Duverger's law

A two-party system is most common under plurality voting. Voters typically cast one vote per race. Maurice Duverger argued there were two main mechanisms by which 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.{{cite journal | title = Maurice Duverger and the Study of Political Parties | journal = French Politics | url = http://www.pratiquesciencessociales.net/exposes/S12.%20Maurice%20Duverger%20and%20the%20Study%20of%20Political%20Parties%20%28Schlesinger%202006%29.pdf | access-date = 2011-12-17 | url-status = dead | archive-url = https://web.archive.org/web/20110724020408/http://www.pratiquesciencessociales.net/exposes/S12.%20Maurice%20Duverger%20and%20the%20Study%20of%20Political%20Parties%20%28Schlesinger%202006%29.pdf | archive-date = 24 July 2011 | doi = 10.1057/palgrave.fp.8200085 | year = 2006 | last1 = Schlesinger | first1 = Joseph A. | last2 = Schlesinger | first2 = Mildred S. | volume = 4 | pages = 58–68 | s2cid = 145281087 }}{{cite book | url = https://books.google.com/books?id=fecTeDjAZZ8C&pg=PA12 | title = The Japanese Election System: Three Analytical Perspectives | first = Junichiro | last = Wada| isbn = 9780203208595 | date = 2004-01-14 | publisher = Taylor & Francis }}{{cite book |last=Alston |first=Eric |chapter-url=https://www.cambridge.org/core/books/institutional-and-organizational-analysis/legislature-and-executive/70DD1949D5C833D7F30FE49A3E0C9A9F |chapter=The Legislature and Executive |editor-last1=Alston |editor-first1=Lee J. |editor-last2=Mueller |editor-first2=Bernardo |editor-last3=Nonnenmacher |editor-first3=Tomas |date=2018 |title=Institutional and Organizational Analysis: Concepts and Applications |publisher=Cambridge University Press |isbn=9781316091340 |pages=173–206 |doi=10.1017/9781316091340.006 |access-date=September 25, 2023}}

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 was the Liberal Democrats in the United Kingdom, whose proportion of seats in the legislature was, until recently, 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.{{Citation needed|date=October 2024}}

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 and one radical party ran candidates, 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.

{{cite book

| first = Maurice

| last = Duverger

| author-link = Maurice Duverger

| chapter = Factors in a Two-Party and Multiparty System

| title = Party Politics and Pressure Groups

| location = New York

| publisher = Thomas Y. Crowell

| year = 1972

| pages = 23–32

| chapter-url = http://janda.org/c24/Readings/Duverger/Duverger.htm

}}

Kenneth Benoit suggested causal influence between electoral and party systems might be bidirectional or in either direction.{{Cite journal |last=Benoit |first=Kenneth |year=2007 |title=Electoral Laws as Political Consequences: Explaining the Origins and Change of Electoral Institutions |journal=Annual Review of Political Science |volume=10 |issue=1 |pages=363–390 |doi=10.1146/annurev.polisci.10.072805.101608 |doi-access=free}} Josep Colomer agreed, arguing 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 happen not in the short term, but in the mid-to-long term.

{{cite journal |last=Colomer |first=Josep M. |author-link=Josep Colomer |year=2005 |title=It's Parties that Choose Electoral Systems (or Duverger's Law Upside Down) |url=http://www.politicalstudies.org/pdf/edsfavourites/colomer.pdf |url-status=dead |journal=Political Studies |volume=53 |issue=1 |pages=1–21 |citeseerx=10.1.1.563.7631 |doi=10.1111/j.1467-9248.2005.00514.x |s2cid=12376724 |archive-url=https://web.archive.org/web/20060203040309/http://www.politicalstudies.org/pdf/edsfavourites/colomer.pdf |archive-date=3 February 2006 |access-date=2009-05-31 |hdl=10261/61619}}

File:UK popular vote.svgSome 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.

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.{{cite journal |last1=Riker |first1=William H. |author-link1=William H. Riker |date=December 1982 |title=The Two-party System and Duverger's Law: An Essay on the History of Political Science |url=https://www.cambridge.org/core/journals/american-political-science-review/article/twoparty-system-and-duvergers-law-an-essay-on-the-history-of-political-science/3CA289C649AFCB8D4CC8F430FC292CC3 |journal=American Political Science Review |volume=76 |issue=4 |pages=753–766 |doi=10.1017/s0003055400189580 |jstor=1962968 |access-date=12 April 2020}}{{cite book |last1=Rae |first1=Douglas W. |title=The political consequences of electoral laws |date=1971 |publisher=Yale University Press |isbn=0300015178 |edition=Rev. |location=New Haven |lccn=74161209 |oclc=993822935 |author-link1=Douglas W. Rae}} In systems outside the United States, like Canada, 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.

{{cite journal |last1=Dunleavy |first1=Patrick |author-link=Patrick Dunleavy |last2=Diwakar |first2=Rekha |year=2013 |title=Analysing multiparty competition in plurality rule elections |url= http://eprints.lse.ac.uk/38452/1/Dunleavy_Analysing%20multiparty_2014_author.pdf|journal=Party Politics |volume=19 |issue=6 |pages=855–886 |doi=10.1177/1354068811411026 |s2cid=18840573}} Riker credits Canada's 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.

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.

Absent a major reform like switching to proportional representation, minor reforms like ranked-choice voting has the potential to allow for more choice in a winner-take-all system.{{Cite journal |last=Kuo |first=Didi |date=Fall 2023 |title=Why Big Reform is Possible |url=https://democracyjournal.org/magazine/70/why-big-reform-is-possible/ |journal=Democracy |volume=70}}. Under proportional representation, legislative seats are allocated according to the percentage of votes a party receives, making their success dependent on their received support. Proportional representation weakens two-party dominance, since smaller parties no longer rely on plurality they have a better chance of success.{{Cite journal |last1=Forand |first1=Jean Guillaume |last2=Maheshri |first2=Vikram |date=December 2015 |title=A dynamic Duverger's law |url=https://doi.org/10.1007/s11127-016-0309-8 |journal=Public Choice |volume=165 |issue=3–4 |pages=285–306 |doi=10.1007/s11127-016-0309-8 |issn=0048-5829}} In a ranked-choice voting system (RCV) voters rank candidates in order of preference rather than casting a single vote. This system is used in countries with multi-party politics like Australia, Ireland, and New Zealand. RCV systems were utilized in the US to manage or create intra-party factionalism but were repealed in most states for being unpredictable.{{Cite journal |last=Santucci |first=Jack |date=2021-06-15 |title=Variants of Ranked-Choice Voting from a Strategic Perspective |url=https://www.cogitatiopress.com/politicsandgovernance/article/view/3955 |journal=Politics and Governance |volume=9 |issue=2 |pages=344–353 |doi=10.17645/pag.v9i2.3955 |doi-access=free |issn=2183-2463}} Duverger argued that "a majority vote on two ballots is conducive to a multiparty system, inclined toward forming coalitions": that the two-round system encourages a multiparty system, but to a lesser degree than proportional representation does.

William Clark and Matt Golder (2006) find the effect largely holds up, noting that different methods of analyzing the data might lead to different conclusions. They emphasize other variables like the nuances of different electoral institutions and the importance that Duverger also placed on sociological factors.{{Cite journal |last1=Clark |first1=William Roberts |last2=Golder |first2=Matt |date=August 2006 |title=Rehabilitating Duverger's Theory: Testing the Mechanical and Strategic Modifying Effects of Electoral Laws |url=http://journals.sagepub.com/doi/10.1177/0010414005278420 |journal=Comparative Political Studies |language=en |volume=39 |issue=6 |pages=679–708 |doi=10.1177/0010414005278420 |issn=0010-4140 |s2cid=154525800 |quote=The central hypothesis Duverger’s theory generates is that social heterogeneity should increase the number of parties only once the electoral system is sufficiently permissive.}} Thomas R. Palfrey argued 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).Palfrey, T. (1989) ‘A mathematical proof of Duverger’s law’, in P. Ordeshook (ed.) [https://archive.org/details/modelsofstrategi0000unse/page/68/mode/2up?view=theater Models of Strategic Choice in Politics], Ann Arbor: University of Michigan Press, 69–91.

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.

The U.S. system has two major parties which have won, on average, 98% of all state and federal seats. There have only 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.

In Matt Golder's 2016 review of the empirical evidence to-date, he concluded that despite some contradicting cases, the law remains a valid generalization.Golder, M. (2016). "Far from equilibrium: The state of the field on electoral system effects on party systems." In E. Herron, R. Pekkanen, & M. Shugart (Eds.), The Oxford Handbook of Electoral Systems. Oxford University Press.

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.{{cite journal |last1=Reed |first1=Steven R. |date=April 2001 |title=Duverger's Law is Working in Italy |journal=Comparative Political Studies |volume=34 |issue=3 |pages=312–327 |doi=10.1177/0010414001034003004 |s2cid=154808991}} He finds a similar effect in Japan through a slow trial-and-error process that shifted the number of major parties towards the expected outcome.{{cite journal |last1=Reed |first1=Steven R. |year=1990 |title=Structure and Behaviour: Extending Duverger's Law to the Japanese Case |journal=British Journal of Political Science |volume=20 |issue=3 |pages=335–356 |doi=10.1017/S0007123400005871 |jstor=193914 |s2cid=154377379}}

Eric Dickson and Kenneth Scheve argued in 2007 that Duverger's law is strongest when a society is homogenous or closely divided, but is weakened when multiple intermediate identities exist.{{cite journal |last1=Dickson |first1=Eric S. |last2=Scheve |first2=Kenneth |author2-link=Kenneth Scheve |date=20 February 2007 |title=Social Identity, Electoral Institutions and the Number of Candidates |url=http://www.nyu.edu/gsas/dept/politics/faculty/dickson/dickson_candidates.pdf |url-status=dead |journal=British Journal of Political Science |volume=40 |issue=2 |pages=349–375 |citeseerx=10.1.1.75.155 |doi=10.1017/s0007123409990354 |jstor=40649446 |s2cid=7107526 |archive-url=https://web.archive.org/web/20180721203318/http://www.nyu.edu/gsas/dept/politics/faculty/dickson/dickson_candidates.pdf |archive-date=2018-07-21 |access-date=2017-10-26}} As evidence of this, Duhamel cites the case of India, where over 25 percent of voters vote for parties outside the two main alliances.{{cite book |last1=Duhamel |first1=Olivier |url=https://books.google.com/books?id=ZWSzDwAAQBAJ&pg=PT297 |title=Droit constitutionnel et institutions politiques |last2=Tusseau |first2=Guillaume |date=2019 |publisher=Éditions du Seuil |isbn=9782021441932 |edition=5e |location=Paris |page=297 |language=fr |trans-title=Constitutional law and political institutions |oclc=1127387529 |quote=[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. |author-link1=Olivier Duhamel |author-link2=Guillaume Tusseau}}

Two-party politics may also emerge in systems that use a form of proportional representation, with Duverger and others arguing that Duverger's Law mostly represents a limiting factor (like a brake) on the number of major parties in other systems more than a prediction of equilibrium for governments with more proportional representation.{{cite book |last1=Cox |first1=Gary W. |url=https://archive.org/details/makingvotescount0000coxg/page/273/mode/1up?view=theater |title=Making votes count: strategic coordination in the world's electoral systems |date=1997 |publisher=Cambridge University Press |isbn=9780521585163 |location=Cambridge |pages=273–274 |oclc=474972505 |author-link1=Gary W. Cox}}

{{Portal|Politics}}

• {{annotated link|Micromega rule}} - a theory that political parties choose voting systems
• {{annotated link|Mouseland}}
• {{annotated link|List of eponymous laws|Observations named after people}}

{{Reflist|30em}}

{{Authority control}}

{{Use dmy dates|date=December 2020}}

Category:Voting theory