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² In Riker, W. H.'s ‘The Two-Party System and Duverger's Law’, American Political Science Review, LXXVI (1982), 753–66CrossRefGoogle Scholar, the law is traced back to 1869. The law has also been criticized by Wildavsky, A., ‘A Methodological Critique of Duverger's Political Parties’, Journal of Politics, XXI (1959), 303–18CrossRefGoogle Scholar and disputed by Rae, D. W., The Political Consequences of Electoral Laws (New Haven, Conn.: Yale University Press, 1971).Google Scholar

³ See Leys, C., ‘Models. Theories and the Theory of Political Parties’, Political Studies, VII (1959), 127–46.CrossRefGoogle Scholar

⁴ Ivor Crewe pointed out to me that in the 1983 election in the United Kingdom the informed press was full of discussions about Labour or Conservative votes flowing to the Alliance in the constituencies where the latter was expected to be the second party.

⁵ See Bensel, R. F. and Sanders, E., ‘The Effect of Electoral Rules on Voting Behavior: The Electoral College and Shift Voting’, Public Choice, XXXIV (1979), 69–85CrossRefGoogle Scholar. Also, see Black, J. H., ‘The Multicandidate Calculus of Voting: Applications to Canadian Elections’, American Journal of Political Science, XXII (1978), 609–38CrossRefGoogle Scholar; Cain, B. E., ‘Strategic Voting in Britain’, American Journal of Political Science, XXII (1978), 639–55.CrossRefGoogle Scholar

⁶ Arrow, K. S., Social Choice and Individual Values (New Haven, Conn.: Yale University Press, 1951).Google Scholar

⁷ Riker, W. H., Liberalism Against Populism (London: W. H. Freeman, 1982), p. 141Google Scholar. For the proof, see Gibbard, A., ‘Manipulation of Voting Schemes: A General Result’, Econometrica, XLI (1973), 587–601.CrossRefGoogle Scholar

⁸ An expected utility approach was proposed by Riker, W. H. and Ordeshook, P. C., ‘A Theory of the Calculus of Voting’, American Political Science Review, LXII (1968), 25–42CrossRefGoogle Scholar; a Minimax Regret approach by Ferejohn, J. A. and Fiorina, M. P., ‘The Paradox of Non-Voting: A Decision Theoretic Analysis’, American Political Science Review, LXVIII (1974), 525–36CrossRefGoogle Scholar; and a game-theoretical approach by Palfrey, T. and Rosenthal, H., ‘Voter Participation and Strategic Uncertainty’, American Political Science Review, LXXIX (1985), 62–78.CrossRefGoogle Scholar

⁹ The point was made forcefully by P. H. Meehl. He claimed that ‘the point is that the “thrown-away-vote” argument, as generally employed in American politics, presupposes that there is such a thing as not throwing away a vote.’ (See Meehl, P. H., ‘The Selfish Voter Paradox and the Thrown-Away-Vote Argument’, American Political Science Review, LXXI (1977), p. 30.Google Scholar) On a different theoretical basis the same point is made by Ferejohn, and Fiorina, in ‘The Paradox of Non-Voting’ (p. 534)Google Scholar, where they claim that ‘voting for one's second choice is never MMR optimal’. Ferejohn, and Fiorina, , ‘Closeness Counts Only in Horseshoes and Dancing’, American Political Science Review, LXIX (1975), 920–5CrossRefGoogle Scholar also presented empirical evidence that the closeness of an election does not affect the calculations of voters. Finally, Owen, G. and Grofman, B. in ‘To Vote or Not to Vote: The Paradox of Non-Voting’, Public Choice, XLII (1984), 311–25CrossRefGoogle Scholar, shifted from descriptive to normative grounds and advised people not to vote tactically: ‘If you are going to bother to vote at all, then never allow yourself to be talked out of voting for the candidate of your choice.’

¹⁰ Przeworski, A. and Teune, H., The Logic of Comparative Social Inquiry (New York: Wiley, 1970), p. 22.Google Scholar

¹¹ See Tsebelis, G., ‘Abstention and Strategic Voting’, paper presented to the Public Choice Society, Phoenix, Arizona, 1984.Google Scholar

¹² In the case of two parties, the point lies on one side of the triangle. The results of this study, however, can easily be generalized by using the unit tetrahedron for four-party systems, the unit polyhedron with five vertices in a four-dimensional space for a five-party system, etc. But these complications are not necessary unless one considers that trade-offs of votes between more than two parties take place.

¹³ For the student of British politics these barycentric coordinates are familiar from the work of Miller, W. L., Electoral Dynamics in Britain Since 1918 (London: Macmillan, 1977)CrossRefGoogle Scholar, and Budge, I. and Farlie, D., Voting and Party Competition (London: Wiley, 1977)Google Scholar. Here I present a different use.

¹⁴ In the figure the width of the area of strategic voting is smaller than that of sincere voting. The reason is that I assume that a voter is less willing to break a tie between his second and third choice than to participate when his first choice is at stake.

¹⁵ See Cox, G. W., ‘Strategic Electoral Choice in Multi-Member Districts: Approval Voting in Practice?’, American Journal of Political Science, XXVIII (1984), 722–38.CrossRefGoogle Scholar

¹⁶ On this point see also Riker, , ‘The Two Party System and Duverger's Law’, p. 762.Google Scholar

¹⁷ See Fisher, S. L., ‘The Wasted Vote Thesis: West German Evidence’, Comparative Politics, V (1973), 293–9.CrossRefGoogle Scholar

¹⁸ von Beyme, K., The Political System of the Federal Republic of Germany (New York: St Martin's, 1983), p. 30Google Scholar, is the exception. He claims that votes ‘were borrowed for the FDP from the SPD to keep the coalition in power’. This is precisely the Inverse Tactical Voting thesis of this Note.

¹⁹ Issue of 2 March 1983.