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Public Choice 76: 313-334, 1993. © 1993 Kluwer Academic Publishers. Printed in the Netherlands. Election closeness and voter turnout: Evidence from California ballot propositions* JOHN G. MATSUSAKA Department of Finance and Business Economics, School of Business Administration, University of Southern California, Los Angeles, CA 90089-1421 Accepted 3 July 1991 Abstract. This paper uses a new data set of 885 California ballot propositions from 1912 through 1990 to test the hypothesis that voter turnout increases as an election becomes closer. Various measures of voter participation are regressed on various measures of election closeness. The main finding is that there is not a systematic relation between closeness and turnout. Two conclusions are drawn: (1) voters are not sensitive to the probability their votes are decisive, and (2) other studies which found higher turnout for close elections probably detected an increased mobilization of party elites in tight races. 1. Introduction No fewer than 25 papers have been published which test if people are more like- ly to vote in close elections (for a list see Matsusaka and Palda, 1991). Most of them found a positive relation between turnout and closeness. However, the number of studies which failed to find a consistent relation is large enough to be troubling. Recent work has suggested that many of the studies used mis- specified models (Foster, 1984), used variables which by construction are biased in favor of finding a closeness-turnout relation (Cox, 1988), or suffered from aggregation bias (Matsusaka and Palda, 1991). The existence of a closeness-turnout relation is important to instrumental theories of voting, theories based on the idea that people vote in order to affect the election outcome. The rational voter theory as developed by Downs (1957) and Riker and Ordeshook (1968) posits that a person's expected benefit from voting is increasing in the probability his vote is decisive, that is, the probability it forces or breaks a tie. A person is more likely to vote, then, in an election where the candidates are running dead even than in an election with an over- * I received helpful comments from Filip Palda, Ian Parry, Jeffrey Smith, members of the Eco- nomics Summer Workshop at The University of Chicago, and an anonymous referee. I am grateful to the Bradley Foundation and Olin Foundation (through grants to the Center for the Study of the Economy and the State) and The University of Chicago for financial support.314 whelming favorite. The prediction that a person is more likely to vote in close elections (other things equal) has many names, in this paper the Downsian Closeness Hypothesis (DCH).l The DCH is counterintuitive because the probability of casting a decisive vote in most elections of interest is essentially zero. However close these races become they are never tight enough that one vote matters. The probability that a single vote will decide a presidential election may differ from year to year, but it is hard to believe voters can perceive or are sensitive to such infinitesimal- ly small changes. In view of the frequent findings of a closeness-turnout rela- tion, Cox and Munger (1989) proposed an alternative explanation: elites are more likely to motivate citizens to vote in close elections. Glazer and Grofman (forthcoming, 1992) offered another way out by demonstrating that causality may run from turnout to closeness. This paper provides new evidence on the relation between closeness and turn- out, giving special attention to the DCH, and suggests a way to interpret the vast, sometimes contradictory, literature. The seminal empirical paper in this literature was by Barzel and Silberberg (1973). They looked for a closeness ef- fect by regressing the turnout percentage in a state on the closeness of the gubernatorial election in the state. Their basic methodology has been widely imitated and embellished. The heart of this paper is a set of regressions in the Barzel-Silberberg tradi- tion which differ in some important and instructive ways from previous research. The data are an extensive set of 885 California ballot propositions. A ballot proposition (or measure) is a proposed law or constitutional amend- ment which takes effect if a majority of the voters approve it. To the best of my knowledge, the only other closeness tests which use ballot propositions are Filer and Kenny (1980) and Hansen, Palfrey, and Rosenthal (1987). According to the DCH, what is important for an individual is the probability his vote affects his final payoff. A vote in an election to pick a representative bears a tenuous relation to final political outcomes. Elected officials require cooperation to pass laws; they do not simply implement their announced plat- forms once elected. To pass the federal budget requires the support of half of the 435 members of the House of Representatives, half of the 100 members of the Senate, and the signature of the president. The link between a citizen's vote for congressman, senator, or president, and the actual government policies is weak, even if the voter is decisive. The connection between a person's vote and political outcomes is clear for ballot propositions: if a proposition passes it becomes law. The probability an individual's vote matters to his welfare is conceptually much easier to calculate, both for the researcher and the citizen. If a closeness effect exists, it is more likely to be evident in proposition elections than representative elections. The data are also well-suited to control for voting costs. On average, 77.5315 percent of Californians who went to the polls from 1912 to 1990 voted on a given measure. What happened is that many people filled out the ballot sec- tions concerning the presidential, gubernatorial, and senatorial races, and a select set of propositions and left the rest blank. Once in the voting booth, the marginal cost of voting is zero: idiosyncratic time and travel costs involved in deciding whether or not to go to the polls are sunk once a person has a ballot in hand. Within-ballot abstention ("drop-off") should occur only when the perceived benefit is zero. If the probability of casting a decisive vote is an im- portant component of the benefit, it should be very evident once voting costs are controlled; ballot drop-off should be low for close propositions


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