Duverger's law

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In political science, Duverger's law holds that in political systems with only one winner (as in the U.S.), two main parties tend to emerge with minor parties typically splitting votes away from the most similar major party.[1][2] In contrast, systems with proportional representation, usually have more representation of minor parties in government.[3]


A two-party system is more common in a plurality voting system (also referred to as first past the post). Voters typically can cast one vote per race. Since the winner of the seat is determined by the candidate with the most votes, the development of third parties is discouraged.

Duverger argued that there were two mechanisms whereby plurality voting systems lead to fewer major parties: (i) small parties are disincentivized to form because they have great difficulty winning seats or representation, and (ii) voters are wary of voting for a smaller party whose policies they actually favor because they do not want to "waste" their votes (on a party unlikely to win a plurality) and therefore tend to gravitate to one of two major parties that is more likely to achieve a plurality, win the election, and implement policy.[4][5][6]

For legislatures where each seat represents a geographical area and the candidate with the most votes wins that seat, minor parties spread fairly evenly across many districts win less representation than geographically concentrated ones with the same overall level of public support. An example of this is the Liberal Democrats in the United Kingdom, whose proportion of seats in the legislature is significantly less than their proportion of the national vote. The Green Party of Canada is another example; the party received about 5% of the popular vote from 2004 to 2011 but had only won one seat (out of 308) in the House of Commons in the same span of time. Another example was seen in the 1992 U.S. presidential election, when Ross Perot's candidacy received zero electoral votes despite receiving 19% of the popular vote. Gerrymandering is sometimes used to try to collect a population of like-minded voters within a geographically cohesive district so that their votes are not "wasted", but tends to require that minor parties have both a geographic concentration and a redistricting process that seeks to represent them. These disadvantages tend to suppress the ability of a third party to engage in the political process.

The second challenge to a third party is both statistical and tactical. Duverger presents the example of an election in which 100,000 moderate voters and 80,000 radical voters are to vote for candidates for a single seat or office. If two moderate parties ran candidates and one radical candidate ran (and every voter voted), the radical candidate would tend to win unless one of the moderate candidates gathered fewer than 20,000 votes. Appreciating this risk, moderate voters would be inclined to vote for the moderate candidate they deemed likely to gain more votes, with the goal of defeating the radical candidate. To win, then, either the two moderate parties must merge, or one moderate party must fail, as the voters gravitate to the two strongest parties. Duverger called this trend polarization.[7]

Ways minor parties win representation[edit]

Effect of Duverger's law in UK. The graph shows the vote share of each political party since 1832. Around 1920 a third party (Labour, red) displaces one of the two major parties at the time (Liberal, yellow). After 1980 several third parties build local strongholds and reduce the vote share of the two major parties.

Some minor parties in winner-take-all systems have managed to translate their support into winning seats in government by focusing on local races, taking the place of a major party, or changing the political system.

Local growth[edit]

William H. Riker, citing Douglas W. Rae, noted that strong regional parties can lead to more than two parties receiving seats in the national legislature, even if there are only two parties competitive in any single district.[8][9] In systems outside the United States, like the United Kingdom and India, multiparty parliaments exist due to the growth of minor parties finding strongholds in specific regions, potentially lessening the psychological fear of a wasted vote by voting for a minor party for a legislative seat.[10]

Replace major party[edit]

The political chaos in the United States immediately preceding the Civil War allowed the Republican Party to replace the Whig Party as the progressive half of the American political landscape. Loosely united on a platform of country-wide economic reform and federally funded industrialization, the decentralized Whig leadership failed to take a decisive stance on the slavery issue, effectively splitting the party along the Mason–Dixon line. Southern rural planters, initially attracted by the prospect of federal infrastructure and schools, aligned with the pro-slavery Democrats, while urban laborers and professionals in the northern states, threatened by the sudden shift in political and economic power and losing faith in the failing Whig candidates, flocked to the increasingly vocal anti-slavery Republican Party.

Change political system[edit]

In addition to a major reform like proportional representation, approval voting or ranked-choice voting provide ways for minor parties to be more competitive in a winner-take-all system.[11]

Direction of effect[edit]

In recent years some researchers have modified Duverger's law by suggesting that causal influence between electoral and party systems might be bidirectional or in either direction.[12] For example, Josep Colomer argues that changes from a plurality system to a proportional system are typically preceded by the emergence of more than two effective parties, and increases in the effective number of parties happens not in the short-term, but in the mid-to-long term.[13]

Thomas R. Palfrey argued that Duverger's law can be proven mathematically at the limit when the number of voters approaches infinity for one single-winner district and where the probability distribution of votes is known (perfect information).[14]

Strength of effect[edit]

Duverger did not regard this principle as absolute, suggesting instead that plurality would act to delay the emergence of new political forces and would accelerate the elimination of weakening ones, whereas proportional representation would have the opposite effect.[7]

Eric Dickson and Kenneth Scheve argue that Duverger's law is strongest when a society is homogenous or closely divided, but is weakened when multiple intermediate identities exist.[15]

Two-party politics may emerge in systems that use a form of proportional representation.[16]



Riker pointed to Canada's regional politics, as well as the U.S. presidential election of 1860, as examples of often temporary regional instability that occurs from time-to-time in otherwise stable two-party systems.[8] He credits the highly decentralized system of government as encouraging minor parties to build support by winning seats locally, which then sets the parties up to get representatives in the House of Commons of Canada.[8]


In Droit constitutionnel et institutions politiques, Olivier Duhamel argues that these 30+ political parties elected in India and the over 25 percent of voting for parties outside the two main alliances shows that the Duverger's law is not as strong in more diverse and less centralized states like India where regional subsystems generate more party competition.[17]


Steven R. Reed argued in 2001 that Duverger's law could be observed in Italy with 80% of electoral districts, gradually but significantly shifting towards two major parties.[18]


Steven R. Reed argued in 1990 that Duverger's law could be observed in Japan through a slow trial-and-error process that shifted the number of major parties towards the expected outcome.[19]

United States[edit]

The U.S. provides a clear example of Duverger's law where two major parties have won, on average, 98% of all state and federal seats.[1] There have been a few rare elections where a minor party was competitive with the major parties, occasionally replacing one of the major parties in the 19th century.[2][8]

See also[edit]


  1. ^ a b Masket, Seth (Fall 2023). "Giving Minor Parties a Chance". Democracy (journal). 70.
  2. ^ a b Blake, Aaron (25 November 2021). "Why are there only two parties in American politics?". Washington Post. ISSN 0190-8286. Retrieved 25 September 2023.
  3. ^ Duverger, Maurice (1964). Political parties: their organization and activity in the modern state. Internet Archive. London : Methuen. p. 239. ISBN 978-0-416-68320-2.
  4. ^ Schlesinger, Joseph A.; Schlesinger, Mildred S. (2006). "Maurice Duverger and the Study of Political Parties" (PDF). French Politics. 4: 58–68. doi:10.1057/palgrave.fp.8200085. S2CID 145281087. Archived from the original (PDF) on 24 July 2011. Retrieved 17 December 2011.
  5. ^ Wada, Junichiro (14 January 2004). The Japanese Election System: Three Analytical Perspectives. Taylor & Francis. ISBN 9780203208595.
  6. ^ Alston, Eric; Alston, Lee J.; Mueller, Bernardo; Nonnenmacher, Tomas (2018). The Legislature and Executive. pp. 173–206. doi:10.1017/9781316091340.006. ISBN 9781316091340. Retrieved 25 September 2023. {{cite book}}: |website= ignored (help)
  7. ^ a b Duverger, Maurice (1972). "Factors in a Two-Party and Multiparty System". Party Politics and Pressure Groups. New York: Thomas Y. Crowell. pp. 23–32.
  8. ^ a b c d Riker, William H. (December 1982). "The Two-party System and Duverger's Law: An Essay on the History of Political Science". American Political Science Review. 76 (4): 753–766. doi:10.1017/s0003055400189580. JSTOR 1962968. Retrieved 12 April 2020.
  9. ^ Rae, Douglas W. (1971). The political consequences of electoral laws (Rev. ed.). New Haven: Yale University Press. ISBN 0300015178. LCCN 74161209. OCLC 993822935.
  10. ^ Dunleavy, Patrick; Diwakar, Rekha (2013). "Analysing multiparty competition in plurality rule elections". Party Politics. 19 (6): 855–886. doi:10.1177/1354068811411026. S2CID 18840573.
  11. ^ Kuo, Didi (Fall 2023). "Why Big Reform is Possible". Democracy (journal). 70.
  12. ^ Benoit, Kenneth (2007). "Electoral Laws as Political Consequences: Explaining the Origins and Change of Electoral Institutions". Annual Review of Political Science. 10 (1): 363–390. doi:10.1146/annurev.polisci.10.072805.101608.
  13. ^ Colomer, Josep M. (2005). "It's Parties that Choose Electoral Systems (or Duverger's Law Upside Down)" (PDF). Political Studies. 53 (1): 1–21. CiteSeerX doi:10.1111/j.1467-9248.2005.00514.x. hdl:10261/61619. S2CID 12376724. Archived from the original (PDF) on 3 February 2006. Retrieved 31 May 2009.
  14. ^ Palfrey, T. (1989) ‘A mathematical proof of Duverger’s law’, in P. Ordeshook (ed.) Models of Strategic Choice in Politics, Ann Arbor: University of Michigan Press, 69–91.
  15. ^ Dickson, Eric S.; Scheve, Kenneth (20 February 2007). "Social Identity, Electoral Institutions and the Number of Candidates" (PDF). British Journal of Political Science. 40 (2): 349–375. CiteSeerX doi:10.1017/s0007123409990354. JSTOR 40649446. S2CID 7107526. Archived from the original (PDF) on 21 July 2018. Retrieved 26 October 2017.
  16. ^ Cox, Gary W. (1997). Making votes count: strategic coordination in the world's electoral systems. Cambridge: Cambridge University Press. pp. 273–274. ISBN 9780521585163. OCLC 474972505.
  17. ^ Duhamel, Olivier; Tusseau, Guillaume (2019). Droit constitutionnel et institutions politiques [Constitutional law and political institutions] (in French) (5e ed.). Paris: Éditions du Seuil. p. 297. ISBN 9782021441932. OCLC 1127387529. [L]a loi selon laquelle le scrutin majoritaire à un tour tend à produire le bipartisme ne vaut que dans une société relativement homogène et un État assez centralisé. Dans le cas contraire, le système de parti national se voit concurrencé par des sous-systèmes régionaux.
  18. ^ Reed, Steven R. (April 2001). "Duverger's Law is Working in Italy". Comparative Political Studies. 34 (3): 312–327. doi:10.1177/0010414001034003004. S2CID 154808991.
  19. ^ Reed, Steven R. (1990). "Structure and Behaviour: Extending Duverger's Law to the Japanese Case". British Journal of Political Science. 20 (3): 335–356. doi:10.1017/S0007123400005871. JSTOR 193914. S2CID 154377379.