Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal "rational choice" models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from state-level forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.

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Economics is not only a social science, it is a genuine science. Like the physical sciences, economics uses a methodology that produces refutable implications and tests these implications using solid statistical techniques. In particular, economics stresses three factors that distinguish it from other social sciences. Economists use the construct of rational individuals who engage in maximizing behavior. Economic models adhere strictly to the importance of equilibrium as part of any theory. Finally, a focus on efficiency leads economists to ask questions that other social sciences ignore. These ingredients have allowed economics to invade intellectual territory that was previously deemed to be outside the discipline’s realm. By almost any market test, economics is the premier social science. The �eld attracts the most students, enjoys the attention of policy-makers and journalists, and gains notice, both positive and negative, from other scientists. In large part, the success of economics derives from its rigor and relevance as well as from its

This paper offers a model of three-party elections which allows voters to combine retrospective economic evaluations with considerations of the positions of the parties in the issue-space as well as the issue-preferences of the voters. We describe a model of British elections which allows voters to consider simultaneously all three parties, rather than limiting voters to choices among pairs of parties as is usually done. Using this model we show that both policy issues and the state of the national economy matter in British elections. We also show how voters framed their decisions. Voters first made a retrospective evaluation of the Conservative party based on economic performance; and those voters that rejected the Conservative party chose between Labour and Alliance based on issue positions. Through simulations of the effects of issues -- we move the parties in the issue space and re-estimate vote-shares -- and the economy -- we hypothesize an alternative distribution of views of the...

In an election, voting power---the probability that a single vote is decisive--- is affected by the rule for aggregating votes into a single outcome. Voting power is important for studying political representation, fairness, and strategy, and has been much discussed in political science. Although power indexes are often considered as mathematical definitions, they ultimately depend on statistical models of voting. Mathematical calculations of voting power have usually been performed under the model that votes are decided by coin flips. This simple

This paper investigates between-voter interactions in a social network model of turnout. It shows that if 1) there is a small probability that voters imitate the behavior of one of their acquaintances, and 2) individuals are closely connected to others in a population (the “smallworld” effect), then a single voting decision may affect dozens of other voters in a “turnout cascade. ” If people tend to be ideologically similar to other people they are connected to, then these turnout cascades will produce net favorable results for their favorite candidate. By changing more than one vote with one’s own turnout decision, the turnout incentive is thus substantially larger than previously thought. We analyze conditions that are favorable to turnout cascades and show that the effect is consistent with real social network data from Huckfeldt and Sprague’s South Bend and Indianapolis-St. Louis election surveys. We also suggest that turnout cascades may help explain over-reporting of turnout and the ubiquitous belief in a duty to vote. I thank Robert Bates, Lars-Erik Cederman, Eric Dickson, Paul E. Johnson, Orit Kedar, Gary King, Ferran Martinez I Coma, and Ken Shepsle for valuable feedback on earlier drafts. How does the turnout decision of a single person affect an election? Decision-theoretic models of voting show that the probability of one vote being “pivotal ” in a large electorate is extremely small (Tullock

The 2000 U.S. presidential election has once again rekindled interest in possible electoral reform including the possible elimination of the Electoral College. Most arguments against

This paper is forthcoming in Public Choice, 1996, in slightly abbreviated form. Of those eligible, about 40 % do not vote in presidential elections. When asked, about a quarter of those nonvoters will lie to the survey takers and claim that they did. Increases in education are associated with higher voting rates and lower rates of lying overall, but with increased rates of lying conditional on not voting. This paper proposes a model of voter turnout in which people who claim to vote get praise from other citizens. Those who lie must bear a cost of lying. The model has a stable equilibrium with positive rates of voting, honest non-voting, and lying. Reasonable parameter changes produce changes in these proportions in the same direction as the changes actually observed across education levels. Acknowledgments:

In an election the probability that a single voter is decisive is affected by the electoral system---that is, the rule for aggregating votes into a single outcome. Under the assumption that all votes are equally likely (i.e., random voting), we prove that the average probability of a vote being decisive is maximized under a popular-vote (or simple majority) rule and is lower under any coalition system, such as the U.S. Electoral College system, no matter how complicated. Forming a coalition increases the decisive vote probability for the voters within a coalition, but the aggregate effect of coalitions is to decrease the average decisiveness of the population of voters. We then review results on voting power in an electoral college system. Under the random voting assumption, it is well known that the voters with the highest probability of decisiveness are those in large states. However, we show using empirical estimates of the closeness of historical U.S. Presidential elections that voters in small states have been advantaged because the random voting model overestimates the frequencies of close elections in the larger states. Finally, we estimate the average probability of decisiveness for all U.S. Presidential elections from 1960 to 2000 under three possible electoral systems: popular vote, electoral vote, and winner-take-all within Congressional districts. We find that the average probability of decisiveness is about the same under all three systems.

Recent literature in voting theory has developed the idea that individual voting preferences are probabilistic rather than strictly deterministic. This work builds upon spatial voting models (Enelow and Hinich 1981, Ferejohn and Fiorina 1974, Davis, DeGroot and Hinich 1972, Farquharson 1969) by introducing probabilistic uncertainty into the calculus of voting decision on an individual level. Some suggest that the voting decision can be modeled with traditional probabilistic tools of uncertainty (Coughlin 1990, Coughlin and Nitzen 1981). Entropy is a measure of uncertainty that originated in statistical thermodynamics. Essentially, entropy indicates the amount of uncertainty in probability distributions (Soofi 1992), or it can be thought of as signifying a lack of human knowledge about some random event (Denbigh and Denbigh, 1985). Entropy in statistics developed with Kolmogorov (1959), Kinchin (1957), and Shannon (1948), but has rarely been applied to social science problems. Exception...