¹ Duverger, Maurice, Political Parties (New York: Wiley, 1963), p. 217.Google Scholar

² For a sociological interpretation of Duverger's Law, see Taagepera, Rein and Grofman, Bernard, ‘Rethinking Duverger's Law: Predicting the Effective Number of Parties in Plurality and PR Systems – Parties Minus Issues Equals One’, European Journal of Political Research, 13 (1985), 341–52.CrossRefGoogle Scholar

³ See Riker, William, ‘Duverger's Law Revisted’Google Scholar, and Sartori, Giovanni, ‘The Influence of Electoral Systems: Faulty Laws or Faulty Method?’, both in Grofman, Bernard and Lijphart, Arend, eds, Electoral Laws and Their Political Consequences (New York: Agathon, 1986).Google Scholar

⁴ See Quattrone, George A. and Tversky, Amos, ‘Contrasting Rational and Psychological Analyses of Political Choice’, American Political Science Review, 82 (1988), 719–36.CrossRefGoogle Scholar

⁵ Riker, William, Liberalism Against Populism (San Francisco: W. H. Freeman and Co., 1982).Google Scholar

⁶ Riker, William, ‘The Two-Party System and Duverger's Law’, American Political Science Review, 76 (1982), 753–66.CrossRefGoogle Scholar

⁷ Since 1955 there has been one single-member district. The redistricting of 1986 created one six-member district and four two-member districts.

⁸ A minimum percentage of the vote is required and run-off elections have been held, but none have been required since the early postwar years. For the relevant rules see Kōshoku Senkyo-hō (Public Election Law), Article 10, section 95.

⁹ Taiwan uses the same system with large districts. See Winkler, Edwin A., ‘Institutionalization and Participation on Taiwan: From Hard to Soft Authoritarianism’, China Quarterly, 89 (1984), 481–99.CrossRefGoogle Scholar

¹⁰ Lijphart, Arend, Pintor, Rafael Lopez and Sone, Yasunori, ‘The Limited Vote and the Single Nontransferable Vote: Lessons from the Japanese and Spanish Examples’Google Scholar, in Grofman, and Lijphart, , eds, Electoral Laws and their Political ConsequencesGoogle Scholar, quoting Mackenzie, W. J. M., Free Elections: An Elementary Textbook (London: Allen & Unwin, 1958).Google Scholar

¹¹ See, for example, Baerwald, Hans, Party Politics in Japan (London: Allen & Unwin, 1986)Google Scholar and Hrebenar, Ronald J., ‘Rules of the Game: The Impact of the Electoral System’ in Hrebenar, , ed., The Japanese Party System (Boulder, Colo.: Westview Press, 1986)Google Scholar. For an approach more similar to the one presented here see Sone, Yasunori, ‘The Japanese Electoral System: Plurality or not Plurality, That is the Question’, paper presented at the Nissan Institute Seminar, Oxford University, 05 1984.Google Scholar

¹² Butler, David E., ‘Electoral Systems’ in Butler, et al. , eds, Democracy at the Polls (Washington, DC: American Enterprise Institute, 1981), p. 14.Google Scholar

¹³ Cox, Gary W., ‘Strategic Electoral Choice in Multi-Member Districts’, American Journal of Political Science, 28 (1984), 722–38.CrossRefGoogle Scholar

¹⁴ See, for example, Mair, Peter, ‘Muffling the Swing: STV and the Irish General Election of 1981’, West European Politics, 5 (1982), 75–90.CrossRefGoogle Scholar

¹⁵ See Soma, Masao, Nihon Senkyo Seido Shi (A History of Japanese Electoral Systems) (Fukuoka, Japan: Kyūshū University Press, 1986).Google Scholar

¹⁶ Taagepera, Rein, ‘Reformulating the Cube Law for Proportional Representation’, American Political Science Review, 80 (1986), 489–504.CrossRefGoogle Scholar

¹⁷ Butler, David E., ‘Reflections on the Electoral Debate in Britain’, in Lijphart, Arend and Grofman, Bernard, eds, Choosing an Electoral System (New York: Praeger, 1984).Google Scholar

¹⁸ How many voters should be represented? The single-member district offers a clear and defensible answer: the majority. Similarly, proportional representation gives a clear and defensible answer: everyone. The Japanese system gives intermediate answers. In a three-member district threequarters of the voters are represented; in a four-member district, four-fifths; and in a five-member district, five-sixths.

¹⁹ The first postwar election in 1946 was held under slightly different rules and in large electoral districts.

²⁰ This calculation is simply the number of seats, 512 in 1986, plus one loser for each of the 130 districts, divided by 512.

²¹ The Laakso-Taagepera index is where v is the proportion of the vote. One normally sums across parties but here I sum across candidates.

²² The French run-off system produces a similar phenomenon of co-operation and competition among members of a coalition. See Tsebelis, George, ‘Nested Games: The Cohesion of French Coalitions’, British Journal of Political Science, 18 (1988), 145–70CrossRefGoogle Scholar, and Rochon, Thomas R. and Pierce, Roy, ‘Coalitions versus Rivalries: French Socialists and Communists, 1967–78’, Comparative Politics, 18 (1985), 437–51.CrossRefGoogle Scholar

²³ On co-operation among the opposition parties see Ishigami, Yamato, ‘Yato Senkyo Kyoryoku’ (‘Electoral co-operation among the Opposition Parties’) Juristo, Special Issue, 35 (1984), 132–9.Google Scholar

²⁴ Pridham, Geoffrey, ‘The Social Democratic Party in Britain: Protest or New Political Tendency?’, in Lawson, Kay and Merkl, Peter H., eds, When Parties Fail (Princeton, NJ: Princeton University Press, 1988), p. 240.Google Scholar

²⁵ For similar results in the British single-member district case see Galbraith, John W. and Rae, Nicol C., ‘A Test of the Importance of Tactical Voting: Great Britain, 1987’, British Journal of Political Science, 19 (1989), 126–36.CrossRefGoogle Scholar

²⁶ Matching those retiring with their successors is not always obvious. For everyone retiring I coded a successor if someone in the same party ran in his place. Successors were matched first if they shared the retiring person's last name and next if they shared the same faction. If no other criteria applied I matched successors and those retiring by order of finish.

²⁷ For descriptions of each of the opposition parties see Hrebenar, Ronald J., ed., The Japanese Party System (Boulder, Colo.: Westview, 1986).Google Scholar

²⁸ Curtis, Gerald L., Campaigning Japanese Style (New York: Columbia University Press, 1972).Google Scholar

²⁹ Curtis, , Campaigning Japanese Style.Google Scholar

³⁰ One quirk is still possible in a competitive district. Maldistribution of a party's vote among its candidates may cause them to lose a seat. However, this quirk has also become rarer. The distribution of votes has become remarkably even in recent elections, a phenomenon deserving further study.

³¹ See Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984) for an evolutionary use of game theory.Google Scholar

³² A few were forcibly retired by a second round of purges.