¹ Henry Brady and Stephen Ansolabehere, ‘The Nature of Utility Functions in Mass Publics’, American Political Science Review, 83 (1989), 143–63; Benjamin Radcliff, ‘The Structure of Voter Preferences’, Journal of Politics, 55 (1993), 714–19.

² The only states that provide for recall elections to take this form are California, Colorado and Michigan. All other states with the recall allow the recalled official to run as a candidate in the election for a replacement. Davis challenged the provision that prohibited him from running in the replacement election, but the California Supreme Court rejected his complaint.

³ Robin Farquharson, Theory of Voting (New Haven, Conn.: Yale University Press, 1969).

⁴ Maurice Duverger, Political Parties: Their Organization and Activity in the Modern State, 2nd revised English edn (London: Methuen, 1964).

⁵ Bruce Cain, ‘Strategic Voting in Britain’, American Journal of Political Science, 22 (1978), 639–55.

⁶ Adopting Myerson’s formulation, which models variation in turnout as a Poisson distribution, Feddersen calculates that if candidate A is expected to receive 49.9 per cent of the votes and candidate B 50.1 per cent, in an electorate of 5 million voters the probability of casting a pivotal vote is 8.1 × 10⁻⁹. If we assume instead that the election is a veritable landslide, and A has an expected percentage of 0.495 and B’s expected share is 0.505, the probability of casting a pivotal vote falls to 2.7 × 10⁻¹⁷⁸. By way of comparison, estimates of the total number of particles in the universe range from around 10⁷² to 10⁸⁷. See Roger Myerson, ‘Large Poisson Games’, Journal of Economic Theory, 94 (2000), 7–45; and Timothy Feddersen, ‘Rational Choice Theory and the Paradox of Not Voting’, Journal of Economic Perspectives, 18 (2004), 99–112.

⁷ William Riker and Peter Ordeshook, ‘A Theory of the Calculus of Voting’, American Political Science Review, 62 (1968), 25–42.

⁸ John Ferejohn and Morris Fiorina, ‘Closeness Counts Only in Horseshoes and Dancing’, American Political Science Review, 69 (1975), 920–5.

⁹ R. Michael Alvarez and Jonathan Nagler, ‘A New Approach for Modelling Strategic Voting in Multiparty Elections’, British Journal of Political Science, 30 (2000), 57–75.

¹⁰ See, inter alia, Paul Abramson, John Aldrich, Phil Paolino and David Rohde, ‘Sophisticated Voting in the 1988 Presidential Primaries’, American Political Science Review, 86 (1992), 55–69; Peter Ordeshook and Langche Zeng, ‘Rational Voters and Strategic Voting: Evidence from the 1968, 1980 and 1992 Elections’, Journal of Theoretical Politics, 9 (1997), 167–87; Sungdai Cho and Jae-Woo Hong, ‘Does Incumbency Matter? Strategic Voting Among Third Party Supporters in US Presidential Elections (1992 and 1996)’ (paper delivered at the Annual Meeting of the Midwestern Political Science Association, Chicago, 2000); Barry Burden, ‘Minor Parties in the 2000 Presidential Election’, in Herbert Weisberg and Clyde Wilcox, eds, Models of Voting in Presidential Elections (Stanford: Stanford University Press, 2003), pp. 206–27.

¹¹ Thomas Palfrey, ‘A Mathematical Proof of Duverger’s Law’, in Peter Ordeshook, ed., Models of Strategic Choice in Politics (Ann Arbor: University of Michigan Press, 1989), pp. 69–91.

¹² Brady and Ansolabehere, ‘The Nature of Utility Functions in Mass Publics’.

¹³ Radcliff, ‘The Structure of Voter Preferences’.

¹⁴ Herbert Weisberg and Arthur Miller, ‘Evaluation of the Feeling Thermometer: A Report to the National Election Study Board Based on Data from the 1979 Pilot Study’ (unpublished, University of Michigan, 1980).

¹⁵ This anomaly may occur because respondents mistakenly flip the poles of the thermometer scale, assigning low scores to candidates they like and high scores to those they dislike. See Larry Bartels, Presidential Primaries and the Dynamics of Public Choice (Princeton, N.J.: Princeton University Press, 1988).

¹⁶ Ordeshook and Zeng, ‘Rational Voters and Strategic Voting’; Cho and Hong, ‘Does Incumbency Matter?’

¹⁷ Brent Dennis, ‘A Survey of Preference Elicitation’ (unpublished, Computer Science Department, North Carolina State University, 2003).

¹⁸ Duncan Luce and Howard Raiffa, Games and Decisions (New York: John Wiley, 1957).

¹⁹ Brady and Ansolabehere, ‘The Nature of Utility Functions in Mass Publics’.

²⁰ Radcliff, ‘The Structure of Voter Preferences’.

²¹ Cain, ‘Strategic Voting in Britain’; Mitchell Sanders, ‘Information, Registration, Indifference, and Turnout’ (paper delivered at the Annual Meeting of the American Political Science Association, San Francisco, 1996).

²² About one in five respondents reported that they had already voted, either by casting an absentee ballot or by going to an ‘early voting’ polling site. Their reported choices are combined with those who indicated that they would vote on election day.

²³ Richard Niemi, ‘Majority Decision Making with Partial Unidimensionality’, American Political Science Review, 63 (1969), 488–97.

²⁴ Richard Niemi and John Wright, ‘Voting Cycles and the Structure of Individual Preferences’, Social Choice and Welfare, 4 (1987), 173–83, at p. 176.

²⁵ Palfrey, ‘A Mathematical Proof of Duverger’s Law’.

²⁶ Simon Jackman, ‘Post-Election Survey’ (unpublished, Stanford University, 2000).

²⁷ Two previous studies of the 2003 California recall have reported evidence of tactical voting. Both, however, are secondary analyses of data derived from commercial polls which included neither the pairwise comparison questions nor the questions concerning minor candidates that were posed to respondents in our survey. These and other data limitations precluded assessment of the competing hypotheses concerning voter preferences and tactical voting that this study is designed to undertake. See Daron Shaw, Mark McKenzie and Jeffrey Underwood, ‘Strategic Voting in the California Recall Election’, American Politics Research, 32 (2005), 216–45, and R. Michael Alvarez, D. Roderick Kiewiet and Betsy Sinclair, ‘Rational Voters and the Recall Election’, in Shaun Bowler and Bruce Cain, eds, Clicker Politics: Essays on the California Recall (Upper Saddle River, N.J.: Pearson Prentice Hall, 2006), pp. 87–97.

²⁸ Robert Groves, Survey Errors and Survey Costs (Hoboken, N.J.: Wiley-Interscience, 2004).

²⁹ We also considered the possibility that these respondents were tactical voters who were just badly misinformed, e.g., a Schwarzenegger supporter choosing to vote for McClintock in the erroneous belief that McClintock had a good chance of winning and Schwarzenegger did not. A few voters actually fell into this category. When we asked respondents about Schwarzenegger’s and McClintock’s prospects of winning the replacement election, we found that five of the 417 Schwarzenegger supporters who voted in the replacement election reported that McClintock was likely to win and Schwarzenegger was not. Two of the five reported voting for McClintock. These are tiny numbers, however, so ordinary survey error appears to account for most occurrences of voters not voting for Schwarzenegger or Bustamante when these candidates were their most preferred.

³⁰ The amount of slippage between thermometer scores and preferences is obviously large enough to seriously compromise estimates of the rate of tactical voting. Cho and Hong, for example, report that 22 per cent of the respondents in the 1992 NES survey who assigned Ross Perot a higher thermometer rating than either Bush or Clinton did not vote for Perot. How many of these respondents were casting tactical votes? How many instead gave Perot the highest thermometer rating, but nonetheless preferred Clinton or Bush in their choice for president? There is no way to know, but the evidence discussed above suggests that the second category of voters may have been as large, or even larger, than the first. See Cho and Hong, ‘Does Incumbency Matter?’

³¹ It is, of course, just as accurate to characterize the declining rate hypothesis as a vicious circle: the lower a candidate’s standing in the polls, the more his or her supporters defect to more viable candidates. Or, the worse they do, the worse they do.

³² William Riker, ‘The Two-party System and Duverger’s Law: An Essay on the History of Political Science’, American Political Science Review, 76 (1982), 753–66.

³³ See, inter alia, Carole Uhlaner and Bernard Grofman, ‘The Race May Be Close but My Horse is Going to Win: Wish Fulfillment in the 1980 Presidential Election’, Political Behavior, 8 (1986), 101–29.

³⁴ Shaun Bowler and Bruce Cain, ‘Introduction’, in Bowler and Cain, eds, Clicker Politics, pp. 1–16.

³⁵ Allison Hoffman, ‘Partial hand-count of ballots reveals few irregularities’, Los Angeles Times, 16 October 2003, p. B-4; R. Michael Alvarez, Melanie Goodrich, Thad Hall, D. Roderick Kiewiet and Sarah Sled, ‘The Complexity of the California Recall Election’, PS: Political Science and Politics, 37 (2004), 23–6.