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A strategic calculus of voting

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  • Thomas Palfrey
  • Howard Rosenthal

Abstract

There are several major insights which this game theoretic analysis has produced. First, we have shown that equilibria exist with substantial turnout even when both the majority is much larger than the minority and the costs of voting are exceptionally high. For example, in large electorates using the status quo rule, we show mixed-pure equilibria with turnout roughly equal to twice the size of the minority when the cost is nearly equal to 37% (e −1 × 100) of the reward (B). Second, with large electorates the many equilibria appear to reduce to just two types, the type just mentioned and a type with almost no turnout. Third, we have shown that turnout may rise as the costs of voting rise. This results when all members of a team “adjust” their turnout probabilities so that the probability of being pivotal increases to match the increased cost of voting. We have also shown that turnout is nearly invariant with costs in large electorates where turnout probabilities approach one or zero. Fourth, the actual split of the vote is likely to be a biased measure of the actual distribution of preferences in the electorate. Because majorities have greater incentives to free-ride, they will turn out less heavily than minorities. Elections can be relatively close, even when one alternative is supported by a substantial majority of the electorate. The probability that the majority will win does not seem to be closely related to the size of the electorate or its size relative to the minority. However, turnout is quite strongly correlated with the relative sizes of the minority and the majority. Copyright Martinus Nijhoff Publishers 1983

Suggested Citation

  • Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
  • Handle: RePEc:kap:pubcho:v:41:y:1983:i:1:p:7-53
    DOI: 10.1007/BF00124048
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    References listed on IDEAS

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    1. Meehl, Paul E., 1977. "The Selfish Voter Paradox and the Thrown-Away Vote Argument," American Political Science Review, Cambridge University Press, vol. 71(1), pages 11-30, March.
    2. Rosenthal, Howard & Sen, Subrata, 1973. "Electoral Participation in the French Fifth Republic," American Political Science Review, Cambridge University Press, vol. 67(1), pages 29-54, March.
    3. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    4. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
    5. Ferejohn, John A. & Fiorina, Morris P., 1974. "The Paradox of Not Voting: A Decision Theoretic Analysis," American Political Science Review, Cambridge University Press, vol. 68(2), pages 525-536, June.
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