Plurality Rule Research Articles

Electoral formula, legal threshold and the number of parties

We exploit a rare natural experiment, a recent reform of local elections in Poland, to study an extension of Duverger’s laws. We analyse party system fragmentation under single-member plurality rule vis-à-vis a proportional representation formula accompanied by a legal threshold. We demonstrate that the presence of a threshold alters Duverger’s ‘psychological’ effect. Proportional representation with a threshold tends to be on a par with single-member plurality as regards restricting the effective number of electoral parties, largely due to the absence of smaller groupings with spatially concentrated support. At the same time, Duverger’s ‘mechanical’ effect takes a rather standard form, single-member plurality being relatively powerful at constraining the effective number of legislative parties.

Analysis of Dynamics of Voting System for Small Number of Candidates

A significant research topic in the area of Computational Social Choice is the complication of different kinds of dishonest behavior like manipulation, dominance and bribery. Whereas most of the work on this issue assumes that the opposite party has incomplete knowledge regarding every agent, they did not know the true preferences of other voters. We have analyzed the dynamics of voting rules with the help of some manipulative and non-manipulative moves. Voters have incomplete information. The voters are aware of the winner at every stage and they make short term rational decisions. The number of candidates and voters are small, and the decisions need to be made quickly. We want the better reply as low as possible while keeping the best reply as high as possible. The voting rules we have used are Plurality rule and Borda rule. We have analyzed the dynamics for these two voting rules for small number of voters and candidates.

A Model of Split-ticket Voting with Uncertainty

This paper models an on-year election in which the presidential and legislative elections are held simultaneously. The president is elected by plurality rule and each legislator is elected in single member districts by simple plurality rule. Policy outcomes are a function of not only which party holds the presidency but which party gets the majority of seats in the legislature. Parties are uncertain about the ideal points of the voters. With this model, we show that first, there are some ticket-splitters in every equilibrium, and second, there exists an equilibrium in which moderate voters split their votes between presidential and legislative elections. In addition, when we apply the equilibrium strategy into two-period election, we find this model also explains the midterm loss phenomena.

The Comparative Effects of Electoral Laws on Voter Rationality: Plurality versus Proportional Election Rules

Electoral rules inherently structure the development of not only a political party system, but also create incentives and disincentives for individuals to participate in politics. Few scholars study the interaction between various electoral arrangements and how they encourage or discourage voting based on the characteristics of individuals. This research uses the Comparative Study of Electoral Systems to investigate the relationship between plurality and proportional electoral arrangements, on the one hand, and how they influence levels of political knowledge, sophistication, and the likelihood to vote, on the other hand. The countries studied are the United States which uses simple plurality rules, Australia which employs the alternative vote with compulsory voting, and Ireland which uses the single transferable vote. We find that plurality electoral arrangements result in consistently lower levels of political knowledge and voter sophistication. Furthermore, low levels of knowledge but not sophistication reduce turnout in plurality systems. These decreased turnout levels are greatest among individuals with the lowest levels of political knowledge, where individuals experience the highest burdens of voting. Strikingly, turnout among the highest educated citizens in the United States is still lower than participation by the least educated in Ireland.

Which Matters Most: Party Strategic Exit or Voter Strategic Voting? A Laboratory Experiment

There is abundant empirical evidence that the plurality rule constrains party competition and favors two-party systems. This reduction of party system fragmentation may be due to parties deciding not to enter elections for which they are not viable and/or voters voting strategically. Yet, no prior research has attempted to estimate the respective role of parties and voters in this process. To fill this gap, we conducted a unique laboratory experiment where some subjects played the role of parties and others played the role of voters, and where the two were able to respond to each other just as in real-life elections. We find that the reduction due to party strategic exit is higher than that due to strategic voting. We conclude that parties play a key role in the effect of the plurality rule on party system fragmentation.

Strategic voting in the 2011 and 2015 Polish Senate elections: Testing Duvergerʼs Law in the second-order elections

AbstractThis article tests Duverger’s law through analysis of the Polish Senate elections in 2011 and 2015. These two elections were held under the new first-past-the-post (or single-member plurality) system, which replaced formerly used unlimited vote. The main aim of the article is to test, whether we can confirm the expectations of strategic voting in the context of the so-called second-order elections, as the Polish Parliament is a classical example of the asymmetrical bicameralism, with the secondary role of the upper chamber, the Senate. The results show that the strategic voting was not universal phenomenon under the plurality rule, as indicated by many violations of Duverger’s law. Our research confirmed that the effect of electoral institutions (institutional structure) is contingent and (at the district level) inhibited by country-specific conditions, with potentially strong influence of the second-order character of the Polish Senate elections.

Contra Koza

Three of our arguments drew no objection from Dr. Koza. One is that plurality rule—the heart of his proposed reform—can be anti-majoritarian. In our three-candidate example, Libby was the plurality favorite but Maude beat each of her rivals, Libby included, by a majority. A plurality can be a majority, of course, but the Electoral College has never reversed a popular majority.

A Calamitous Compact

ABSTRACTThe National Popular Vote Interstate Compact (joined so far by ten states and DC) would replace the current presidential-election system, based on the electoral college and the winner-take-all rule, with nationwide plurality rule, and it would do so by changes in state law, not a Constitutional amendment. The mischief that would create (especially procedural instability, noncompliant electors, nation-wide recounts, vote manipulation, and narrowed support), the compact’s questionable Constitutionality, the weakness of its defense, and the availability of less calamitous alternatives are reasons enough to reject it.

Approval voting and scoring rules with common values

We compare approval voting with other scoring rules for environments with common values and private information. For finite electorates, the best equilibrium under approval voting is superior to plurality rule or negative voting. For large electorates, if any scoring rule yields a sequence of equilibria that efficiently aggregates information, then approval voting must do so as well.

Strategic party formation on a circle and Duverger’s Law

Duverger’s Law states that plurality rule tends to favor a two-party system. We study the game-theoretic foundations of this law in a spatial model of party formation and electoral competition. The standard spatial model assumes a linear agenda space. However, when voters vote sincerely, electoral competition on the line under plurality rule gravitates towards a single party located at the median. We therefore depart from the linear space and instead adopt the unit circle as the space of agendas. We characterize pure-strategy (subgame-perfect) Nash equilibria under both sincere and strategic voting. Under both voting behaviors, multiple configurations of parties are possible in equilibrium. We refine our predictions using a new notion called defection-proof (subgame-perfect) Nash equilibrium. Under sincere voting, either two or three parties are effective in defection-proof Nash equilibria, whereas under strategic voting, either one or two parties are effective in defection-proof subgame-perfect Nash equilibria. These results are partially consistent with Duverger’s Law.

Voting in legislative elections under plurality rule

Models of single district plurality elections show that with three parties anything can happen – extreme policies can win regardless of voter preferences. I show that when single district elections are used to fill a legislature, we get back to a world where the median voter matters. An extreme policy will generally only come about if it is preferred to a more moderate policy by the median voter in a majority of districts. The mere existence of a centrist party can lead to moderate outcomes even if the party itself wins few seats. I also show that, while some voters in a district will not vote for their nationally preferred party, in many equilibria they will want the candidate for whom they vote to win that district. This is never the case in single district elections. There, some voters always want the candidate they voted for to lose.

Invalid Voting in German Constituencies

This article studies invalid voting, which has received very little attention so far, given the broad interest and substantial relevance of voting behaviour research. Existing evidence is mostly limited to rather specific and hardly representative countries. Yet, the extent of invalid ballots is not negligible. Despite undemanding electoral rules, more invalid votes are cast in German general elections than votes for niche parties. Against this backdrop, the article describes prevalence of invalid voting in the mixed electoral system of Germany and tests explanations of its variation between constituencies. Analysing data from the most recent Bundestag Election, results give clear support to politico-institutional explanations: voters are more willing to waste their vote if second-order elections are held concurrently. Specifically under the plurality rule, more (first) votes are wasted if there are large shares for parties without direct candidates and many competing candidates.

Characterizing plurality rule on a fixed population

Plurality rule on a fixed population is characterized by anonymity, neutrality, tops-only and a monotonicity property.

A Strategy‐Proofness Characterization of Plurality Rule

AbstractAssuming at least four individuals and at least four alternatives, a social choice function on the domain of profiles at which there is an alternative ranked first by more individuals than any other alternative is nondictatorial, strategy‐proof, and has full range if and only if it is plurality rule.

National sovereignty and lawmaking

Abstract A democratic state involves the existence of a fundamental Law which expressly states values and democratic principles that are universally, internationally and regionally recognized. Specialized literature has shown that the mission of the modern state can only be fulfilled by a public power that is its essential characteristic, namely, through sovereignty [1]. The connection between sovereignty and political power is reflected in the complex relationships between the principle of separation and balance of powers, rule of law, political pluralism and state institutions and organizations.

Party nationalization and the translation of votes into seats under single-member plurality electoral rules

This study uses empirical evidence from a nearly comprehensive set of electoral democracies that use single-member plurality systems or mixed electoral systems with single-member plurality components in order to establish empirically the impact of territorial patterns of electoral support upon vote-to-seat conversion. The analysis, employing individual parties as units of analysis and multiple linear regression with cluster-robust standard errors as its main methodological tool, confirms the hypothesis that single-member plurality rules give a representational bonus to parties with low levels of nationalization. This effect is contingent upon absolute and relative party size, so that very large parties, and particularly frontrunners in party competition, receive an advantage irrespective of their nationalization. Mixed electoral rules further facilitate their advantage, while the gains of very small parties tend to be enhanced by large assembly size. These findings contribute to a better understanding of the dynamics of party system development under Duvergerian conditions.

A decomposition of strategy-proofness

Strategy-proofness has been one of the central axioms in the theory of social choice. However, strategy-proofness often leads to impossibility results. We find that strategy-proofness is decomposed into three axioms: top-restricted AM-proofness, weak monotonicity, and individual bounded response. We present possibility results by dropping individual bounded response from strategy-proofness. One of the results supports the plurality rule which is one of the most widely used rules in practice.

A note on Approval Voting and electing the Condorcet loser

Analytical representations are developed for the probability that Approval Voting (AV) elects the Condorcet Loser in three-alternative elections with large electorates. A comparison of AV is then made to Plurality Rule (PR) to show that AV is much less susceptible to the risk of electing the Condorcet loser than PR. All calculations in this analysis are based on IAC-like assumptions.

Further Support for Ranking Candidates in Elections

We compare the Condorcet Efficiencies of the plurality rule, the negative plurality rule, and the Borda rule to examine what might be gained by using a voting rule that requires candidate rankings. Previous analyses have considered (1) voting situations for which the three rules determine different candidates as winners (and the Condorcet Efficiencies might actually differ across the three rules) as well as (2) refined measures of Group Mutual Coherence that assess the presence of underlying models of rational behavior that governs voter preferences. In this paper, we present the final step of this particular line of analysis by analyzing (1) and (2) simultaneously. We conclude that there is a considerable benefit on the basis of Condorcet Efficiency from asking voters to submit candidate rankings in three-candidate elections.

Multiwinner Analogues of the Plurality Rule: Axiomatic and Algorithmic Perspectives

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (i.e., the problem of computing the winners is NP-hard), but we also show some examples of polynomial-time winner determination procedures, exact and approximate.