Approval voting, Condorcet's principle, and runoff elections

This essay reasses the assumptions of the Brams-Fishburn theory of approval voting, and proposes modifications to make the theory correspond better with likely voting choices. With a small number of candidates, voters who use the ‘inadmissible’ strategy of voting for all candidates can help to produce a result that better reflects the voters' wishes than is possible with ‘admissible’ strategies, so we propose a widening of the definition of admissibility to encompass this case. With more than three candidates, we define ‘first-order admissible’ strategies, which are the most likely strategies to be used in practice, and are also strongly sincere, in that a vote for any candidate is always accompanied by votes for all more or equally-preferred candidates. Their number is less under approval voting than under plurality voting. Both proposed modifications strengthen the technical arguments favoring approval voting over plurality voting.

In a single-winner voting system, approval voting gives voters the possibility to cast a ballot for (or ‘approve of’) as many candidates as they wish – that is, voters are freed from the constraint of voting for only one candidate. The candidate receiving the greatest total number of votes is declared the winner. Approval voting has several compelling advantages over other voting procedures, and has been used by various governments and organisations around the world.KeywordsApproval votingCondorcet winnerStrategic votingVoting systemsJEL ClassificationsD71D72

Game theoreticians usually deal with standard voting methods, such as plurality voting or approval voting. In reality however, some complicated non-standard voting methods are used. In this paper we shall present the voting method and rotation scheme used by the Governing Council of the European Central Bank (ECB), as it enlarges to accommodate new members of the economic and monetary union. We present game theoretical approaches to analyzing this method and different methods of computing the Shapley value for games connected with voting under such rotation schemes.

We have observed that some recent results cast serious doubts uponthe applicability of majority rule as a device for forming a group-willout of individual wills. On the other hand, majority rule has manyproperties to recommend it. Especially, the decisiveness propertyshould please anyone interested in efficiency considerations. How-ever, when it comes to the second major criterion, consistency, major-ity rule with pairwise comparison of alternatives often leads to diffi-culties. Indeed, we have seen that there is typically no core or Con-dorcet winner when the policy space is multidimensional real space.And when there is no core, the situation looks grim indeed for major-ity rule: literally any outcome may become the majority winner. Somerelief of this very strong result is provided by the fact that no majoritycycles can go through the outcomes that belong to the M2 bargainingset. This finding, of course, solves the problem facing majority rule onlyinsofar as a method can be devised by which the M2 bargaining set out-comes can be determined in a reliable way. Here, thus, we are con-fronted with the sincerity problem. The absence of the core can lead to chaotic trajectories of votingoutcomes in multidimensional space. However, there are ways of over-coming the difficulties if a sufficient amount of flexibility is allowedin institutional design. If we consider the various nonequilibrium solu-tion concepts, and the minimax set in particular, we can always designa decision rule which (under mild restrictions) makes the vote-maximiz-ing outcome trajectory enter the solution set. The flexibility needed isgreat, indeed: the decision rule, λ-majority, must be alterable for eachvoting situation. The determination of the winner in a pair-wise comparison of alter-natives is not the main source of the difficulties surrounding majorityrule. As a matter of fact, the method of building the agenda is the mostcrucial part of the problem of cyclical majorities. In multicandidatecontests the occurrence of cyclical majorities has motivated the studyof other.decision procedures in addition to the majority comparisonof alternatives. The most recent proposal, approval voting, is morestrategyproof than its competitors in the class of single-ballot, non-ranked voting systems. At the moment the relationships betweenapproval voting and majority rule are not clear. It seems that furtherstudy of the interrelationships of these procedures is called for. Thefeatures in which approval voting is superior to majority comparisonof pairs of alternatives, however, are not, strictly speaking, procedural,but are external to the method of making collective decisions.

A variety of electoral systems for single-winner, multicandidate elections are evaluated according to their tendency to (a) select the Condorcet candidate-the candidate who could beat each of the others in a two-way race-if one exists, and (b) select a candidate with high social (average) utility. The proportion of Condorcet candidates selected and a measure of social-utility efficiency under either random society or spatial model assumptions are estimated for seven electoral systems using Monte Carlo techniques. For the spatial model simulations, the candidates and voters are generated from multivariate normal distributions. Numbers of candidates and voters are varied, along with the number of spatial dimensions, the correlation structure, and the relative dispersion of candidates to voters. The Borda, Black, and Coombs methods perform well on both criteria, in sharp contrast to the performance of the plurality method. Approval voting, plurality with runoff, and the Hare system (preferential voting) provide mixed, but generally intermediate results. Finally, the results of the spatial model simulations suggest a multicandidate equilibrium for winningoriented candidates (under plurality, runoff, and Hare) that is not convergent to the median.

This chapter places ranked choice voting (RCV) within the context of electoral systems. Preferential voting elections include the alternative vote (AV) for choosing a single winner and the single transferable vote (STV) to select multiple winners. Electoral systems for parliamentary elections in Australia and Ireland provide the rationale and history of these forms of RCV. Plurality or first-past-the-post elections serve as the benchmark for comparisons, and other broad electoral systems such as proportional representation and mixed-member proportional systems are introduced and contrasted with ranked choice. Similar electoral systems with complementary goals are discussed. Cousins to RCV include the supplementary vote, approval voting, cumulative voting, and the Borda count. Examples are introduced and compared to preferential systems. The philosophical origins of STV and RCV from Thomas Hare forward are outlined. RCV may lead to computational paradoxes such as Condorcet cycling and violations of fundamental assumptions such as monotonicity.

The Problem of the Divided Majority: Preference Aggregation Under Uncertainty

We use preference data from the 2015 parliament election in the Austrian federal state of Styria to analyze different voting rules. An exit poll right after the election collected data on ordinal and cardinal preferences from approximately 1000 actual voters. Our analysis is threefold. First, we determine the hypothetical social outcomes under different voting rules; second, we investigate the stability of the outcomes under those rules. Finally, we provide a categorization of different types of parties and analyze the impact of certain voting rules (Plurality Rule, Plurality Run Off, Hare System, Condorcet Method, Approval Voting, Borda Rule, Evaluative Voting, and Majority Judgment) on the performances of parties in those scenarios.

A simple model is used to compare, under different electoral systems, the incentives for candidates to create inequalities among otherwise homogeneous voters, by making campaign promises that favor small groups, rather than appealing equally to all voters. In this game model, each candidate generates offers for voters independently out of a distribution that is chosen by the candidate, subject only to the constraints that offers must be nonnegative and have mean 1. Symmetric equilibria with sincere voting are analyzed for two-candidate elections and for multicandidate elections under rank-scoring rules, approval voting, and single transferable vote. Voting rules that can guarantee representation for minorities in multiseat elections generate, in this model, the most severely unequal campaign promises.

This article focuses on decision making by voting in systems at the levels of the organization, the community, the society, and the international system. It examines the compatibility of the plurality and approval voting procedures with a number of normative properties commonly used to evaluate the desirability of voting procedures by social choice theorists. This analysis assumes both sincere and sophisticated voting under each procedure and thus extends previous analyses of the same issues which were restricted to sincere voting. We show that neither sophisticated plurality voting nor sophisticated approval voting is compatible with any of the normative properties under examination. This is so despite the fact that the sincere versions of these voting procedures satisfy most of these properties. We relate our findings to other theoretical and empirical examinations of these issues and discuss the possible implications of the violations for actual implementation of these procedures.

One of three of more candidates is to be elected using a voting system that allows each voter to vote for a subset of candidates. Different systems allow voters to vote for different numbers of candidates, but in each case the candidate with the most votes is elected. Strategies are subsets of candidates, and each system specifies the strategies available to the voters. Dominance relations over strategies are specified for voter preference orders on the candidates and used to identify the set of admissible strategies for each combination of a voting system and a preference order. The extents to which different systems are strategyproof or sincere are then examined. A system is strategyproof for a preference order on the candidates if the associated admissible set is a singleton, and it is sincere if no admissible strategy contains a candidate who is less preferred than a candidate not in the strategy. Strategyproofness and sincerity partial orders are developed on the set of voting systems.

In 1988 the French voters gave François Mitterrand a second term as president. Although it was clear long in advance that the Socialist leader would be one of two candidates in the run-off election, his final victory was far from certain. In the end his margin of victory was relatively strong: 54.01 per cent to Jacques Chirac’s 45.98 per cent. The 1988 campaign took place, as do all campaigns, in the context of a national political system, consisting of four key components: the constitutional system, the party system, the electoral system and the campaign system.KeywordsPrime MinisterPresidential ElectionElectoral SystemParty SystemPresidential CampaignThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

How widespread is strategic voting in two-round electoral systems, and which types of voters are most likely to engage in such behavior? While runoff elections are common in presidential systems around the world, research on strategic voting in these settings remains limited. This paper explores four different types of strategic behavior that are possible in two-round systems, including some types, such as “strong-to-weak” strategic voting, which are not possible in single-shot elections. We use a nationwide survey to assess the incidence and correlates of strategic voting in Brazil’s 2018 presidential election, where thirteen candidates competed in the first round. We find evidence of “weak-to-strong” strategic voting at a similar rate to that documented in single-round elections in other countries. We find little evidence of other types of strategic voting. Furthermore, we show that voters’ confidence in their predictions of the likely electoral outcome and their ideological preferences strongly predict strategic voting. These results point to the importance of accounting for voter beliefs and attitudes in addition to objective voter characteristics to explain strategic voting.

Hungary has a particularly complicated electoral system: a type of mixed system that incorporates three tiers of seat allocation, the use of a proportional allocation formula, and the allocation of a number of seats by a two-round system in single-member constituencies. Examination of the strategic incentives facing parties explains some surprising outcomes, such as the majoritarian impact on the party system and the possibility of the second strongest party in votes becoming the strongest in seats. Despite its complexity and alleged shortcomings, it is unlikely to be abandoned; it serves the interests of the largest parties, and these effectively wield a veto over electoral reform.

This chapter summarizes the concerns about electoral representative democracy identified in the previous chapters, sorts them into either constitutive or conditional problems of electoral democracy, and presents (and raises concerns about) several possible reforms that retain elections as a central component of the political system. The chapter argues that although these comparatively modest responses might result in some improvements, they do not effectively address the core concerns, and so we should be open to more radical reforms. The reforms discussed include introducing epistocratic or technocratic elements such as plural voting or “modelled” democracy, implementing broad public education and media reform, reducing the size of political communities, regulating campaign finance and providing public financing of electoral campaigns, restricting lobbying and revolving door politics, regulating political speech, reducing background socioeconomic inequality, and implementing approval voting or single-transferable vote systems. Although many of these reforms are worth pursuing, and many would make a positive difference, the chapter also argues that we should not put all of our eggs in these baskets, and that we should develop alternative ideas in case we end up doubting the viability of the basic electoral mechanism in the modern political context.