Duverger's law

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In political science, Duverger's law holds that plurality-rule elections (such as first past the post) structured within single-member districts tend to favor a two-party system and that "the double ballot majority system and proportional representation tend to favor multipartism."[1][2] The discovery of this tendency is attributed to Maurice Duverger, a French sociologist who observed the effect and recorded it in several papers published in the 1950s and 1960s. In the course of further research, other political scientists began calling the effect a "law" or principle.

Duverger's law suggests a nexus or synthesis between a party system and an electoral system: a proportional representation (PR) system creates the electoral conditions necessary to foster party development while a plurality system marginalizes many smaller political parties, resulting in what is known as a two-party system.

While a principle of political science, in practice most countries with plurality voting have more than two parties. While the United States is very much a two-party system, the United Kingdom, Canada and India have consistently had multiparty parliaments.[3][4] Eric Dickson and Ken Scheve argue that there is a counter force to Duverger's Law, that on the national level a plurality system encourages two parties, but in the individual constituencies supermajorities will lead to the vote fracturing.[5]


A two-party system often develops in a plurality voting system. In this system, voters have a single vote, which they can cast for a single candidate in their district, in which only one legislative seat is available. In plurality voting (i.e. first past the post), in which the winner of the seat is determined purely by the candidate with the most votes, several characteristics can serve to discourage the development of third parties and reward the two major parties.

Duverger suggests two reasons this voting system favors a two-party system. One is the result of the "fusion" (or an alliance very much like fusion) of the weak parties, and the other is the "elimination" of weak parties by the voters, by which he means that voters gradually desert the weak parties on the grounds that they have no chance of winning.[6][7]

A prominent restrictive feature unique to this system is purely statistical. Because the system gives only the winner in each district a seat, a party which consistently comes third in every district will not gain any seats in the legislature, even if it receives a significant proportion of the vote. This puts geographically thinly spread parties at a significant disadvantage. 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 also a good example. The party received approximately 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 getting 19% of the popular vote. Gerrymandering is sometimes used to counteract such geographic difficulties in local politics but is controversial on a large scale. These numerical disadvantages can create an artificial limit on the level at which a third party can engage in the political process.

The second unique problem is both statistical and tactical. Duverger suggested an election in which 100,000 moderate voters and 80,000 radical voters are voting for a single official. If two moderate parties ran candidates and one radical candidate were to run, the radical candidate would win unless one of the moderate candidates gathered fewer than 20,000 votes. Observing this, moderate voters would be more likely to vote for the candidate most likely to gain more votes, with the goal of defeating the radical candidate. Either the two parties must merge, or one moderate party must fail, as the voters gravitate to the two strong parties, a trend Duverger called polarization.[8]

A third party can enter the arena only if it can exploit the mistakes of a pre-existing major party, ultimately at that party's expense. For example, 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 lured by the prospect of federal infrastructure and schools, quickly aligned themselves 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.

In countries that use proportional representation (PR), and especially in countries such as Israel where the whole country forms a single constituency, the electoral rules discourage a two-party system. The number of votes received for a party determines the number of seats won, and new parties can thus develop an immediate electoral niche. Duverger identified that the use of PR would make a two-party system less likely. However, other systems do not guarantee new parties access to the system: Malta provides an example of a stable two-party system using the single transferable vote, although it is worth noting that its presidential elections are won by a plurality, which may put a greater two-party bias in the system than in a purely proportional system.


Duverger himself did not regard his principle as absolute. Instead, he suggested that plurality would act to delay the emergence of a new political force and would accelerate the elimination of a weakening force;[8] PR would have the opposite effect. The following examples are partly due to the effect of smaller parties that have the majority of their support concentrated in a small number of electorates rather than diluted across many electorates. William H. Riker noted that strong regional parties can distort matters, leading to more than two parties receiving seats in the national legislature, even if there are only two parties competitive in any single district.

The following example seems counter to the law:

  • In the Philippines since 1987, no party has been able to control the House of Representatives; although the party of the president usually has the plurality of seats, it still has to seek coalition partners to command a majority of seats. It may be relevant that the Philippines' governance structure changed repeatedly before 1987 and that the country has many distinct social groups. Also, 80% of the seats in the House of Representatives are elected via FPTP, while the senators are elected via plurality-at-large voting. The average number of candidates in the 2013 House of Representatives elections in every district is only 2.69.

There are also cases where the principle is in effect, but is simply not as strong:

  • In India, there are 38 political parties represented in the Parliament. Like the UK and Canada, India has a winner-takes-all system.[9] In practice, however, most parties are understood to be part of two larger electoral coalitions which makes the Indian system functionally much closer to a two-party system than it appears.
  • In Canada there are five parties represented in the House of Commons (the number has averaged in between 4 and 5 since 1935); however, only three of these (governing Liberals, opposition Conservatives and third place NDP) are considered "major parties" (the other two parties lack official party status as they have under 12 seats). Canada has not had a strict two party system, with only two registered parties in the House of Commons, since before 1921, and at only three relatively brief periods in Canadian history have there been only three parties represented (1921–1935, 1958–1962, and 1980–1993).
  • In the United Kingdom, the SDP–Liberal Alliance, and later Liberal Democrats, have, since the February 1974 General Election, obtained 1–10% of seats forming a third party, albeit with significantly fewer seats.[10] This share of seats is despite gathering around a fifth of votes consistently over the same time period.[11]
    In the UK there is no president and thus no unifying election to force party mergers and regional two party systems are formed. This is because Duverger's law says that the number of viable parties is one plus the number of seats in a constituency. In Scotland, Labour and the SNP are the two dominant parties. The SNP has replaced the Lib Dems in this role. In southwest England, the Lib Dems face off against the Conservatives. Labour voters will vote for the Lib Dems to prevent a Conservative from winning.
    More than three parties have won constituencies recently[when?] (eight other parties), but they are either elected outside England, where the British FPTP system is used in parallel to the national (Welsh, Scottish, and Northern Irish) proportional-representation multiparty democracy, or through by-elections (such as the Respect Coalition).

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 (Riker, 1982). In the case of Canada, the highly regionalised parties are evident in province-by-province examination: while the multiparty system can be seen in the Canadian House of Commons, many of the provinces' elections are dominated by two-party systems. Quebec, for instance, is driven mainly by the sovereigntist, center-(left) Parti Québécois and the center-right Liberal Party, while in Saskatchewan, it is the left-wing New Democratic Party and the centre-right Saskatchewan Party (a coalition of those affiliated with the Conservative and Liberal Parties). Unlike in the United States, where the two major parties are organized and unified at the federal, state and local level, Canada's federal and provincial parties generally operate as separate organizations.


The converse of Duverger's Law is not always valid;[12] two-party politics may emerge even when the plurality vote is not used. This is particularly true in the case of countries using systems that even if they do not use the plurality vote, do not fully incorporate PR either. For instance, Malta has a single transferable vote (STV) system and (what seems to be) stable two-party politics.

In the Australian Senate, there is proportional voting on a state-by-state basis, but even though smaller parties have been able to win seats, there is still a trend towards the major parties, whose dominance in the lower house effectively promotes their upper house candidates.

Some systems are even more likely to lead to a two-party outcome: for example, elections in Gibraltar use a partial block vote system (which is classified as majoritarian) in a single constituency, so the third most popular party is unlikely to win any seats.

In recent years some researchers have modified Duverger's Law by suggesting that electoral systems are an effect of party systems rather than a cause.[13] It has been shown that changes from a plurality system to a proportional system are typically preceded by the emergence of more than two effective parties, and are typically not followed by a substantial increase in the effective number of parties.[14]

See also[edit]


  1. ^ Grzymala-Busse, Anna (31 December 2014). "Remembering Duverger". Mischiefs of Faction. 
  2. ^ Sartori, Giovanni (1994). Comparative Constitutional Engineering: An Inquiry into Structures, Incentives and Outcomes. Macmillan. 
  3. ^ Dunleavy, Patrick (18 June 2012). "Duverger's Law is a dead parrot. Outside the USA, first-past-the-post voting has no tendency at all to produce two party politics". blogs.lse.ac.uk. 
  4. ^ Dunleavy, Patrick; Diwakar, Rekha (2013). "Analysing multiparty competition in plurality rule elections" (PDF). Party Politics. 19 (6): 855–886. doi:10.1177/1354068811411026. 
  5. ^ Dickson, Eric S.; Scheve, Kenneth (2010). "Social Identity, Electoral Institutions and the Number of Candidates". British Journal of Political Science. 40 (2): 349–375. doi:10.1017/s0007123409990354. JSTOR 40649446. 
  6. ^ 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. Archived from the original (PDF) on 24 July 2011. Retrieved 2011-12-17. 
  7. ^ Wada, Junichiro. The Japanese Election System: Three Analytical Perspectives. 
  8. ^ 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. 
  9. ^ Lok Sabha
  10. ^ See references in United Kingdom general elections, 1974 to 2010.
  11. ^ Liberal Democrats#Electoral results
  12. ^ Cox, Gary W. Making Votes Count: Strategic Voting in the World's Electoral Systems. San Diego, CA: University of San Diego Press, 1997.
  13. ^ 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. 
  14. ^ Colomer, Josep M. (2005). "It's Parties that Choose Electoral Systems (or Duverger's Law Upside Down)" (PDF). Political Studies. 53 (1): 1–21. doi:10.1111/j.1467-9248.2005.00514.x. Archived from the original (PDF) on 3 February 2006. Retrieved 2009-05-31.