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The Paradox of Not Voting: A Decision Theoretic Analysis*

Published online by Cambridge University Press:  01 August 2014

John A. Ferejohn  and
Morris P. Fiorina
John A. Ferejohn
Affiliation:
California Institute of Technology
Morris P. Fiorina
Affiliation:
California Institute of Technology
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Abstract

Various analysts have noted that the decision to vote in mass elections is difficult to justify from the standpoint of an expected utility maximization model. Put simply, the probability that a citizen's vote will affect the outcome is so small that the expected gains from voting are outweighed by the costs in time and effort. Such analyses treat rational behavior as synonymous with expected utility maximization. In this paper we show that an alternative criterion for decision making under uncertainty, minimax regret, specifies voting under quite general conditions. Both two and three candidate plurality elections are considered. Interestingly, a minimax regret decision maker never votes for his second choice in a three candidate election, whereas expected utility maximizers clearly may. Thus, the model proposed has implications for candidate choice as well as turnout.

Type
Articles
Information
American Political Science Review , Volume 68 , Issue 2 , June 1974 , pp. 525 - 536
Copyright
Copyright © American Political Science Association 1974

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Footnotes

*

We should like to acknowledge the encouragement of Charles Plott, the critical acumen of John Benton, James Quirk, Kenneth Shepsle, Peter Aranson, Peter Ordeshook, and Duff Spafford, and, finally, the prescience of David Seidman.

References

1 For a summary of theoretical work in this area see Davis, Otto, Hinich, Melvin, and Ordeshook, Peter, “An Expository Development of a Mathematical Model of the Electoral Process,” American Political Science Review, 64 (06 1970), 426–448 CrossRefGoogle Scholar. For attempts to interpret data within the framework of rational choice models, see two papers presented at the 1972 Public Choice Convention: John Jackson, “The Importance of Issues and Issue Importance in Presidential Elections: A Test of a ‘Rational’ Model”; George Rabinowitz, “A Spatial Look at U. S. Politics.” We should remark that throughout this paper we use the expression “rational behavior” in a nontechnical sense denoting purposeful behavior.

2 Downs, Anthony, An Economic Theory of Democracy (New York: Harper & Row, 1957), pp. 260–276 Google Scholar.

3 Ibid., chapter 14.

4 Tullock, , Toward a Mathematics of Politics (Ann Arbor, Michigan: University of Michigan Press, 1967), chapter 7Google Scholar.

5 Riker, William and Ordeshook, Peter, “A Theory of the Calculus of Voting,” American Political Science Review, 62 (03 1968), 25 CrossRefGoogle Scholar.

6 Brian Barry draws this table from Riker's and Ordeshook's Table 3. See Barry, , Sociologists, Economists and Democracy (London: Collier-Macmillan Ltd., 1970), p. 17. Riker and Ordeshook, Table 3, p. 38.Google Scholar

7 Barry, p. 16.

8 A strategy i dominates a strategy j if i's consequences are at least as good as j's consequences (and at least one is better), for every conceivable state of nature.

9 Some scholars would deny the usefulness of this distinction. In particular, if one holds a subjectivist view of probability, no state probability necessarily is unknown or unknowable. But we still believe the distinction makes some intuitive sense. For an excellent discussion of the issues surrounding the risk-uncertainty distinction see Shepsle, Kenneth, “Essays on Risky Choice in Electoral Competition” (Ph.D. dissertation, University of Rochester, 1970), chapter 1Google Scholar.

10 There are several major classical decision rules. These are surveyed on an elementary level in Luce, R. Duncan and Raiffa, Howard, Games and Decisions: Introduction & Critical Survey (New York: Wiley, 1957)Google Scholar, chapter 13, and on a more advanced level in White, D. J., Decision Theory (Chicago: Aldine, 1969), chapter 2Google Scholar.

11 See the description of this criterion in Luce and Raiffa, pp. 280–282; White, pp. 28–29.

12 In computing regrets we assume c < ½, i.e., the utility cost of voting is less than ½ the utility difference between having one's preferred candidate in office rather than his opponent. The assumption is not very restrictive in our view. Essentially we are analyzing average voters, those who have a preference for C 1 or C 2, and for whom the costs of voting are the typical costs in time and effort. Clearly our assumption may be violated for blind arthritics or those totally indifferent between the candidates. Such groups, however, normally will not constitute a very significant proportion of the electorate. The assumption does not let us get away with anything, because all conditions we derive for voting are even stronger. The assumption is necessary, of course, because from Table 2 one sees that unless it is satisfied one never votes: A would dominate V 1 as well as V 2. Analogous considerations lead us to make the same assumption in the three-candidate case. If it did not hold, A would dominate V 1 for all states except S 16 and would not fail to dominate then if k were large.

13 For a more extensive analysis of the voting behavior of expected utility maximizers in multicandidate contests see McKelvey, Richard and Ordeshook, Peter, “A General Theory of the Calculus of Voting,” in Mathematical Applications in Political Science, VI, ed. Herndon, James and Bernd, Joseph (Charlottesville, Va.: The University of Virginia, 1972)Google Scholar. Our conclusions from this brief analysis seem consonant with theirs, although we pay more attention to the possibility of voting for one's second choice.

14 Casstevens, Thomas, “A Theorem about Voting,” American Political Science Review, 62 (03 1968), 205–207 CrossRefGoogle Scholar. Kramer, Gerald, Comment, APSR, 62 (09 1968), 955–956 CrossRefGoogle Scholar. Casstevens, Reply; Kramer, Rebuttal, APSR, 65 (03 1971), 187–189 CrossRefGoogle Scholar. Mayer, Lawrence, Comment, APSR, 65 (09 1971), 779 CrossRefGoogle Scholar. Kramer, Rebuttal, APSR, 66 (03 1972), 183 CrossRefGoogle Scholar.

15 Downs, pp. 146–150.

16 Casstevens, footnote 14.

17 Kramer, footnote 14.

18 Actually, we describe here subjective expected utility maximizers. One can also axiomatize utility maximizing with given objective probabilities.

19 In Table 2, the worst outcomes for V 1, V 2, and A are —c, —c, and 0, respectively. The worst outcome for A—0—is the best of the worst. Similarly, in Table 4 the worst outcomes for V 1, V 2, V 3 and A are —c, —c, —c, and 0, respectively. Again, the worst outcome of A—0—is the best of the worst.

20 Milbrath, Lester, Political Participation (Chicago: Rand McNally, 1965)Google Scholar.

21 Strictly speaking we say only that an individual behaves as if he were using a particular rationality criterion.

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