Duverger's law

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. In contrast, systems with proportional representation usually have more representation of minor parties in government.

Mechanism
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.

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.

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.

Direction of effect
Kenneth Benoit suggested causal influence between electoral and party systems might be bidirectional or in either direction. 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.

Exceptions
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
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. 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. 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.

Replace major party
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.

Different voting systems
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. 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.

Systems that satisfy the sincere favorite criterion are not subject to Duverger's law.

Strength of effect
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. 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).

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.

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. 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.

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. As evidence of this, Duhamel cites the case of India, where over 25 percent of voters vote for parties outside the two main alliances.

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.