Duverger's Law Research Articles

Turnout, Polarization, and Duverger's Law

We reexamine the impact of abstention due to alienationon policy outcomes and the choices of strategic candidates. We establish the existence of a unique equilibrium under plurality rule in which only two candidates enter, choose divergent policy positions, and deter subsequent entry. This equilibrium is simultaneously consistent with the dual empirical regularities of Duverger's Law and policy divergence. Driving our results is the observation that when abstention is included, a third candidate optimally enters the election by differentiating himself from the incumbent candidates, consistent with entry observed in practice. Our results confirm that not only are the platforms of candidates important to the turnout decisions of voters, but that the turnout decisions of voters are important to platform positions. The model provides a causal mechanism linking these two variables, offering a theoretical basis for the decrease in turnout and increase in polarization experienced in the United States after the 1...

Ballot Regulations and Multiparty Politics in the States

American politics is dominated by two major parties and has been for a century. The duopoly enjoyed by the Democrats and Republicans is largely the result of Duverger's Law: the tendency of a single-member district system to produce two-party competition (Duverger 1963). Minor parties ultimately fail in a single-member district system because (1) the winner-take-all approach does not reward candidates who finish third and (2) citizens vote strategically to avoid “wasting” their votes on hopeless candidates and spoiling the election (Cox 1997; Riker 1982). Because the U.S. two-party system is so dependent on its majoritarian electoral rules, one might suspect that other election regulations would have little effect on the number of parties. A longer version of this paper was presented at the conference, “2008 and Beyond: The Future of Election and Ethics Reform in the States,” Columbus, OH, January 16–17, 2007. I thank Richard Winger ofBallot Access Newsfor comments and information.

WHEN TO RUN AND WHEN TO HIDE: ELECTORAL COORDINATION AND EXIT

Elections represent a coordination problem for voters and candidates for office. Electoral coordination is also the causal mechanism behind any explanation of the relationship between electoral systems and the number of parties. I present a dynamic model of electoral coordination with candidate exit. The model extends two important results from the literature to a dynamic setting. The extension of Duverger's Law and the median‐voter theorem also offers a simultaneous prediction of the number of parties and their ideological positions. Coordination failure is shown to be possible in a mixed‐strategy equilibrium.

Duverger's Law and the Size of the Indian Party System

Duverger's law postulates that single-member plurality electoral systems lead to two-party systems. Existing scholarship regards India as an exception to this law at national level, but not at district level. This study tests the latter hypothesis through analysis of a comprehensive dataset covering Indian parliamentary elections in the period 1952—2004. The results show that a large number of Indian districts do not conform to the Duvergerian norm of two-party competition, and that there is no consistent movement towards the Duvergerian equilibrium. Furthermore, inter-region and inter-state variations in the size of district-level party systems make it difficult to generalize about the application of Duverger's law to the Indian case. The study concludes that a narrow focus on electoral rules is inadequate, and that a more comprehensive set of explanatory variables is needed to explain the size of the Indian party system even at the district level.

Strategic Voting Under Conditions of Uncertainty: A Re-Evaluation of Duverger's Law

Political scientists have long recognized that the number of parties in a country influences the way that interests are represented in that country. One explanation for the number of parties in a system relies on the idea of strategic voting, i.e. voters may not want to ‘waste a vote’ by voting for a third party. However, work in this area does not address the role of an important factor that may affect party systems through strategic voting: information. Without polls, how could voters know which parties were likely to win, and hence how to vote strategically? Using an agent-based model, this article assesses the role that information plays in shaping the party system through strategic voting. The results of this model demonstrate that, contrary to Duverger's Law, more than two parties may emerge in single-member plurality systems, even when all voters are strategic.

Population Uncertainty and Duverger's Law

We show that the waste vote argument in Palfrey (1989) has to be complemented by strategic candidacy to fully explain Duverger's law. Using distributional strategies, we completely characterize the set of limit Bayesian voting equilibria in the presence of population uncertainty. The waste vote argument is in full force to induce the Duvergerian outcomes when one candidate has the least expected vote share in equilibrium. When more than two candidates equally trail in equilibrium vote shares, extreme aversion drives some non-centrist candidate to strategically withdraw from the election. Thus, strategic candidacy restores the Duvergerian two-party equilibrium in case when the waste vote argument fails to work.

On the Theory of Strategic Voting1

Many analyses of plurality-rule elections predict the complete coor- dination of strategic voting, and hence support for only two candidates. Here I suggest that stable multi-candidate support will arise in equilibrium. A group of voters must partially coordinate behind one of two challenging candidates in order to dislodge a disliked incumbent. In a departure from existing models, the popular support for each challenger is uncertain. This support must be inferred from the private observation of informative signals, such as the social communication of pref- erences throughout the electorate, or the imperfect observation of opinion polls. The uniquely stable voting equilibrium entails only limited strategic voting and hence incomplete coordination. This is due to the surprising presence of negative feed- back: an increase in the degree of strategic voting by others reduces the incentives for an individual to vote strategically. The incentive to vote strategically is lower in relatively marginal elections, after controlling for the distance from contention of a trailing preferred challenger. A calibration of the model applied to the UK General Election of 1997 is consistent with the impact of strategic voting and the reported accuracy of voters' understanding of the electoral situation. It suggests that nearly 50 seats may have been lost by the Conservative party due to strategic voting. 1. Plurality-Rule Elections and Strategic Voting 1.1. Strategic Voting and Duverger's Law. Plurality-rule elections, where the winner is the candidate who receives the largest number of votes, are vulnerable to strategic voting: a voter might well switch away from her preferred candidate and toward a perceived leader, in the hope of exerting a greater influence over the outcome of the election. This phenomenon has long been the focus of both economic and political scientific study. In an influential essay, Riker (1982b) cited Droop's (1871) eloquent exposition of the strategic-voting problem: 1 I oer my grateful thanks to the many friends, colleagues, seminar participants, referees, and editors who have oered insightful comments during the long gestation of this paper, its antecedents, and companion work. Special thanks go to Steve Fisher, whose empirical analysis of strategic voting raised many of the questions that I seek to answer in this paper, and to Chris Wallace. This particular paper brings together much of the analysis previously circulated in the papers A New Theory of Strategic Voting, Strategic Voting Under the Qualified Majority Rule, and Idiosyncrasy, Information, and the Impact of Strategic Voting.

Strategic voting in Canada: A Cross Time Analysis

Canada seems to refute Duverger's Law by sustaining more than two political parties in a plurality system, suggesting that Canadian voters do not utilize the “wasted vote” calculus. However, many studies have found evidence of strategic voting in the electorate, although the work is limited because scholars have typically tested varying models at single points in time. This paper uses data from Canadian federal elections from 1988 to 2000 to test the expected utility model, developed by McKelvey and Ordeshook (1972), on those with an incentive to vote strategically across all four elections. We extend the model to test hypotheses related to party system changes and individual factors (minor party support and political sophistication). Our findings strongly support the model and many of the individual level hypotheses, although the results pertaining to the system level hypotheses are mixed.

Duverger's Law and the Study of Electoral Systems

Since its first publication in 1951, Duverger's Political Parties has influenced an entire branch of political science devoted to the study of the political consequences of electoral laws. This essay examines the two propositions known as Duverger's law and Duverger's hypothesis, both concerned with how electoral institutions shape party systems. First explaining the propositions and their context, the essay examines their influence on political science, and concludes by assessing where future research in the area might be best concentrated.

Maurice Duverger and the Study of Political Parties

Over a half century's experience with Duverger's Les Partis Politiques offers an opportunity to test his theory. His explanations for the numbers of parties survives as Duverger's Law, while his predictions for the development of the ‘membership party’ have not. Since the two rest on divergent explanations of electoral politics, the success of one and the failure of the other present an excellent test of our theories of electoral politics. Duverger's explanation of the numbers of parties understands free elections as markets in which candidates and voters alter their behavior as they try to get as close as possible to their preferred outcome. Duverger, in contrast, saw party organization as a product of ‘social forces’, notably the composition of the electorate. The ‘cadre’ party was the product of limited suffrage, while universal suffrage would lead to the ‘mass-based membership’ party. Given that the latter never developed, we argue that the logic Duverger applied to the numbers of parties also applies to their organization. We note how periodic free elections create markets where individuals pursue three fundamental political drives: ambition, choice, and benefits; whatever political organization develops, must respond to these three drives.

The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India, and the United States

The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India, and the United States, Pradeep K. Chhibber and Ken Kollman, Princeton: Princeton University Press, 2004, pp. xvi, 276.Mining electoral data to arrive at theories about the relationship between political party performance and party system determination and electoral and governmental institutions forms the main stream of political science. And one of its most enduring puzzles is the explanation of the patterns and diversities of party systems. With the famous “Duverger's Law” about single-member plurality systems and two-party political systems forming its point of departure, political scientists have attempted to substantiate their discipline's status as a “science” by producing theories about relationships between measurable political variables.

Robust Political Equilibria Under Plurality and Runoff Rule

A central problem for the game theoretic analysis of voting is that voting games have very many Nash equilibria. In this paper, we consider a new refinement concept for voting games that combines two ideas that appear reasonable for voting games: First, trembling hand perfection (voters sometimes make mistakes when casting their vote) and second, coordination of voters with similar interests. We apply this refinement to an analysis of multicandidate elections under plurality rule and runoff rule. For plurality rule, we show that our refinement implies Duverger's law: In all equilibria, (at most) two candidates receive a positive number of votes. For the case of 3 candidates, we can completely characterize the set of equilibria. Often, there exists a unique equilibrium satisfying our refinement; surprisingly, this is even true, if there is no Condorcet winner. We also consider the equilibria under a runoff rule and analyze when plurality rule and runoff rule yield different outcomes.

Duverger's Law, Penrose's Power Index and the Unity of the UK

As predicted by Duverger's Law, the UK has had two-party competition for long periods in most electoral districts. However, there are different patterns of two-party competition in different districts and more than two effective parties in the Commons. Since 1874, parliament has always contained parties wishing to modify the Union and contesting seats only outside England. By calculating the Penrose power index for all parties in the House of Commons for all general elections since 1874, we identify when such parties were pivotal. We explain various legislative changes (for example the Crofters Act 1886, the first three Irish Home Rule Bills, the Parliament Act 1911) and non-changes (for example the failure to enact female suffrage before 1914) by reference to the Penrose index scores. The scores also explain how and why policy towards Scotland, Wales and Northern Ireland changed and did not change in the 1970s.

Approval voting with endogenous candidates

We present a formal model of political competition under approval voting which allows for endogenous candidate entry. Our analysis yields a number of novel insights. First, we develop a notion of sincere voting behavior under approval voting, called relative sincerity. We then show that the relatively sincere voting behavior is consistent with the strategic calculus of voting. Second, we show that in a one-dimensional model with distance preferences, equilibria in relatively sincere strategies and without spoiler candidates always generate outcomes close to the median voter. Moreover, approval voting satisfies Duverger's Law in the sense that there are at most two winning positions! Finally, we extend our analysis to arbitrary policy spaces. In the general setting, approval voting is shown to be susceptible to the same kinds of problems as the plurality rule, such as the possibility of non-majoritarian outcomes, failure to elect the Condorcet winner and existence of spoiler candidates.

It's Parties that Choose Electoral Systems (or Duverger's Law Upside Down)

This article presents, discusses and tests the hypothesis that it is the number of parties what can explain the choice of electoral systems, rather than the other way round. Already existing political parties tend to choose electoral systems that, rather than generate new party systems by themselves, will crystallize, consolidate or reinforce previously existing party configurations. A general model develops the argument and presents the concept of 'behavioral-institutional equilibrium' to account for the relation between electoral systems and party systems. The most comprehensive dataset and test of these notions to date, encompassing 219 elections in 87 countries since the 19th century, are presented. The analysis gives strong support to the hypotheses that political party configurations dominated by a few parties tend to establish majority rule electoral systems, while multiparty systems already existed before the introduction of proportional representation. It also offers the new theoretical proposition that strategic party choice of electoral systems leads to a general trend toward proportional representation over time.

Duverger's law: An application to local elections in Britain

Duverger's law: An application to local elections in Britain

Why Vote for Losers?

Voting theory generally concludes that, in first-past-the-post elections, all votes should go to effective candidates (Duverger's Law), and parties should adopt a similar platform (median voter theorem). However, such predictions are not always met in practice. We show why divergence and vote dispersion is a natural outcome when (a) parties are opportunistic, (b) there is uncertainty on the position of the median voter and (c) elections are repeated. “Voting for losers” increases the informational content of elections, and may induce mainstream parties to relocate towards extremists. As a result, to maximize their probability of being elected, they do not adopt median platforms, but instead diverge to a certain extent.

What Mechanism Causes the M + 1 Rule? A Simple Simulation

The M + 1 Rule, that at equilibrium there should be only one more candidate running than seats available, extended Duverger's Law to the cases of more than one seat per district. Both the M + 1 rule and Duverger's Law have been confirmed repeatedly, albeit always with qualification. Yet we have reached no consensus on the mechanism that produces these two empirical regularities. In this paper I use a simple simulation to test the hypothesis that the mechanism is that candidates retire after some fixed number of consecutive losses. I test the results of the simulation against several different empirical results and find a reasonably good fit. I also add a mechanism for increasing the number of candidates. These results suggest that the M + 1 rule and Duverger's law may be the result not of rational calculation but of some simple set of decision rules. The analysis also illustrates the usefulness of a simulation approach to hypothesis testing.

Unexpected Outcomes: Electoral Systems, Political Parties, and Representation in Russia by Robert s> Moser (review)

376 SEER, 8i, 2, 2003 this book is warmly welcomed by both Central Asian specialists and transitologistsalike. Department ofPolitics J.GLENN Universityof Southampton Moser, Robert. Unexpected Outcomes. ElectoralSystems,Political Parties,and Representation inRussia.Pitt Seriesin Russian and East European Studies. University of PittsburghPress,Pittsburgh,PA, 200I. X+ 183 pp. Tables. Notes. Index. $I9.95 (paperback). ONE of the more welcome byproductsof the end of Communist rule has been the erosion or even disappearance of long-established boundaries between 'area'and 'discipline'.In most cases, specialistsin voting, legislativebehaviour or whatever else have simply added one or more of the post-Communist countries to their list of examples. But in other cases there has been a team approach, combining the skillsof the mainstreamsocial scientistwith those of an area expert. In just a few cases, of which Robert Moser's book is an excellent example, the study of the area has led in the reverse direction, to conclusions that will require some reconsideration in the parent discipline. Moser'sconcern isthe politicaleffectsof electoralsystems,a subjectpioneered by Maurice Duverger. Yet, he finds, Duverger's Law fails to work in postCommunistRussia ;andgiven thattheRussianexperiencemaybe increasingly typicalof countriesthat are currentlydemocratizing,it is comparativepolitics itselfthat needs to make the adjustment. This is a book for specialists, and some of what the author conveys will already be known to them through parts of his chapters that have appeared elsewhere.Itscentralfocus isthe effectsof electoralsystemson politicalparties and representation, not just in Russia but on a broader comparative basis. Since I993, Russia has had a mixed electoral system consisting equally of deputies elected through a party-list contest across the country as a whole, and of deputies elected by simple majority in single-member constituencies. The outcome, in Russia, has confounded political science orthodoxy; the reason, Moser suggests,is the weak institutionalizationof political parties. In other words, 'institutionsmatter',but so does the social context;or, as he puts it himself, the 'institutionaleffects of electoral systems are dependent on the social contexts in which they operate' (p. 55) There are challengesto the comparativeliteraturein otherchaptersaswell. Women, for instance, should have been expected to secure a greater share of representation in the party-list contest, in which seats are shared out in proportion to the nationalvote; but in fact, in three elections, they have done better in single-memberconstituencies.There is a chapteron the effectsof the electoral system on the representation of ethnic minorities in fact, fairly minimal;and a chapteron the I996 presidentialcontest, where the numberof candidatesdoes appearto have been constrainedby the electoralsystemitself. Presidentialismas such is less satisfactorilyconceived in thisbook:notjust the effectsof the electoralsystemon an individualcontest,but the implicationsfor REVIEWS 377 party competition of a system in which a directly elected president is the dominant political actor. There are severalplaces in which furtherresearchis required. One of these is at the level of vote choice in single member constituencies. Earlierresearch has suggested that party affiliationis a very minor consideration for electors, but this may be changing (in a national survey conducted in spring 200 I, a colleague and I found that candidates with a known party affiliationwould gain about twice as much as they would lose, but largernumberssaid it would make no differenceor that they would find it hard to say).Not the least of the virtues of this challenging book is that it encourages the formulation of such questions in a rigorous way, and in the light of the comparative evidence. Could one reasonablyaskfor more? lUniversity ofGlasgow STEPHEN WHITE Jeffries, Ian. TheNewRussia.A Handbook ofEconomic andPoliticalDevelopments. RoutledgeCurzon, London, 2002. xii + 643 pp. Tables. Bibliography. Index. [95.00. SINCE the collapse of the Soviet Union, the scholarlycommunity has found it extremely difficult to keep pace with the constant changes in the Russian Federation. Although a large amount of literature has been published discussing the various nuances of post-Soviet Russia, a paucity of literature has attempted to lay out the full range of events that constitute the postsocialistexperience of the Russian Federation.The dynamic nature of events in the region in the last ten years makes cataloguing such developments extremely difficult. Nevertheless, with TheJNfew Russia,Ian Jeifries makes a serious effort to offer a detailed and timely review of economic and political developments in post...

Why Vote for Losers?

Theory generally concludes that -in first-past-the-post elections- 1) All votes should go to effective candidates (Duverger's Law); 2) Parties' platforms should converge (Median Voter Theorem). Observations, though, suggest that such predictions are not met in practice. We show that divergence and dispersion of votes is a natural election outcome when there is uncertainty and repetition of elections. Voting for Losers increases the informational content of elections, and forces main parties to relocate towards extremists. As a result, parties maximize their probability of being elected, not by converging to the median but by diverging to a certain extent. Ideological behavior (divergence) results then from optimizing considerations alone.