Duverger's law

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In political science, Duverger's law is a principle that asserts that plurality-rule elections structured within single-member districts tend to favor a two-party system. This is one of two hypotheses proposed by Duverger, the second stating that "the double ballot majority system and proportional representation tend to multipartism."[1]

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 one of the only theories in political science elevated to the level of a law, in practice it 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, India and Australia have consistently had multiparty parliaments.[2] Eric Dickson and Ken Sheve 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.[3]


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.[4][5]

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.[6]

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.


While there are indeed many plurality systems with two highly dominant parties, such as the United States, there are counterexamples:

  • In the United Kingdom, the Liberal party/Alliance/Liberal Democrats have, since the February 1974 General Election, usually obtained between 15% and 25% of the vote forming a "third party" and creating a three-party system.[7] But despite gathering around a fifth of votes consistently for over twenty years, their share of seats in parliament has not been more than a tenth in that time.[8] This is because Duverger's law says that the number of viable parties is one plus the number of seats in a constituency. In the UK there is no presidential and thus no unifying election to force party mergers. However the tendency towards two parties in that tactical voting occurs. In Scotland, Labour and the SNP are the two dominant parties. The SNP replaced the Lib Dems in this roll. In southwest England the Lib Dems face off against the Conservatives. Labor voters will vote for the Lib Dems to prevent a conservative from winning. Thus regional two party systems are formed.
  • More than three parties have won constituencies recently (eight other parties), but they are either elected outside England, where the British FPTP system is used in parallel to the national (Welsh, Scottish, Northern Irish) PR-multiparty democracy, or through by-elections (such as the Respect Coalition).
  • In Canada, there are four political parties represented in Parliament. However there is an incentive to vote for a party that elects no candidate, as it may reach the threshold for public financing, though this is changing. As a result of policy change at the hands of the Conservative government and supported by the Liberals, there will be no more subsidy for votes given to smaller parties after the next federal election. That doesn't alter the fact that most governments are one-party majority governments.[9]
  • In India, there are thirty-eight political parties represented in the Parliament. Like the UK and Canada, India has a winner-takes-all system.[10]
  • 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. Currently, there are six major political parties, with the ruling Liberal Party controlling less than one-third of the seats.[11] The party situation in the 24-member Senate has fragmented into five parties having at least 2 seats, with the largest party only controlling five seats.[12] Only the president's party has been able to run at majority of the districts in the House of Representatives, while no party has completed a 12-person electoral slate for the Senate since 1998 without inviting other non-party members, allowing for multiple parties to win seats. About 80% of the seats in the House of Representatives are elected via FPTP, while the senators are elected via plurality-at-large voting (essentially a multi-member variation of FPTP).[13] However, Senate elections in the Philippines have (generally) been a contest between two slates, and the average number of candidates in the 2013 House of Representatives elections in every district is 2.69.

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[14] — PR would have the opposite effect.

These counterexamples 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. He 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;[citation needed] 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 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.[15] 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.[16]

See also


  1. Sartori, Giovanni, Comparative Constitutional Engineering, An Inquiry into Structures, Incentives and Outcomes.
  2. 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
  3. "Social Identity, Electoral Institutions and the Number of Candidates." British Journal of Political Science / Volume 40 / Issue 02 / April 2010, pp 349-375
  4. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
  5. The Japanese election system: three ... - Junichiro Wada - Google Books
  6. Maurice Duverger, "Factors in a Two-Party and Multiparty System," in Party Politics and Pressure Groups (New York: Thomas Y. Crowell, 1972), pp. 23-32. http://janda.org/c24/Readings/Duverger/Duverger.htm
  7. See references in United Kingdom general elections, 1974 to 2010.
  8. Liberal Democrats#Electoral results
  9. House of Commons of Canada
  10. Lok Sabha
  11. House of Representatives of the Philippines
  12. Senate of the Philippines
  13. Congress of the Philippines
  14. Crowell, Thomas Y. (1972). "Factors in a Two-Party and Multiparty System - The Technical Factor: The Electoral System". Party Politics and Pressure Groups: 23–32.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  15. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
  16. Colomer, Josep M. (March 2005). "It's Parties that Choose Electoral Systems (or Duverger's Law Upside Down)" (PDF). Retrieved 2009-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>