is equal to U U, p j is the exogenous pobability that j assigns to thei vote being pivotal, and C j is the disutility o cost that j incus fom
voting. A simplifying assumption is made that p and C ae constant acoss all i N, and that p > 0. It is assumed that a monopolist that would like to maximize the value of contols the agenda fo the efeendum. The agenda-sette has complete knowledge of all pefeences, as well as the costs of voting and the exogenous pobability that all potential votes assign to being pivotal. The budget maximizing agenda-sette has agenda powe not only ove amount of the efeendum, but also the timing of the efeendum. The efeendum can be bought up at the same time as egulaly scheduled elections fo political offices, o in a special election on only school expenditue. In egulaly scheduled elections it is assumed that C = 0. As a esult, the entie electoate will vote on the school efeendum. In contast, it is assumed that C < 0 in the special election. As a esult, full tunout will not always occu in a special election. Lemma 1: Suppose patial tunout occus in a special election. Thee will exist expenditue cutpoints A and B vote. i A B s.t. only those i N with A o i B Poofs of this lemma and the subsequent popositions ae pesented in the appendix. This lemma shows that in special elections membes of the electoate with exteme pefeences ae moe likely to tunout to vote. Define A as the lagest expenditue ideal point such that an individual tuns out to vote against a efeendum with value. Likewise, B as the smallest expenditue ideal point such that an individual
tuns out to vote fo a efeendum with value. We can then define N A as the numbe of i N s.t. i < A, and Y B as the numbe of i N s.t. i > B. Using this lemma, thee popositions ae deived. Poposition 1: The agenda-sette will popose a efeendum of value s m, max{ }, whee s is the lagest value s.t. s s Y B = N A. If s m, the agenda-sette will popose the efeendum in a special election, othewise the agenda-sette will popose the efeendum as pat of a egulaly scheduled election. Poposition : The pecent of the electoate that tunout to vote against efeendum is weakly inceasing in the amount of the efeendum. Poposition 3: The pecent of the electoate that tunout to vote fo a efeendum is weakly inceasing in the amount of the efeendum up to some amount. The pecent of the electoate that tunout to vote fo a efeendum is weakly deceasing in the amount of the efeendum fo all efeendum geate than.
IV. mpiical Pedictions Poposition 1 indicates that a budget-maximizing agenda sette will be moe likely to popose a efeendum as pat of a special election if thee ae moe membes of the electoate with pefeences fo extemely high expenditue than fo extemely low expenditue. Thus, we would like to identify chaacteistics of the electoate that would indicate the pesence of extemely high o extemely low pefeences. Paents of those childen who cuently attend public schools ae likely to have high expenditue pefeences. Convesely, paents of those childen who cuently attend pivate schools ae likely to have low expenditue pefeences. It is expected, theefoe, that holding all othe factos constant, a school boad in a distict with a high pecentage of votes with childen in public schools will be moe likely to call a special election. In contast, a school boad in a distict with a high pecentage of votes with childen in pivate schools would be expected to be less likely to call special election. Rubinfeld 1977 and Begstom, Rubinfeld, and Shapio 198 analysis of vote behavio in individual school efeenda empiically veify that paents of students who attend public and pivate school ae moe and less likely espectively to suppot a school efeendum. Additionally, Rubinfeld and Thomas 1980 find that individuals with childen both in public and pivate school wee moe likely to tunout in a special school election. ldely individuals ae anothe potential goup of votes that ae likely to have low expenditue pefeences. Hais, vans, and Schwab 001, Rome, Rosenthal, and Munley 199, and Stevens and Mason 1996 all show a negative elationship between the pecentage of eldely individuals in a school distict and the amount of spending
passed by efeendum. mpiical esults, howeve, have not always indicated that eldely individuals ae less likely to suppot school efeendum. Rubinfeld 1977 and Begstom, Rubinfeld, and Shapio 198 both find eldely individuals ae insignificantly moe likely to suppot a school efeendum. Tedin, Matland, Weihe 001 find that white individuals ove 50 wee significantly less likely to suppot a bond efeendum, but find no significant elationship between Afican-Ameican and Hispanic individuals ove 50 and suppot fo the efeendum. Still, it is expected a high pecentage of eldely individuals in the voting population would make the school boad less likely to call special election. Popositions and 3 ae moe staightfowad to test empiically. Using yes and no tunout as the dependent vaiables in egessions, it can be tested how the amount of the efeendum affects the pecent of the electoate that tuns out to vote yes and no. It is expected that the numbe of no votes will continuously gow as the size of the efeendum inceases, while the numbe of yes votes will begin deceasing at some level of expenditue. It can also be tested whethe the geneal assumption that amount of the efeendum affects tunout, and affects tunout moe in special elections than in egulaly scheduled elections, is empiically tue. Finally, it can be tested whethe disticts with a highe pecentage of paents with students enolled in public schools have highe tunout in favo of efeenda in special elections. Similaly, it can be tested whethe disticts with a highe pecentage of paents with childen in pivate schools and eldely individuals have highe tunout against efeenda in special elections.
V. Data The emainde of this pape this pape tests the empiical pedictions made in section IV. A dataset of school efeendum in the state of Wisconsin fom 1990 003 is constucted fo this pupose. The state of Wisconsin esticts the amount a school distict can expend on a pe pupil basis. A school distict, howeve, may exceed this evenue limit by passing a efeendum. The amount of the efeendum and the timing of when it is scheduled to vote ae detemined by the school boad. Refeenda ae classified as being fo one of thee diffeent types of expenditues: debt, eoccuing costs, o noneoccuing costs. Debt efeenda ae geneally fo lage poject, like building maintenance and constuction. Reoccuing cost efeenda ae often fo geneal opeating costs, while noneoccuing cost efeenda ae typically fo specific pojects like a new compute lab o ADA compliance. If a efeendum is fo eoccuing costs, it can eithe be fo a tempoay o pemanent incease in the evenue limit. Data on school efeenda wee downloaded fom the Wisconsin Depatment of Public Instuction. This data included infomation on the dates of election, the amount of the efeendum, votes in favo of the efeendum, votes against the efeendum, the type of efeendum, school yeas fo which the efeendum applies, and a bief vebal desciption of the specific pupose fo the efeendum. A total of 1778 sepaate efeenda occued ove this time peiod. Dates of pimay and geneal statewide elections wee obtained fom volumes of the Wisconsin Blue Book. An election was assumed to be a special election if it occued on a day in which a pimay o geneal statewide election
was not occuing. A beakdown of the numbe of special and egulaly scheduled school efeenda by yea is given in Table I in the appendix. Repoted efeendum amounts ae conveted to thei eal pesent value at the time of the election. A continuously compounded social discount ate of 5% is used to discount the amount of the efeendum between the election date and the time of expenditue. xpenditues on debt efeendum wee assumed to occu immediately. xpenditues on non-debt efeendum wee assumed to occu on Septembe 1 st of thei listed stating yea. xceptions to this ule wee efeenda that wee voted on afte Septembe 1 st of the listed stating yea, which wee assumed to stat on the election date. If no stat yea was povided, expenditues wee assumed to occu on the fist Septembe 1 st following the election. Pemanent inceases in the evenue limit wee piced as an infinite steam. 000 Census data by school distict wee obtained fom Wisconsin s Depatment of Administation. The Wisconsin Depatment of Administation compiled this data fom the National Cente fo ducation Statistics. This povided infomation on population by age goup, pecent of individuals age 5 and olde obtaining cetain levels of education, pecent of stuctues occupied by ownes, median household income, population by acial goup, and pecent of population living in a ual aea. In addition, the numbe of students enolled in both public and pivate schools in the school distict in 000 wee obtained fom Wisconsin s Depatment of Public Instuction. Measues of yes and no tunout ae constucted by dividing the numbe in votes suppoting and opposing the efeendum in each election by the population of individuals ove the age of 18 in the school distict in the 000 census. To ceate a measue of the numbe of paents with
kids enolled in the public and pivate schools, the espective distict wide enollment totals ae divided by the total population of the school distict of the school distict in the 000 census. Desciptive statistics fo all of the vaiables ae listed in Table II of the appendix. VI. mpiical Results The fist set of egessions test what factos ae coelated with whethe a efeendum is scheduled as a special election. The hypothesis is that disticts with a high pecentage of thei population enolled in the public and pivate schools should be moe and less likely espectively to schedule special elections. In addition, disticts in which the eldely make up a lage pecentage of the electoate should be less likely to schedule special elections. Since the dependent vaiable is binay, Pobit egessions using obust standad eos clusteed by school distict wee used to pefom the analysis. Thee sepaate egessions ae pesented. In all thee egessions the pecent of the population in public and pivate schools and the pecent of the electoate ove 65 ae included as explanatoy vaiables. In egession 1, the natual log of the eal amount of the efeendum pe vote, a dummy fo the type of the efeendum with the dummy fo an unknown type excluded, and a dummy indicating whethe the election took place in an odd yea ae also included as contol vaiables. The odd yea dummy is necessay since thee ae no fall statewide elections in odd yeas. In egessions and 3, a numbe of othe additional vaiables that ae often included in egessions to pedict the level of school
distict spending ae included as contol vaiables. In egession, the pecent of owne occupied popeties, the pecent of population in ual aeas, the pecent of population that in non-white, and the natual log of the median household income ae included in addition to the vaiables fom egession 1. Regession 3 contains all of the contol vaiables fom egession, plus the pecent of the population with high school and college degees and the log of the size of the electoate. Results fom all thee egessions ae listed in Table III of the appendix. The esults fom egessions 1,, and 3 povide some evidence to suppot the hypothesizes that disticts with moe childen attending public schools and fewe childen attending pivate schools ae moe likely to call a special election. The suppot, howeve, is not vey obust. Regession 1 indicates that the pecentage of the population enolled in public and pivate schools ae positively and negatively elated espectively to whethe a efeendum occus in a special election. In both cases this esult is significant at the 90% level. While the signs on the coefficients emain the same in egessions and 3, the esults ae no longe statistically significant. Since none of the additional contol vaiables ae statistically significant, it is unclea whethe this change in statistical significance is a esult of omitted vaiable bias in egession 1 o attenuation due to the inclusion of ielevant vaiables in egessions and 3. In none of the egessions is the pecent of the electoate eldely close to being statistically significant. Two othe inteesting esults ae found in the egessions 1,, and 3. In all thee egessions the eal amount of the efeendum pe adult is significantly positively elated to the pobability that the efeendum is bought up in a special election.
Convesely, in all thee egessions noneoccuing efeenda ae significantly less likely to be voted on in a special election than a debt o eoccuing efeendum. Both of these esults ae consistent with extensions of ideas developed in the theoetical model. In the theoetical model, a special election will only be called when it will poduce geate expenditue than desied by the median membe of the electoate. Suppose we assume that a disticts median vote ideal point is distibuted independently of the tails of the distibution. This would esult in the efeenda poposed in special elections to on aveage be moe expensive. In addition, suppose we modified the model to diffeentiate pefeences ove diffeent types of expenditue. Specifically, imagine that modeate votes ae moe likely to suppot tangible expenditues athe than blank check of equal amount fo opeating costs. As a esult, noneoccuing efeendums, which ae often fo puposes like building maintenance, ADA equiements, and technological impovements may be moe likely to get suppot fom modeate membes of the electoate than debt efeendum and eoccuing efeendum, which ae often fo less specific o tangible puposes. This would lead to noneoccuing efeenda being poposed moe often in egula elections than compaable debt and eoccuing efeendum. The second set of egessions test how tunout vaies with the amount and timing of the efeendum. This analysis is done using linea egessions with White s standad eos clusteed by school distict. Regessions 4, 5, and 6 use yes, no, and total tunout as dependent vaiables espectively, with dummy vaiables indicating the type of election Febuay Geneal, Apil Geneal, Septembe Pimay, Novembe Geneal, with special elections excluded, the pecent of the electoate ove 65, the pecent of the population attending public and pivate schools, and the natual log of the eal amount of
efeendum pe potential vote, the pecent of owne occupied popeties, the pecent of ual population, the pecent of non-white population, the natual log of the median household income, and the natual log of the size of the electoate included as explanatoy vaiables. In addition, the pecent of the electoate ove 65, the pecent of the population attending public and pivate schools, and the natual log of the eal amount of efeendum pe potential vote wee inteacted with the special election dummy vaiable. These inteaction tems test whethe these demogaphic goups do in fact impact tunout moe in special elections and whethe amount has a bigge influence on tunout in special elections. Regessions 7, 8, and 9 ae the same as 4, 5, and 6, except the log amount of efeendum pe vote is eplaced by the amount of the efeendum and the amount of the efeendum squaed. This is done to test the claims of popositions and 3 that no tunout should be inceasing with espect to the amount, while yes tunout should be initially inceasing, then deceasing with espect to the amount. The appendix contains esults fom egessions 4, 5, and 6 in Table IV and esults fom egessions 7, 8, and 9 in Table V. Results fom the second set of egessions indicate that the amount of the efeendum is positively coelated with tunout. In egessions 4, 5, and 6, the effect of the log amount of the efeendum pe vote on tunout is positive and significant. A one standad deviation incease in the log of the eal amount of spending pe vote is coelated with appoximately a 0.75% and 1.5% incease in yes and no tunout espectively. In addition, the inteaction tem between the amount of the efeendum and the special election is significantly positively elated to yes tunout in egessions. A one standad deviation incease in the log of the spending pe vote inceases yes tunout
0.75% moe in a special election than in a egula election. In contast, no tunout is not significantly moe affected by the amount of the efeendum in special elections. Regessions 7, 8, and 9 povide some evidence in suppot of popositions and 3. Regession 7 shows that the deivative of yes tunout with espect to amount initially inceases and then deceases in both egula and special election. It should be noted, howeve, that the coefficient on the amount squaed tem is essentially zeo in special elections. Regession 8 shows that the deivative of no tunout with espect to amount is stictly inceasing fo all amounts. Again, howeve, the squaed tem cannot be shown to be statistically significant diffeent fom zeo. It should be also be noted thee is nothing in poposition o 3 that suggests that the elationship between the amount of efeendum and tunout should be quadatic. A semi-paametic estimation stategy in which the effects of amount on tunout wee allowed to vay nonpaametically, may be a moe effective means of testing popositions and 3. Regessions 4 9 povide little suppot to the hypothesis that the pesence of cetain demogaphics should lead to highe tunout in special elections. In geneal the egessions do show the expected stong positive statistical elationship between yes tunout and the pecentage of the population in public school. The elationship between yes tunout and the inteaction tem between the pecentage of the population in public school and a special election, howeve, while positive, is not statistically significant. The esults ae less clea about the how the pecentage of the population in pivate school affects no tunout. Thee exist no significant elationship between both no tunout and the pecentage of the population attending pivate school and no tunout and the inteaction tem between the pecentage of the population in pivate school and a special
election. Finally, while the pecentage of the population ove 65 shows a positive statistical elationship with both yes and no tunout, thee exists no statistical elationship between eithe measue of tunout and the population ove 65 inteacted with the special election dummy. VII. Conclusions This pape has attempted to fomally model and empiically test the ability of budget maximizing agenda-settes to stategically schedule elections. The fomal model pedicts that the budget maximizing agenda-sette will be moe likely to schedule elections when those individuals with exteme expenditue pefeences ae moe like to favo high expenditue. The empiical evidence povides some suppot of this hypothesis, but is this suppot not paticulaly obust. The empiical testing elies on the assumption that a high pecentage of population attending public schools is a good indicato of high demandes, and that a high pecentage of students in pivate schools and eldely is a good indicato of low demandes. vidence fom subsequent egessions bings the validity of these assumptions into question. In paticula, thee is not stong evidence that tunout against efeenda is highly coelated with the pecentage of students attending pivate schools o the pecentage of eldely in the electoate. Thus, stonge empiical esults may esult fom identifying stonge maco indicatos of the pesence high and low demand individuals within a school distict. In the liteatue diect democacy is often justified nomatively on the gounds that it epesents the will of the median vote. This agument is not as convincing if
cetain individuals have the ability to pick amongst a numbe of median votes. Thus, iespective of the stength of the empiical esults, this pape identifies a seious concen that must be addessed in both futue eseach and public policy. In most eseach on diect democacy, the agenda is exogenously set though some black box. This pape demonstates the need fo subsequent eseach to explicitly model and account fo the agenda-setting pocess.
Appendix Poof of Lemma 1: Let be the set of all individuals that tunout to vote fo a efeendum of expenditue. Since ou agenda sette is a budget maximize, we only need to conside efeenda s.t. V N >. Suppose V N j i \,, and define. Let ], [ i j I = I ˆ, and suppose that an individual k with an ideal expenditue of Ê tuned out to vote. Case 1: Individual k votes fo the efeendum. Since k votes fo the efeendum, it must be that. Reaanging tems, this can be ewitten as. Since and / p C k k / p C k + j k > >, it is tue that + + k j / p C j j. This contadicts that individual j abstains fom voting. Case : Individual k votes against efeendum. Since k votes fo the efeendum, it must be that. / p C k k
Reaanging tems, this can be ewitten as. Since and / p C k k i > >, it is tue that k i / p C i i. This contadicts that individual i abstains fom voting. Poof of Poposition 1: As in Rome and Rosenthal 1978, the budget maximizing agenda-sette makes the median vote indiffeent between the efeendum and the evesion expenditue. In the egulaly scheduled the budget-maximizing agenda sette s maximization poblem can be witten as: s.t.. Since the constaint binds at the maximum, we know. Taking the squae oot of both sides, we know o. This implies that max m U U m m = m m = m m = = o. Since it is assumed that, is always pefeed by the agenda-sette. m m > m Now suppose that the agenda sette poposes a efeendum in a special election. The budget maximizing agenda-sette still wants to make the median vote indiffeent between the efeendum and the evesion expenditue. The identity of the median vote, howeve, depends on which membes of the electoate tunout. Fom lemma 1, we know that fo each efeendum, thee exist cutpoints and. We can epesent the budget-maximizing agenda-sette s poblem in the special election as: A B
max s.t. Y B N A. Since the constaint binds at the maximum, we know Y B = N A. s is defined as the lagest value of such that this equality holds. Knowing the values of the efeendum that could be passed in each type of election, the budget maximizing agenda-sette will schedule the efeendum fo the type of election in which the lage efeendum will pass. If s m a lage efeendum can be passed in the special election, and thus the agenda-sette will schedule the efeendum as pat of a special election. Convesely, if m > s, then the agenda-sette will bing the efeendum to a vote in a egulaly scheduled election. Poof of Poposition : Suppose i N votes against a efeendum, and let ˆ >. This implies that U i > U i ˆ i i, and hence that ˆ i i U U U U. Since i voted fo i i i i, it must be that U U C / p, which implies U U ˆ C / p. Poof of Poposition 3: Fom lemma 1, we know that fo all efeendum, thee exists a cutpoint B, whee only vote s with ideal points fo expenditue geate than B tunout to vote. Define = min B and let Ê be anothe efeendum. We must show that fo any
= αˆ + 1 α, α 0,1, that any votes that tunout to vote yes fo efeendum Ê also tunout to vote yes fo efeendum, and that any votes that tunout to vote yes fo efeendum also tunout to vote yes fo efeendum. By the definition of, the second half of the statement is tue. Theefoe we know i N who vote fo Ê that U i ˆ U i C / p and that i i U U C / p. Thus, we know fo some α 0,1 that i αu ˆ + 1 α U implies that U efeendum. i i U αˆ + 1 α i C / p. By the concavity of the utility function this U i C / p, and hence that all i vote fo
Table I Counts of lections By Yea Reg. lection Sp. lection Total 1990 4 1 5 1991 3 34 199 0 31 51 1993 17 34 51 1994 85 49 134 1995 51 91 14 1996 115 88 03 1997 73 14 197 1998 173 67 40 1999 69 91 160 000 14 49 191 001 9 73 165 00 91 13 104 003 65 36 101 Total 999 779 1,778
Table II Desciptive Statistics Vaiable Obs Mean Std. Dev. Min Max Special lection Dummy 1778 0.44 0.50 0 1 Yes Tunout 1717 16.44 8.18 1.7 6.05 No Tunout 1717 16.51 8.6 0.78 54.18 Total Tunout 1717 3.95 13.67 4.85 89.18 Log Real Refeendum Amount / Pop. 18+ 177 6.10 1.48 0.11 9.36 Pecent lectoate 65+ 1778 18.10 4.98 5.19 34.0 Pecent of Pop. Attending Public Schools 1778 16.84 4.83 5.10 91.0 Pecent of Pop. Attending Pivate Schools 1778 1.80 1.93 0 19.4 Debt Refeendum Dummy 1778 0.69 0.46 0 1 Nonoccuing Refeendum Dummy 1778 0.10 0.9 0 1 Reoccuing Refeendum Dummy 1778 0.18 0.38 0 1 Pemenent Refeendum Dummy 1778 0.08 0.8 0 1 Pecent of Popety Owne Occupied 1778 77.1 7.78 45.31 97.06 Pecent of Population Rual 1778 60.38 36.8 0 100 Pecent of Population Non-White 1778 4.51 5.8 0 87.84 Log Median Household Income 1778 10.73 0. 10.17 11.51 Pecent of Pop. 5+ w/ High School Diploma 1778 85.87 5.01 70.10 97.98 Pecent of Pop. 5+ w/ College Degee 1778 19.5 9.40 6.3 70.9 Log lectoate 1778 8.79 1.01 5.75 1.96 Novembe Statewide lection Dummy 1778 0.11 0.31 0 1 Septembe Statewide lection Dummy 1778 0.08 0.7 0 1 Febuay Statewide lection Dummy 1778 0.10 0.30 0 1 Apil Statewide lection Dummy 1778 0.7 0.45 0 1 Odd Yea lection Dummy 1778 0.48 0.50 0 1
Table III Pobit Regession on the ffects of the Scheduling of Special lections Robust os Clusteed By School Distict N = 177 Independent Vaiable 1 3 Constant -0.397.348 6.838 0.319 3.974 4.916 Log Real Refeendum Amount / Pop. 18+ 0.050 0.05 0.055 0.07 0.07 0.07 Pecent of lectoate 65+ 0.003-0.007-0.013 0.010 0.015 0.016 Pecent of Pop. Attending Public Schools 0.01 0.010 0.009 0.006 0.006 0.007 Pecent of Pop. Attending Pivate Schools -0.035-0.05-0.013 0.01 0.0 0.03 Debt Refeendum -0.560-0.569-0.554 0.156 0.156 0.155 Reoccuing Cost Refeendum -0.53-0.538-0.5 0.174 0.174 0.173 Noneoccuing Cost Refeendum -0.93-0.91-0.936 0.199 0.01 0.199 Odd Yea 0.651 0.65 0.651 0.080 0.080 0.080 Pecent of Popety Owne Occupied -0.009-0.003 0.009 0.009 Pecent of Population Rual 0.00 0.003 0.00 0.00 Pecent of Population Non-White 0.004 0.004 0.007 0.007 Log Median Household Income -0.188-0.815 0.360 0.460 Pecent of Pop. 5+ w/ High School Diploma 0.017 0.019 Pecent of Pop. 5+ w/ College Degee 0.010 0.009 Log lectoate 0.014 0.063
Table IV Linea Regession on the ffects of Refeendum Amount on Tunout Robust os Clusteed By School Distict N = 1716 7 8 9 Independent Vaiable Yes Tunout No Tunout Total Tunout Constant -5.88-18.587-44.469 0.66 4.856 37.853 Log Real Refeendum Amount / Pop. 18+ 0.575 0.914 1.489 0.153 0.194 0.58 Log Real Refeendum Amount / Pop. 18+ x 0.443-0.016 0.47 Special lection Dummy Vaiable 0.0 0.318 0.440 Novembe Geneal lection 18.371 10.517 8.888.919 3.468 5.09 Septembe Pimay lection 6.319 0.81 7.131.780 3.485 5.097 Apil Geneal lection 7.467 3.660 11.17.774 3.404 5.036 Febuay Pimay lection 4.548 1.063 5.611.795 3.600 5.35 Pecent of lectoate 65+ 0.375 0.310 0.685 0.089 0.08 0.139 Pecent of lectoate 65+ x 0.036-0.004 0.03 Special lection 0.083 0.095 0.138 Pecent of Pop. Attending Public Schools 0.77 0.106 0.384 0.088 0.084 0.138 Pecent of Pop. Attending Public Schools x 0.16 0.06 0.15 Special lection 0.118 0.17 0.195 Pecent of Pop. Attending Pivate Schools 0.63 0.048 0.311 0.18 0.173 0.9 Pecent of Pop. Attending Pivate Schools x -0.87 0.16-0.071 Special lection 0.31 0.68 0.369 Pecent of Popety Owne Occupied 0.011 0.087 0.099 0.044 0.050 0.079 Pecent of Population Rual -0.005 0.007 0.001 0.013 0.013 0.03 Pecent of Population Non-White 0.008-0.040-0.03 0.058 0.073 0.15 Log Median Household Income 3.5 1.58 4.806 1.861.7 3.438 Log lectoate -1.755-0.504 -.59 0.466 0.451 0.803
Table V Linea Regession on the ffects of Refeendum Amount on Tunout Robust os Clusteed By School Distict N = 1716 7 8 9 Independent Vaiable Yes Tunout No Tunout Total Tunout Constant -0.590-16.640-37.30 0.01 3.455 35.514 Real Refeendum Amount thousands / Pop 18+ 1.443 1.93.736 0.417 0.597 0.760 Real Refeendum Amount thousands / Pop 18+ x 0.305-0.136 0.169 Special lection Dummy Vaiable 0.710 0.775 1.163 Real Refeendum Amount thousands / Pop 18+^ -0.19 0.06-0.013 0.090 0.164 0.190 Real Refeendum Amount thousands / Pop 18+^ x 0.03 0.074 0.77 Special lection Dummy Vaiable 0.03 0.199 0.319 Novembe Geneal lection 15.965 10.569 6.534.605.679 4.4 Septembe Pimay lection 3.895 0.961 4.857.493.68 4.165 Apil Geneal lection 5.05 3.940 8.99.444.565 3.998 Febuay Pimay lection.137 1.037 3.174.460.766 4.41 Pecent of lectoate 65+ 0.376 0.308 0.685 0.088 0.079 0.135 Pecent of lectoate 65+ x 0.03 0.001 0.03 Special lection 0.084 0.091 0.136 Pecent of Pop. Attending Public Schools 0.78 0.078 0.356 0.086 0.079 0.133 Pecent of Pop. Attending Public Schools x 0.101 0.00 0.11 Special lection 0.116 0.13 0.188 Pecent of Pop. Attending Pivate Schools 0.61 0.070 0.331 0.180 0.168 0.85 Pecent of Pop. Attending Pivate Schools x -0.54 0.8-0.06 Special lection 0.8 0.56 0.351 Pecent of Popety Owne Occupied 0.010 0.096 0.106 0.043 0.047 0.074 Pecent of Population Rual -0.005 0.009 0.004 0.01 0.01 0.01 Pecent of Population Non-White 0.006-0.050-0.044 0.059 0.076 0.17 Log Median Household Income 3.188 1.365 4.55 1.804.1 3.43 Log lectoate -1.739-0.068-1.807 0.460 0.444 0.781
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