An assessment of voting systems under the proximity and directional models of the vote

I evaluate five single-winner voting systems according to their tendency to elect Condorcet candidates under alternative models of issue voting derived from behavioral research. These behavioral models posit that voters have both issue and nonissue motivations; within this framework, I study the effects of both the directional and proximity voting models, with varying degrees of issue voting. Under the proximity metric, all voting systems are most efficient when voters attach little importance to issues, while the opposite is generally the case under directional voting. In contrast to previous results, voting systems tend to be more efficient for large than for small electorates. All voting systems – including the widely-criticized plurality method – are extremely efficient when voters in mass elections are inattentive to issues.     

Frequency of paradox in a common n-winner voting scheme

This paper investigates the extent to which a commonly used electoral scheme — voting for n candidates when there are n vacancies to fill — is likely to lead, in practice, to paradoxical results. Two types of paradox are investigated. One occurs when an increase in the number of vacancies causes a candidate to drop from the list of winners. The second occurs when the Condorcet candidate fails to win. Using a Monte Carlo study, we show that the likelihood of paradox can be substantial and depends critically on the degree of homogeneity of voters' preferences and on the number of voters.     

If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule

We consider four factors relevant to picking a voting rule to be used to select a single candidate from among a set of choices: (1) avoidance of Condorcet losers, (2) choice of Condorcet winners, (3) resistance to manipulability via strategic voting, (4) simplicity. However, we do not try to evaluate all voting rules that might be used to select a single alternative. Rather, our focus is restricted to a comparison between a rule which, under the name ‘instant runoff,’ has recently been pushed by electoral reformers in the US to replace plurality-based elections, and which has been advocated for use in plural societies as a means of mitigating ethnic conflict; and another similar rule, the ‘Coombs rule.’ In both rules, voters are required to rank order candidates. Using the instant runoff, the candidate with the fewest first place votes is eliminated; while under the Coombs rule, the candidate with the most last place votes is eliminated. The instant runoff is familiar to electoral system specialists under the name ‘alternative vote’ (i.e., the single transferable vote restricted to choice of a single candidate). The Coombs rule has gone virtually unmentioned in the electoral systems literature (see, however, Chamberlin et al., 1984). Rather than considering the properties of these two rules in the abstract, we evaluate them in the politically realistic situations where voters are posited to have (at least on balance) single-peaked preferences over alternatives. Evaluating the two rules under this assumption, we argue that the Coombs rule is directly comparable in that Coombs is always as good as AV with respect to two of our four criteria and it is clearly superior to AV with respect to one of the four criteria, namely criterion (2), and is potentially inferior only with respect to criterion (3). Key to this argument are two new propositions. The first new result shows that, under the posited assumption, for four alternatives or fewer, AV is always as likely or more likely to select the Condorcet winner than plurality. The second new result shows that, under the same assumptions, the Coombs rule will always select the Condorcet winner regardless of the number of alternatives.     

Trading places

This paper examines effects that alternative voting systems can have on electoral outcomes in multicandidate elections. Using ballots collected from a county Republican Party special election, we recount the votes using preference-based voting systems and compare the results to the special election outcome. Relative rankings of candidates change across vote counting rules and voting systems. Because candidates trade places depending on rules, there are strong strategic implications for candidates and for those establishing the rules.     

Preference votes without preference? Institutional effects on preference voting: an experiment

A classical question of political science is to what extent electoral systems influence voting behaviour. Yet, many of these studies examine how different electoral systems affect the election results in terms of vote distribution across parties. Instead, we investigate how electoral rules affect intra party preference voting. Given the importance of the debate on the personalization of politics, insight into how electoral rules shape intra-party choice is a valuable contribution to the literature. In our study, we focus on the effect of two specific rules: the option to cast a list vote and on a single versus multiple preference votes. The results of experiments conducted in Belgium and the Netherlands show that electoral rules indeed influence voting behaviour with regard to intra party preference voting, although differences exist between the Netherlands and Belgium. Moreover, we find that the option to cast a list vote equally affects votes for the first candidate on the list, as well as lower positioned candidates. This suggests that preference votes might be less preferential than has often been assumed.     

Approval voting,Condorcet's principle,and runoff elections

Approval voting allows each voter to vote for as many candidates as he wishes in an election but not cast more than one vote for each candidate of whom he approves. If there is a strict Condorcet candidate — a candidate who defeats all others in pairwise contests — approval voting is shown to be the only nonranked voting system that is always able to elect the strict Condorcet candidate when voters use sincere admissible strategies. Moreover, if a strict Condorcet candidate must be elected under ordinary plurality voting when voters use admissible strategies, then he must also be elected under approval voting when voters use admissible strategies, but the converse does not hold. The widely used plurality runoff method can also elect a strict Condorcet candidate when voters use admissible strategies on the first ballot, but some of these may have to be insincere to get the strict Condorcet candidate onto the runoff ballot. Furthermore, there is no case in which the strict Condorcet candidate is invariably elected under the plurality runoff method when voters use admissible first-ballot strategies. Thus, approval voting is superior to the plurality runoff method with respect to the Condorcet principle in its ability to elect the strict Condorcet candidate by sincere voting and in its ability to guarantee the election of the strict Condorcet candidate when voters use admissible strategies. In addition, approval voting is more efficient since it requires only one election and is probably less subject to strategic manipulation.     

Dead Heat: The 2006 Public Choice Society Election

In 2006, the Public Choice Society chose a new president using approval voting. There were five candidates, and the election was extremely close. We indicate the sources of support of the different candidates, based in part on spectral analysis, by voters who cast between one and five votes. Using preference information that was also gathered, we show that two candidates different from the approval voting winner, including the apparent Condorcet winner, might have won under different voting systems. Because most voters did not indicate their complete preference rankings, however, these differences are hardly robust, especially since the outcome was essentially a dead heat.     

Some properties of Hare voting with strategic voters

From the perspective of some common criteria for evaluating voting procedures, the results we offer in this essay will almost certainly be interpreted as inditments of STV. Even if we restrict preferences with conditions R1 and R2, STV is not necessarily incentive compatible. Moreover, strategic voting does not ensure the selection of Condorcet winning candidates or of Condorcet outcomes. This fact, moreover is not dependent on the existence of bogus equilibria — outcomes that exclude Condorcet candidates cannot be avoided under all circumstances even if we limit our analysis to strong or to individually stable equilibria.It is not the case, though, that the Condorcet criterion is the unique or even the most important criterion with which to evaluate election procedures. For example, we have not examined the extent to which STV ensures proportionality and we have not compared STV to other procedures. Despite the apparent deficiencies described in this essay, STV may yet prove to be a viable alternative to systems that seek to ensure proportionality by other means.     

Do voters really prefer more choice? Determinants of support for personalised electoral systems

Which voters prefer having more choice between parties and candidates in an election? To provide an answer to this question, we analyse the case of a radical change from a closed-list PR system to a highly complex open-list PR system with cumulative voting in the German states of Bremen and Hamburg. We argue that the approval of a personalised electoral system is structured in similar ways as support for direct democracy. Using representative surveys conducted prior to all four state elections under cumulative voting in 2011 and 2015, we analyse which individual factors determine the approval, disapproval, or indifference towards the new electoral law. The results indicate that younger voters as well as supporters of left parties are much more likely to support a personalised electoral system. In contrast to previous studies, political interest only has an impact on the indifference towards the electoral system. More generally, our results show that a large proportion of voters does not appreciate personalised preferential electoral systems which seems to be a result of the complexity and magnitude of choice between parties and candidates.     

Selecting the Condorcet Winner: single-stage versus multi-stage voting rules

In this paper, I study elections where voters are strategic. I find that the commonly used voting rules, such as Plurality Rule, Majority Rule, Approval Voting, and Single Transferable Vote, do not always select the Condorcet Winner and suffer from multiple equilibria. Multi-stage voting rules offer a way to get around this problem. I introduce two voting rules—Multi-Stage Runoff and the Nominate-Two Rule—that select the Condorcet Winner as the unique equilibrium outcome under mild conditions. I show that a third class of voting rules—Binary Voting Trees—also select the Condorcet Winner.     

Condorcet Polling

For a single-winner multi-candidate election, it is broadly accepted that the Condorcet candidate (if one exists) should win. Voting systems do not always elect the Condorcet winner. Public opinion polls are not generally designed to try to identify a Condorcet candidate. They could easily be constructed to do so, however. The resulting process may be called Condorcet polling, for which various designs are presented herein. Information from Condorcet polling may enable some voters, under a plurality or runoff system, to bring about an outcome they prefer by voting strategically for the Condorcet candidate when they would not otherwise do so.     

Income-based voting and polarization over redistribution under alternative electoral systems

Democracies that have proportional electoral systems spend substantively more on welfare policies than those that have majoritarian systems. Theoretical accounts of this empirical regularity are generally tested using macro-level data, leaving micro-level implications untested. In this paper, I take an alternative approach, leveraging the fact that the theories in question make predictions about the electoral coordination between parties and voters around broad-based redistribution under alternative institutional arrangements. To test the theories, I create a novel measure of income-based voting, which captures the sensitivity of vote choice to changes in income and forms the dependent variable in a second stage model. Overall, I find robust support for more proportionality leading to more income-based voting.     

Tacit co-operation in three-alternative non-cooperative voting games: A new model of sophisticated behaviour under the plurality procedure

Two models, one due to Farquharson and the other to Niemi-Frank, attempt to account for sophisticated voting behaviour when the voters' preference orderings are common knowledge and communication among Voters is impossible. Having subjected these two models to experimental testing, we have found them lacking. Hence, we propose a new model of sophisticated voting for 3-alternative n-person non-cooperative games under the plurality procedure, which can be extended to other voting procedures and more than three alternatives.The model assumes that voters whose first preference is (one of) the Condorcet winner(s) will (tacitly) co-ordinate their strategies and vote for their first preference, and specifies the conditions under which voters whose second preference is (one of) the Condorcet winner(s) will vote for their second (rather than their first) preference. Consequently, our model predicts that: (i) if there is a single Condorcet winner he or she will be elected; (ii) if there is more than one Condorcet winner the final outcome will be a tie between them; and (iii) when there are cyclical majorities with a single maximin alternative, this alternative will be elected.     

Presidential coattails and electoral coordination in multilevel elections: Comparative lessons from Brazil

This article seeks to understand how concurrent presidential and gubernatorial elections in strong federal systems affect electoral coordination and coattails voting between national and subnational levels of government. We seek to determine whether the nationalizing effect of presidential elections can overcome the strong incentives for regionalization that can arise in federal systems. We use individual-level survey data and time-series cross-sectional electoral data from Brazil, a federal country with decentralized electoral institutions that has recently adopted concurrent presidential and gubernatorial elections. We find that the congruence between national and subnational elections increases when elections are temporally proximate and the effective number of presidential candidates is low. In short, the coattails effect can not only operate “horizontally,” by shaping national legislative elections, but also “vertically,” by shaping subnational elections.     

Territorial representation

Abstract This paper examines the opinion congruence of voters and representatives in European Parliament elections taking nation as the constituency of interest, an implied model of representation similar to that in a classic Miller and Stokes analysis. Congruence is greater for some countries than others. MEPs are even less representative of their voters than are candidates in general, and all are more pro–integrationist than the electorate. Differences between countries are explained by variations in electoral systems and in national party systems. A genuine European party system and a common and PR electoral system would make MEPs more representative, but almost certainly less integrationist.     

Territorial representation

This paper examines the opinion congruence of voters and representatives in European Parliament elections taking nation as the constituency of interest, an implied model of representation similar to that in a classic Miller and Stokes analysis. Congruence is greater for some countries than others. MEPs are even less representative of their voters than are candidates in general, and all are more pro–integrationist than the electorate. Differences between countries are explained by variations in electoral systems and in national party systems. A genuine European party system and a common and PR electoral system would make MEPs more representative, but almost certainly less integrationist.     

The paradox of grading systems

We distinguish between (i) voting systems in which voters can rank candidates and (ii) those in which they can grade candidates, using two or more grades. In approval voting, voters can assign two grades only—approve (1) or not approve (0)—to candidates. While two grades rule out a discrepancy between the average-grade winners, who receive the highest average grade, and the superior-grade winners, who receive more superior grades in pairwise comparisons (akin to Condorcet winners), more than two grades allow it. We call this discrepancy between the two kinds of winners the paradox of grading systems, which we illustrate with several examples and whose probability we estimate for sincere and strategic voters through a Monte Carlo simulation. We discuss the tradeoff between (i) allowing more than two grades, but risking the paradox, and (ii) precluding the paradox, but restricting voters to two grades.     

The Alternative Vote and Coombs Rule versus First-Past-the-Post: a social choice analysis of simulated data based on English elections, 1992–2010

This paper presents a social choice analysis, using simulated data based on English general elections from 1992 through 2010, of the properties of three voting rules: First-Past-the-Post, the Alternative Vote, and the Coombs Rule. More specifically, the paper examines (1) the plurality, anti-plurality, and Condorcet status of candidates in each election and the interrelationships among these statuses, (2) the effects of strict and partial single-peakedness of voter preferences, and (3) the identity of winners, Condorcet efficiency, and the relationship between votes and seats under the three voting rules. The analysis considers only the case of three candidates and, in the manner of basic social choice theory, the set of candidates and voter preferences over them are taken to be fixed.     

Party registration and party self-identification: Exploring the role of electoral institutions in attitudes and behaviors

How do electoral institutions affect self-identified partisanship? I hypothesize that party registration acts to anchor a person's party identification, tying a person to a political party even when their underlying preferences may align them with the other party. Estimating a random effects multinomial logit model, I find individuals registered with a party are more likely to self-identify with that party and away from the other party. Party registration also affects voting in presidential elections but not in House elections, leading to greater defection in the former where voters have more information about the candidates. These insights illuminate varying rates of electoral realignment, particularly among southern states, and the makeup of primary electorates in states with and without party registration.