Duverger's Law Research Articles

What accounts for Duverger's law? The behavioral mechanisms underpinning two-party convergence in India

Duverger's Law states the single-member district plurality rules should produce two-party competition. In district-level election races where this expectation holds, what political behaviors—ranging from elites' strategic formation of political parties to voters' strategic abandonment of losing candidates—account for these outcomes? Using data from state elections in India, this article demonstrates that no single mechanism accounts for most electoral outcomes consistent with Duverger's Law. However, mechanisms related to the behavior elites, far more than voters, produce convergence on two-party competition. This article uncovers relatively little evidence of outcomes driven by strategic voting, instead finding that much of the convergence on two parties is attributable to various forms of strategic entry in which parties selectively field candidates in certain races. In particular, elite collusion—when multiple parties coordinate on where to field candidates—is especially important. Data from other countries confirm that these findings are not unique to India.

Duverger's psychological effect: A natural experiment approach

A large body of work suggests that electoral systems influence the strategic calculus of voters and parties. But electoral rules are endogenous as they originate in the decision making process of voters and parties, making empirical analyses vulnerable to reverse causality and contamination effects. This paper studies a unique case where an electoral system change is exogenously imposed by a supra-national body. I exploit an EU ruling which forced the UK to adopt proportional representation (PR) for European Parliament elections. Using a difference-in-differences design, I estimate the causal impact of the reform on electoral outcomes. I find that the shift to PR leads to more “effective parties” and thus to a more proportional electoral outcome. In line with Duverger's law, the reform causally increased the number of newly entering parties. Existent small parties did not appear to exert more effort. The findings survive several robustness checks.

Multicandidate elections: Aggregate uncertainty in the laboratory

The rational-voter model is often criticized on the grounds that two of its central predictions (the paradox of voting and Duverger's Law) are at odds with reality. Recent theoretical advances suggest that these empirically unsound predictions might be an artifact of an (arguably unrealistic) assumption: the absence of aggregate uncertainty about the distribution of preferences in the electorate. In this paper, we propose direct empirical evidence of the effects of aggregate uncertainty in multicandidate elections. Adopting a theory-based experimental approach, we explore whether aggregate uncertainty indeed favors the emergence of non-Duverger's law equilibria in plurality elections. Our experimental results support the main theoretical predictions.

Endogenous Candidacy in Electoral Competition: A Survey

We survey the literature on electoral competition under plurality rule where candidacy decisions are endogenous. We organize the differentcontributions into three families based on the paradigm to which they belong and on the part of the set of candidates they endogenize. We argue that endoegenous candidacy offers both theoretical and empirical advantages over the standard Hotelling-Downs model. On the theoretical front, these models can provide a more satisfactory microfoundation for the emergence and/or stability of the two party system under plurality rule. On the empirical front these models offer a better account of the stylized facts about elections, particularly regarding Duverger's law and policy polarization. We also point to shortcomings of these models and propose some directions for future research.

Electoral Competition Amongst Citizen-Candidates and Downsian Politicians

In this paper we study a model of political competition where citizens vote sincerely and candidates may be either citizens or Downsian politicians. The model extends the citizen-candidate model proposed by Osborne and Slivinski [1996] by including Downsian politicians similar to those studied by Osborne [1993]. We give necessary and sufficient conditions for existence, together with complete characterisation, of one party and two party Nash equilibria in our model. An important feature, in view of the Duverger's Law, of the two-party equilibrium is that these equilibria cannot have any Downsian contestant. Moreover, we compare our model with that studied by Osborne and Slivinski [1996], showing that in both cases there exist po- litical configurations that can appear in one of the models only. We show also that in our settings it is possible to have Nash equilibria with Downsian candidates, without requiring to have very restrictive constraints on the dis- tribution function. We also argue that as the number of parties in equilibrium increases, the `likelihood' of an ideology driven citizen-candidate winning the elections and running the government falls. Finally we argue that in any equilibrium extremist parties proposing their policies uniquely are typically ideology-driven as well.

Duverger's Law in mixed legislative systems: The impact of national electoral rules on district competition

AbstractHow do institutional factors shape district competition in mixed legislative systems? Preliminary evidence suggests the distinction between sub‐types of mixed systems alone poorly explains variation in district results. Consistent with the contamination thesis, this analysis suggests three additional national‐level factors at play: fused ballots, the electoral threshold for proportional representation seats, and the existence of compulsory voting laws. Regression analysis on an original dataset covering 90 mixed system elections in 23 countries (1990–2012) finds that while mixed member majoritarian systems correlate with fewer district candidates, these three often overlooked factors are also statistically significant. This analysis highlights the complexity of mixed systems and suggests why many of them diverge from Duverger's Law.

Is Duverger's Law Working in South Korea? An Analysis of District-Level Elections 1988–2012

How do electoral rules shape competition? District level data from South Korea's seven legislative elections since democratization (1988-2012) provides a means to test one of the oldest findings in political science: Duverger's Law. South Korea provides a unique opportunity to analyze variation in mixed election rules, where seats are allocated in both single member districts (SMDs) and by a nationwide party list by proportional representation (PR), as the country has used three different electoral formulas over the time period. Through quantitative analysis, evidence of a gradual reduction in the number of candidates is evident as is a more nuanced influence of regionalism on vote concentration.

How to Operationalize Two-Partyness

Because of the prominence of Duverger's law, a great deal of work has focused on assessing whether or not given election outcomes can be regarded as exhibiting two-party competition. The most common metric for assessment is whether the effective number of parties is close to two. We introduce two statistics that better measure conformity to two-partyness, briefly survey their logical properties, and then demonstrate their utility with data on parliamentary elections in England.

Duverger's Law and Regionalism : A Comparison of Korean and Japanese Elections

In the 19th National Assembly Election in Korea held in 2012, Democratic Unified Party, the second largest party, had to garner 1.05 times as many votes as Saenuri Party garnered, the first largest party, to win a local constituency seat. However, in Japanese Lower House election held in 2009, Liberal Democratic Party, the second largest party, had to acquire 2.82 times as many votes as Democratic Party, the first largest party acquired to win a local constituency seat. It is well known from the so-called “Duverger's law” that single member district system favors the largest party. Korea and Japan both use single member district system. But why is there so much difference in the advantage of the largest party in Korea and in Japan?

Why Just Two Parties? A Voting Game to Illustrate Duverger's Law

AbstractWith the 2012 presidential elections approaching, student interest in (and frustration with) the US two-party system is likely to grow. Although many explanations exist for this phenomenon, their number and complexity often overwhelm students. This article describes an iterative game, designed for a single class session, that illustrates one of the major institutional explanations for the US two-party system—Duverger's Law. The game can also spur discussion of some of the major criticisms of the Law.

Was Duverger Correct? Single-Member District Election Outcomes in Fifty-three Countries

In districts where only one seat is contested, the electoral formula (plurality or majority) should be a major determinant of the number of parties that receive votes. Specifically, plurality rule should generate two-party competition while other institutional arrangements should generate electoral fragmentation. Yet tests of these propositions using district-level data have focused on a limited number of cases; they rarely contrast different electoral systems and have reached mixed conclusions. This study analyses district-level data from 6,745 single-member district election contests from 53 democratic countries to test the evidence for Duverger's Law and Hypothesis. Double-ballot majoritarian systems have large numbers of candidates, as predicted, but while the average outcome under plurality rule is generally consistent with two-party competition, it is not perfectly so. The two largest parties typically dominate the districts (generally receiving more than 90 per cent of the vote), and there is very little support for parties finishing fourth or worse. Yet third-place parties do not completely disappear, and ethnic divisions shape party fragmentation levels, even under plurality rule. Finally, institutional rules that generate multiparty systems elsewhere in the country increase electoral fragmentation in single-member plurality districts.

Miscounts, Duverger's Law and Duverger's Hypothesis

In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small.All robust equilibria of plurality voting games satisfy Duverger's Law: In any robust equilibrium, exactly two candidates receive a positive number of votes. Moreover, robustness (only) rules out a victory of the Condorcet loser.All robust equilibria under runoff rule satisfy Duverger's Hypothesis: First round votes are (almost always) dispersed over more than two alternatives. Robustness has strong implications for equilibrium outcomes under runoff rule: For large parts of the parameter space, the robust equilibrium outcome is unique.

Seymour Martin Lipset and political sociology1

Seymour Martin Lipset and political sociology¹

The political context and Duverger's theory: Evidence at the district level

A central tenet of electoral systems' research is that more parties should get votes in districts with large magnitudes than in districts with smaller magnitudes. This proposition is largely untested at the district level, even though that is the level at which relevant pressures are expected to work. At the aggregate level, research has found that there are systematic deviations from Duverger's law related to incentives from ethnolinguistic fragmentation, institutions, and strategic voting. This analysis confirms that many of these results hold at the district level, which is the most appropriate level for testing Duverger's law. District level party-system fragmentation patterns in 44 countries support Duverger's basic hypotheses. The effect of electoral institutions is contingent, however, upon the presence of social cleavages that generate pressures for additional parties, the establishment of patterns of party-system competition that help voters evaluate contenders' viability, and the absence of competing incentives generated by districts of varying magnitudes. These effects are robust to different specifications of social heterogeneity. However, we find no evidence that institutional features like federalism or presidentialism reduce the strategic effects of district level factors.

Strategic Voting in Plurality Elections: A Simulation of Duverger's Law

Experiments designed as an election simulation involve participants in an investigation of strategic voting. Participants assigned political preferences and informed of candidate/party positions on an ideological dimension respond to and learn the results of two public opinion polls before voting. When given two alternatives, the participants vote sincerely. Confronted with three or more alternatives, participants make tactical decisions to narrow the field. Strategic behavior quickly reduces the number of alternatives to two. Consistent with Duverger's law, candidate/party viability encourages strategic voting and the development of a two-party system. The election simulation serves as a useful tool to teach about electoral behavior and to explore topics such as strategic voting.

Understanding Ukrainian Politics: Power, Politics, and Institutional Design by Paul D'Anieri , M. E. Sharpe (review)

Understanding Ukrainian Politics: Power, Politics, and Institutional Design by Paul D'Anieri , M. E. Sharpe (review)

Duverger's Law is Working in Japan

Duverger's Law is Working in Japan

The Impact of Taiwan’s 2008 Elections on Cross-Strait Relations: A Game-Theoretical Analysis

As an index case of Third-Wave democracies facing existential threat, Taiwan's elections entail important implications for study in comparative politics and international relations. In 2008, three important elections help define the course of Taiwan's democratic development and its relationship with China: the January legislative election, the March presidential election, and a controversial referendum on Taiwan's United Nations entry. This article employs theory to analyze the impact of Taiwan's 2008 elections on cross-strait relations. It develops an game by examining each principal player's preferences regarding each election. It analyzes Beijing's possible reaction to the potential outcomes, and then examines the actual election outcomes against the model and offers observations on the prospect of cross-strait relations. Overall, the model predicts that cross-strait relations after the 2008 elections will present a historic opportunity, which can be seized or squandered, depending on political leadership. Key words: China-Taiwan relations, Democracy - East Asia, East Asian politics Introduction: The Internal-External Nexus The year 2008 marks a turning point in Taiwan's democratic political development and cross-strait relations. A key reason for this prospect is the momentous elections that took place in this year. On January 12, a parliamentary election was conducted under a new, mixed electoral system that selected candidates from single-member districts (SMDs) through the firstpast- the-post (FPTP) method and from lists nominated by political parties. Taking the so-called Duverger's Law (i.e., that a correlation exists between the plurality method and a two-party system) 1 at its face value and hoping to emulate other states that have adopted a mixed electoral system (e.g., Japan),2 many analysts hoped this new electoral system would contribute to a more healthy electoral competition between the two centrist parties, the Kuomintang (KMT) and the Democratic Progressive Party (DPP). They also hoped this new system would reduce the influence of fringe candidates and money politics that became somewhat common under the old system of single non-transferable vote (SNTV) in multi-member districts (MMDs). On March 22, 2008, the presidential election, featuring the KMT's and the DPP's former chairmen, decided whether Taiwan's voters wanted a leader who will solidify the Taiwan or one who promises to improve the economy and ease crossstrait relations. That the identity issue became a key issue in these elections,3 as it had been in recent years, was an important reason why Taiwan's elections entail implications for its external relations, particularly vis-a-vis China and the United States, and for regional stability.4 The electoral link between Taiwan's domestic politics and its external relations was further accentuated by the two referenda regarding the issue of Taiwan's entry into the United Nations that were conducted on the same day as the presidential election. The DPP-sponsored referendum called for the country's entry into the UN under the name Taiwan. Not to be outdone by the DPP, the KMT sponsored a referendum calling for the country's return to the UN under flexible means. Various powers opposed the DPP's UN referendum, most significantly the United States, Taiwan's chief security backer.5 Chinese officials expressed their concerns that crossstrait relations during the lead-up to the March 2008 presidential elections might enter a high danger period. Passage of DPP's UN referendum would constitute a step toward a declaration of de jure independence of Taiwan.6 For China, such a declaration would be considered a major incident as defined in its Anti- Secession Law (ASL), and would call for a response using non- peaceful means.7 The United States, while stating that it did not oppose Taiwan's holding referenda, tried hard but to no avail to dissuade the DPP government from conducting the most controversial UN referendum, and, failing that, to appeal directly to voters. …

Poisson Games, Strategic Candidacy, and Duverger's Law

Duvergers law predicts a long-run two-candidate stable outcome under a plurality voting system. The waste vote argument explains the law by emphasizing strategic voters' tendency to abandon candidates commonly perceived to have the least support. However, the argument does not apply to cases where two or more candidates have the same least expected equilibrium vote share, so there is no unique candidate to abandon and a three-candidate equilibrium outcome is possible. We show that the incentive of candidates to strategically withdraw from elections in order to avoid extreme outcomes eliminates such non-Duvergerian equilibria. We model the election situation as a two-stage game where candidates first make strategic entry decisions, followed by plurality voting, which is modeled as a Poisson game a la Myerson (2000). In this framework with strategic voting, strategic candidacy, and uncertainty about voter preferences, Duverger's law is obtained except when there exists a Condorcet winner.

Leading the Party: Coordination, Direction, and Communication

Party activists face a coordination problem: a critical mass—a barrier to coordination—must advocate a single policy alternative if the party is to succeed. The need for direction is the degree to which the merits of the alternatives respond to the underlying fundamentals of the party's environment. An individual's ability to assess the fundamentals is his sense of direction. These three factors—the barriers to coordination, the need for direction, and an individual's sense of direction—combine to form an index of both the desirability and the feasibility of leadership. We offer insights into Michels' Iron Law: a sovereign party conference gives way to leadership by an individual or oligarchy if and only if the leadership index is sufficiently high. Leadership enhances the clarity of intraparty communication, but weakens the response of policy choices to the party's environment. Our model can also be applied to the coordination problems faced by instrumental voters in plurality-rule elections, and so relates to the psychological effect of Duverger's Law.