¹ William Riker and Peter Ordeshook have estimated the probability of an individual voter being decisive to the outcome of a U.S. presidential election as p = 10^–8–that is, a 1 in 100,000,000 chance. See Riker, and Ordeshook, , “A Theory of the Calculus of Voting,” American Political Science Review 62 (03 1968): 25CrossRefGoogle Scholar. Perhaps the earliest formulation of the economic approach is due to Downs, Anthony, An Economic Theory of Democracy (New York: Harper and Brothers, 1957), ch. 14Google Scholar. Downs formulates matters in terms of the “party differential” rather than the differential between the two individual candidates, but this difference is incidental.

² Parfit, Derek, Reasons and Persons (Oxford: Clarendon Press, 1984), 73–75.Google Scholar

³ Kant, Immanuel, Foundations of the Metaphysics of Morals, trans. Beck, L. W. (Indianapolis: Bobbs-Merrill, 1959), 39.Google Scholar

⁴ Meehl, Paul, “The Selfish Voter Paradox and the Thrown-Away Vote Argument,” American Political Science Review 71 (03 1977): 11–30.CrossRefGoogle Scholar

⁵ Ibid., 13. Later, Meehl sketches his favored rationale as follows: “I would say that some sort of prima facie obligation or obligation vector exists for me as a voter to participate in the electoral process, relying on the general principle that unless people do, the system won't work…” (ibid., 21).

⁶ Brennan, Geoffrey and Lomasky, Loren, “Large Numbers, Small Costs: The Uneasy Foun dation of Democratic Rule,” in Politics and Process: New Essays in Democratic Thought, ed. Brennan, Geoffrey and Lomasky, Loren (Cambridge: Cambridge University Press, 1989), 49–50.CrossRefGoogle Scholar

⁷ Benn, Stanley, “The Problematic Rationality of Political Participation’ in Philosophy, Politics, and Society, Fifth Series, ed. Laslett, Peter and Fishkin, James (New Haven: Yale University Press, 1979), 310.Google Scholar

⁸ Lewis, David, “Causation,”Google Scholar in Lewis, , Philosophical Papers, vol. 2 (New York: Oxford University Press, 1986).Google Scholar

⁹ The term “swing vote” perhaps suggests a vote that tilts the outcome either toward one candidate or toward the other; it does not suggest a tie as a possible outcome. In the present context, however, we want to consider possible abstentions as well as votes for different candidates. And a decision to abstain rather than vote could change the outcome from a victory for one candidate to a tie—perhaps requiring a run-off election. (For that matter, even switching a vote from one candidate to another can result in a tie, when the number of votes is even.) The counterfactual analysis also invites consideration of abstentions. If a citizen votes for candidate X and we ask, “What would have happened if the citizen had not cast this vote?,” one possible scenario is that the citizen abstains rather than votes for an opposing candidate.

¹⁰ In other cases, of course, credit or thanks might be given for mere effort, even if it makes no causal contribution. In this case, however, the effort plays a causal role; it is not merely fruitless effort.

¹¹ I draw the examples that follow from Moore, Michael S., “Causation and Responsibility,” elsewhere in this volume. Moore, in turn, cites Richard Wright, “Causation in Tort Law,” California Law Review 73 (1985): 1775–98, as an excellent discussion of such cases.Google Scholar

¹² See Lewis, David, “Postscripts to ‘Causation’,”Google Scholar in Lewis, , Philosophical Papers, 2:193–212.Google Scholar

¹³ Ibid., 194, 212.

¹⁴ In a similar spirit, Louis Loeb offers an account of causation that includes overdeter- mining causes. See his “Causal Theories and Causal Overdetermination,” Journal of Philosophy 71, no. 15 (1974): 525–44.Google Scholar

¹⁵ Lewis, , “Postscripts,” 212.Google Scholar

¹⁶ I say it “may” be right because it is not entirely clear. If the ten pushings had not occurred, would no pushings have occurred? Not obviously. Perhaps five pushings would still have occurred, which would have been sufficient to free the car.

¹⁷ Mackie, J. L., “Causes and Conditions,” American Philosophical Quarterly 2, no. 4 (10 1965): 245–64.Google Scholar

¹⁸ Ibid., 245.

¹⁹ Ibid.

²⁰ There are a number of objections to Mackie's INUS account. One of them is that it requires causation to feature sufficient conditions, and this ostensibly implies that there is no causation without determinism. This is too restrictive, as many writers point out. Causation can take place even in chancy situations, where merely probabilistic laws hold sway. See Suppes, Patrick, A Probabilistic Theory of Causality (Amsterdam: North-Holland, 1970)Google Scholar; Cartwright, Nancy, “Causal Laws and Effective Strategies,” Noûs 13 (1979): 419–37CrossRefGoogle Scholar; Salmon, Wesley, Scientific Explanation and the Causal Structure of the World (Princeton, NJ: Princeton University Press, 1984)Google Scholar; and Lewis, , “Postscripts,” 175–84Google Scholar. I concede this point, and therefore grant that the INUS account is not fully comprehensive. In the context of voting, however, we do not need to worry about probabilistic causation. Wherever an electoral outcome occurs, some set of votes is sufficient for the outcome. So the analysis sketched above is adequate for present purposes.

²¹ For simplicity, I assume an election with a single race.

²² Goldman, Alvin I., Knowledge in a Social World (Oxford: Oxford University Press, 1999), ch. 10.CrossRefGoogle Scholar

²³ The types of relevant information to gather would not be exhausted, of course, by campaign promises and accusations against one's opponent. Other relevant types of information would include each candidate's past experience and track record, her party affiliation and supporters, and so forth.

²⁴ The critical role of political information in producing good outcomes is elaborated in my Knowledge in a Social World, ch. 10.

²⁵ John Staddon points out that these forces can be treated as scalars rather than vectors, because there is just one dimension of movement, and forces can be treated as either positive or negative along this dimension. In election cases, however, at least in races where there are more than two candidates, the scalar approach will not work. In any case, the term “vector” is here used loosely to depict an interplay of conflicting forces.

²⁶ There may be ways to influence the outcome above and beyond one's personal vote, for example, by persuading other voters. But this goes beyond the present subject.

²⁷ Thanks to Tom Christiano for calling my attention to this problem and for highlighting its importance.

²⁸ Lewis, , “Postscripts,” 199.Google Scholar

²⁹ There are, to be sure, all sorts of deals made by members of Congress that depend upon voting order. This is not the occasion to enter into a close analysis of what such deals imply or presuppose.

³⁰ It might be objected that not all votes do have equal weights under all systems. For example, under the American system of electing presidents, the electoral college, not all citizens' votes count equally. However, this is not a clear instance of unequal weights. The electoral college involves a two-step system, in which citizens first choose electors who then choose a president. In the race for any given elector, all votes count equally; and in the race for president, all electors' ballots count equally.

³¹ Thanks to Ellen Frankel Paul for highlighting this issue.

³² In principle, of course, someone who votes for Brown might incur the wrath of those who oppose Brown's election. But a voter for Brown will probably have fewer associations with people who oppose Brown's election, and is less likely to inform them of his vote.

³³ Feeling as if one is part of a team that is working toward victory is undoubtedly a major factor in the psychology of political participation. But the integrity of team spirit derives from the fact that team members can all make causal contributions toward mutually sought outcomes.

³⁴ This question was properly urged on me by David Sobel.

³⁵ This consideration was suggested by Roderick Long and Susan Sauvé Meyer.

³⁶ David Schmidtz suggested this consideration.

³⁷ Thanks to Tom Christiano for pressing this problem on me.

³⁸ Similarly, many commentators on the Holocaust morally censure people—especially people in official capacities—who failed to speak out against it at the time, even if such speech would not have single-handedly changed the outcome.

³⁹ Strictly, the causal responsibility approach I propose could be subsumed under the expected-consequences, or rational-choice, perspective. Suppose we view the state of being a partial cause of a good electoral result, or the state of deserving moral credit (or discredit), as themselves possible outcomes or consequences of voting or not voting. Then the approach I favor may just be a special case of the rational-choice framework. The choice matrix now confronting the voter will differ from the matrix that would exist under the standard analysis. In addition to the outcomes being different, the probability of getting a more preferred outcome from voting than from abstaining is no longer linked to the probability of being a swing voter. Even if one is not a swing voter, one's act of voting can raise the probability of one's earning more causal credit for a superior candidate's victory and of avoiding causal discredit for such a candidate's loss. If citizens value some of these kinds of outcomes over others to a sufficient degree, the new choice matrix might make it “rational” for them to vote on numerous occasions. Since the outcomes have a moral nature, however, it may be controversial whether the choices should be considered a matter of “prudence” or “self-interest.” I do not try to address this issue here.