We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove tha...

We give a characterization of majority voting rules with quorums in the framework of May (Econometrica 20:680–684, 1952)’s seminal article. According to these voting rules, an alternative is socially chosen if and only if it obtains the relative majority of votes and the total number of voters not abstaining reaches the quorum.

We reassess the possibility of full information pooling in a Condorcet jury environment featuring heterogeneous and privately known preference types. We find that in general, with uncorrelated preference types, only very limited heterogeneity is compatible with full pooling. We provide a sufficient condition, based on a simple measure of preference misalignment, under which the set of voting rules compatible with full pooling is at most a singleton. As a caveat to any simplistic conclusions, we identify a case in (...) which an increase in heterogeneity systematically generates the possibility of full pooling. Increased jury size, in contrast, is shown to always render full pooling more difficult. (shrink)

Sparked by a remarkable result due to Hemaspaandra et al. [9], the voting rule attributed to Charles Dodgson has become one of the most studied voting rules in computational social choice. However, the computer science literature often neglects that Dodgson's rule has some serious shortcomings as a choice procedure. This short note contains four examples revealing Dodgson's deficiencies.

In this paper we study collective identity functions that deal with formation of clubs. Usually the choice offered to individuals is to cast a vote in favor of qualification or not, and the final outcome is qualification or non-qualification. In this context we show that independent collective identity functions are naturally characterized by voting rules, and in particular, consent rules can be represented by one single collection of weighted majorities. In addition, we consider the extended model where (...) voters are allowed to abstain and we distinguish between disqualification and a neutral outcome. We show that this environment allows agents to act in different capacities that cannot be distinguished in the original formulation of the problem. (shrink)

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. (...) We also consider sequential quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of (...) the decision-makers’ capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers. (shrink)

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak (...) Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule. (shrink)

Scholars exploring the logic of Rousseau's voting rules have typically turned to the connection between Rousseau and the Marquis de Condorcet. Though Condorcet could not have had a direct influence on Rousseau's arguments about the choice of decision rules in "Social Contract," the possibility of a connection has encouraged the view that Rousseau's selection of voting rules was based on epistemic reasons. By turning to alternative sources of influence on Rousseau--the work of Hugo Grotius and (...) particularly that of Samuel Pufendorf--a moral, and not purely epistemic, logic of rules governing collective decision making emerges. For Rousseau, as for Pufendorf, the proper choice of voting rule can elicit the appropriate attitude of an individual with respect to the decision of the whole, and can support the morally significant activity of acknowledging error upon discovering that one has voted against the general will. (shrink)

Multiple-vote majority rule is a procedure for making group decisions in which individuals weight their votes on issues in accordance with how competent they are on them. When individuals are motivated by the truth and know their relative competence on different issues, multiple-vote majority rule performs nearly as well, epistemically speaking, as rule by an expert oligarchy, but is still acceptable from the point of view of equal participation in the political process.Send article to KindleTo send this article to your (...) Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ - cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise value-restriction, itself the most general classic condition. We also prove a (...) new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule. (shrink)

What is the moral value of formal democratic decision-making? Egalitarian accounts of democracy provide a powerful answer to this question. They present formal democratic procedures as a way for a society of equals to arrive at collective decisions in a transparent and mutually acceptable manner. More specifically, such procedures ensure and publicly affirm that all members of a political community, in their capacity as autonomous actors, are treated as equals who are able and have a right to participate in collective (...) decision-making. Recently, a number of authors have raised what I describe as the ‘no impact’ objection. This objection focuses on the egalitarian emphasis on autonomy to cast doubt on the moral value of formal democratic procedures. It holds that individual participation in formal democratic decision-making has no impact on the eventual result, and therefore cannot be understood as an exercise in autonomy. Consequently, the ‘no impact’ objection claims that the moral value of formal democracy cannot be explained with reference to an egalitarian ideal of ‘rule by the people’. In this article, I refute this objection by complementing an egalitarian account of democracy with an account of basic autonomy. (shrink)

We construct a new measure of voting power that yields reasonable measurements even if the individual votes are not cast independently. Our measure hinges on probabilities of counterfactuals, such as the probability that the outcome of a collective decision would have been yes, had a voter voted yes rather than no as she did in the real world. The probabilities of such counterfactuals are calculated on the basis of causal information, following the approach by Balke and Pearl. Opinion leaders (...) whose votes have causal influence on other voters' votes can have significantly more voting power under our measure. But the new measure of voting power is also sensitive to the voting rule. We show that our measure can be regarded as an average treatment effect, we provide examples in which it yields intuitively plausible results and we prove that it reduces to Banzhaf voting power in the limiting case of independent and equiprobable votes. (shrink)

We characterize two lexicographic-type preference extension rules from a set X to the set ? of all orders on this set. Elements of X are interpreted as basic economic policy decisions, whereas elements of ? are conceived as political programs among which a collectivity has to choose through majority voting. The main axiom is called tournament-consistency, and states that whenever majority pairwise comparisons based on initial preferences on X define an order on X, then this order is also (...) chosen by a majority among all other orders in ?. Tournament-consistency thus allows to predict the outcome of majority voting upon orders from the knowledge of majority preferences on their components. (shrink)

I assume that voters mark ballots exclusively to express their true preferences among parties, leaving aside any considerations about an election’s possible outcome. The paper then analyzes the resulting voting behavior. In particular, it studies how effective different voting systems such as plurality rule, approval voting, and range voting are in fostering high turnout rates of such expressive voters.

It is a platitude among decision theorists that agents should choose their actions so as to maximize expected value. But exactly how to define expected value is contentious. Evidential decision theory (henceforth EDT), causal decision theory (henceforth CDT), and a theory proposed by Ralph Wedgwood that this essay will call benchmark theory (BT) all advise agents to maximize different types of expected value. Consequently, their verdicts sometimes conflict. In certain famous cases of conflict—medical Newcomb problems—CDT and BT seem to get (...) things right, while EDT seems to get things wrong. In other cases of conflict, including some recent examples suggested by Andy Egan, EDT and BT seem to get things right, while CDT seems to get things wrong. In still other cases, EDT and CDT seems to get things right, while BT gets things wrong. It's no accident, this essay claims, that all three decision theories are subject to counterexamples. Decision rules can be reinterpreted as voting rules, where the voters are the agent's possible future selves. The problematic examples have the structure of voting paradoxes. Just as voting paradoxes show that no voting rule can do everything we want, decision-theoretic paradoxes show that no decision rule can do everything we want. Luckily, the so-called “tickle defense” establishes that EDT, CDT, and BT will do everything we want in a wide range of situations. Most decision situations, this essay argues, are analogues of voting situations in which the voters unanimously adopt the same set of preferences. In such situations, all plausible voting rules and all plausible decision rules agree. (shrink)

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We (...) introduce three notions of manipulability for a set of voting methods: sure, safe, and expected manipulability. With the help of a computer program, we identify voting scenarios in which uncertainty about the voting method may reduce or even eliminate a voter's incentive to misrepresent her preferences. Thus, it may be in the interest of an election designer who wishes to reduce strategic voting to leave voters uncertain about which of several reasonable voting methods will be used to determine the winners of an election. (shrink)

In a three-candidate election, a scoring rule s (s in [0,1]) assigns 1, s, and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule s has the greatest Condorcet efficiency? After recalling the known (...) answer to this question, we investigate the impact of social homogeneity on the optimal value of ?. One of the most salient results we obtain is that the optimality of the Borda rule (s=1/2) holds only if the voters act in an independent way. (shrink)

Majority rule is often regarded as an important democratic principle. But modern democracies divide voters into districts. So if the majority should rule, which majority should rule? Should it be the popular majority, or an electoral majority (i.e., either the majority of voters in the majority of districts, or the majority of voters in districts that contain the majority of the population)? I argue that majority rule requires rule by the popular majority. This view is not novel and may seem (...) obvious. But it is rarely defended, and often rejected. I defend it by arguing that this view about which majority should rule is best supported by the arguments for why the majority should rule, and best avoids the arbitrary and perverse verdicts of rule by electoral majorities. I close by considering the significant practical implications of the view. The Electoral College is often criticized on the basis that the winner of the popular vote doesn’t always win the election. But all district-based democracies have this feature, so all district-based democracies must be reformed if they are to satisfy the principle of majority rule. (shrink)

Voting lies at the center of collective decision-making in corporate law. While scholars have identified various problems with the voting mechanism, insincere voting—in the forms of strategic voting and conflict of interests voting—is perhaps the most fundamental. This article shows that insincere voting distorts the voting mechanism at its core, undermining its ability to determine transaction efficiency. As further demonstrated, strategic and conflict of interests problems frequently coincide with one another: voting strategically (...) often means being in conflict, and many fact patterns present aspects of both problems. Finally, this article claims that although the two problems have seemingly different solutions, these solutions are essentially similar in nature: all solutions to insincere voting are variations on two basic rules, namely, property rules and liability rules. (shrink)

Since the early 1990s, Steven Reed and Gary Cox have changed our understanding of Japan's multimember SNTV electoral system, by highlighting its institutional effects similar to what is known as Duverger's law in the Anglo-American context. While we offer some additional evidence to consolidate their findings, we also address an issue left unexplored in these studies, namely the role of partisan information. Under Japan's system, party labels matter in elections. We show that, while Japanese voters are generally willing to abandon (...) the candidates without affiliation with established parties, the partisan effects produce constraints for strategic coordination. (shrink)

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.

In 1946, the French constitution made colonial subjects in Africa into citizens. Having been content to rule ‘tribes’ via their ‘chiefs’, at that point it had to track individuals entitled to vote and receive social benefits. The new citizens retained their personal status — regulating marriage, filiation, and inheritance — under Islamic law or local ‘customs’ rather than through the civil code. That posed a dilemma for French officials, for the état-civil did not just record life events, but symbolized the (...) integration of all into a single body of citizens. French officials and legislators — including African representatives — could not agree on whether the multiple status regimes necessitated two états-civils or one. In the end, officials were too torn between their recognition of difference among peoples under French rule and their desire for singularity to put in place a consistent policy of identification, registration, and surveillance. They bequeathed the problem to their successors. (shrink)

We assume that people have a need to make statements, and construct a model in which this need is the sole determinant of voting behavior. In this model, an individual selects a ballot that makes as close a statement as possible to her ideal point, where abstaining from voting is a possible (null) statement. We show that in such a model, a political system that adopts approval voting may be expected to enjoy a significantly higher rate of (...) participation in elections than a comparable system with plurality rule. (shrink)

This book is a theoretical and completely rigorous analysis of voting in committees that provides mathematical proof of the existence of democratic voting systems, which are immune to the manipulation of preferences of coalitions of voters. The author begins by determining the power distribution among voters that is induced by a voting rule, giving particular consideration to choice by plurality voting and Borda's rule. He then constructs, for all possible committees, well-behaved representative voting procedures which (...) are not distorted by strategic voting, giving complete solutions for certain important classes of committees. The solution to the problem of mass elections is fully characterised. (shrink)

Some philosophers have recently argued that decision-makers ought to take normative uncertainty into account in their decisionmaking. These philosophers argue that, just as it is plausible that we should maximize expected value under empirical uncertainty, it is plausible that we should maximize expected choice-worthiness under normative uncertainty. However, such an approach faces two serious problems: how to deal with merely ordinal theories, which do not give sense to the idea of magnitudes of choice-worthiness; and how, even when theories do give (...) sense to magnitudes of choice-worthiness, to compare magnitudes of choice-worthiness across different theories. Some critics have suggested that these problems are fatal to the project of developing a normative account of decision-making under normative uncertainty. The primary purpose of this article is to show that this is not the case. To this end, I develop an analogy between decision-making under normative uncertainty and the problem of social choice, and then argue that the Borda Rule provides the best way of making decisions in the face of merely ordinal theories and intertheoretic incomparability. (shrink)

In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation coefficient decreases the probability of a correct verdict for any voting rule below the correlation-robust quota, and increases that probability for any above the correlation-robust quota. (...) The jury may be less competent under the correlation-robust rule than under simple majority rule and less competent under simple majority rule than a single juror alone. The jury is always less competent than a single juror under unanimity rule. (shrink)

The main aim of this final essay is to draw on the insights gathered in the Debate “Do Referendums Enhance or Threaten Democracy” to inform future normative and empirical discussions about the design of popular vote processes. We first offer some clarifications regarding three of the concerns raised by respondents about our introductory essay. We then propose a systematic classification of the lines of variation along which the design of popular vote processes usually varies. More precisely, we highlight nine lines (...) of variation: trigger, origin of the text, legal basis, scope, trigger requirements, time, ballot, information, and decision rule. We conclude by emphasizing the relevance and necessity of debating the formal institutional design of popular vote processes. (shrink)

The objective of this article is to propose a precise characterization of the collective practice behind at least an important part of the phenomena named “decision by consensus”. First, I provide descriptions of the use of this rule, and give a definition of the non-opposition rule, both as a specific sequence of acts and as a stopping rule. Second, I challenge the usual way of understanding the non-opposition rule by contrast with voting, stating that the contrast between logic of (...) approval and logic of consent also has to be taken into account. Third, I examine the conditions of its use. The non-opposition rule satisfies groups whose concern is to decide without dividing. Finally, from the analytic benefit of opening up decision by consensus as the use of the non-opposition rule, I will examine, in a fourth part, whether consensus in decision-making is as democratic a procedure as is sometimes thought. (shrink)

Should voting rights be conditional upon competence? Proponents of epistocracy think so, but most political theorists dismiss this view. At the same time, the practice of disenfranchising citizens below a certain age is widely endorsed. This paper raises a challenge for proponents of the voting age. Drawing on a revised version of Estlund’s influential account, I argue that electoral inequality is justifiable only if all qualified points of view can accept that it promotes the epistemic reliability of democratic (...) procedures. This condition rules out epistocracy, but it also implies that the voting age is harder to justify than commonly assumed. (shrink)

This study considers a voting rule wherein each player sincerely votes when he/she has no information about the preferences of the other players. We introduce the concept of rank-dominant strategies to discuss the situation where a player is completely ignorant in the preferences of the other players and decision theoretic justification of the concept. We show that under the plurality voting rule with the equal probability random tie-breaking, sincere voting is always the rank-dominant strategy of each voter. (...) We also discuss other scoring rules and show that sincere voting may not be a rank-dominant strategy of a voter even with the equal probability random tie-breaking. (shrink)

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing (...) a direct link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. (shrink)

Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely (...) used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained. (shrink)

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals will (...) have the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility. The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization. The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior. (shrink)

The Dodd‐Frank Wall Street Reform and Consumer Protection Act, signed into law by President Obama in July 2010, included two significant corporate governance mandates: “say‐on‐pay” shareholder voting and the frequency of such votes among all publicly traded companies. The say‐on‐pay rule requires publicly traded companies subject to proxy rules to offer their shareholders an advisory, or nonbinding, vote at least once every three years on the compensation packages of the most highly compensated executives. The actual data for the (...) first five years of say‐on‐pay voting indicates one intractable conclusion: that shareholder say‐on‐pay voting has not verified what many shareholder activists originally believed, i.e., that the majority of shareholders held similar opinions about business executives being significantly overpaid for their managerial performances. During its first five years in effect, the results of say‐on‐pay voting indicate that shareholders are overwhelmingly satisfied with executive compensation packages, as a 92 percent average shareholder say‐on‐pay approval result (i.e., exceeding 70 percent) among companies listed in the Russell 3000 Index attests. (shrink)

To investigate the relationship between logical reasoning and majority voting, we introduce logic with groups Lg in the style of Gentzen’s sequent calculus, where every sequent is indexed by a group of individuals. We also introduce the set-theoretical semantics of Lg, where every formula is interpreted as a certain closed set of groups whose members accept that formula. We present the cut-elimination theorem, and the soundness and semantic completeness theorems of Lg. Then, introducing an inference rule representing majority (...) class='Hi'>voting to Lg, we introduce logic with majority voting Lv. Formalizing the discursive paradox in judgment aggregation theory, we show that Lv is inconsistent. Based on the premise-based and conclusion-based approaches to avoid the paradox, we introduce logic with majority voting for axioms Lva, where majority voting is applied only to non-logical axioms as premises to construct a proof in Lg, and logic with majority voting for conclusions Lvc, where majority voting is applied only to the conclusion of a proof in Lg. We show that both Lva and Lvc are syntactically complete and consistent, and we construct collective judgments based on the provability in Lva and Lvc, respectively. Then, we discuss how these systems avoid the discursive paradox. (shrink)

In the voting-power literature the rules of decision of the US Congress and the UN Security Council are widely misreported as though abstention amounts to a `no' vote. The hypothesis (proposed elsewhere) that this is due to a specific cause, theory-laden observation, is tested here by examining accounts of these rules in introductory textbooks on American Government and International Relations, where that putative cause does not apply. Our examination does not lead to a conclusive outcome regarding the (...) hypothesis, but reveals that the rules in question are also widely misreported in these textbooks. A second hypothesis---that the widespread misreporting is explicable by the relative rarity and unimportance of abstention in the two bodies concerned---is also tested and found to be untenable. (shrink)

In the citizen–candidate approach each citizen chooses whether or not to run as candidate. In a single-peaked preference domain, we find that the strategic entry decision of the candidates eliminates one of the most undesirable properties of Plurality rule, namely to elect a poor candidate in three-candidate elections since as we show, the Condorcet winner among the self-declared candidates is always elected. We find that the equilibria with three candidates are basically 2-fold, either there are two right-wing candidates and a (...) left-wing candidate who wins the elections (or its symmetric), or there is a right-wing candidate, a left-wing candidate, and a candidate located in between the two others who becomes winner. We also show that when four or more candidates enter the contest, Plurality rule can elect the Condorcet-loser among the self-declared candidates. (shrink)

In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_k$$\end{document}, each time he/she is ranked k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}th by one voter and the candidates are ordered according to the (...) total number of points they receive. In order to identify the best scoring rule to use in each situation, we need to know which properties are met by each of these procedures. Although some properties have been analyzed extensively, there are other properties that have not been studied for all scoring rules. In this paper, we consider two desirable social choice properties, the Pareto-optimality and the immunity to the absolute loser paradox, and establish characterizations of the scoring rules that satisfy each of these specific axioms. Moreover, we also provide a proof of a result given by Saari and Barney, where the scoring rules meeting reversal symmetry are characterized. From the results of characterization, we establish some relationships among these properties. Finally, we give a characterization of the scoring rules satisfying the three properties. (shrink)

This paper provides a philosophical critique of social choice theory insofar as it deals with the normative evaluation of voting and voting rules. I will argue that the very method of evaluating voting rules in terms of whether they satisfy various conditions is deeply problematic because introducing strategic behaviour leads to a violation of any condition that makes a difference between voting rules. I also argue that it is legitimate to make interpersonal comparisons (...) of utilities in voting theory. Combining a realistic account of voters’ behaviour with a utilitarian evaluation of the outcomes then leads to the judgment that strategic voting is beneficial. If it is, then Arrow's theorem does not have far-reaching consequences for democracy because one of its conditions is not normatively acceptable. (shrink)

In this paper we discuss the meaning of Owen's coalitional extension of the Banzhaf index in the context of voting situations. It is discussed the possibility of accommodating this index within the following model: in order to evaluate the likelihood of a voter to be crucial in making a decision by means of a voting rule a second input (apart from the rule itself) is necessary: an estimate of the probability of different vote configurations. It is shown how (...) Owen's coalitional extension can be seen as three different normative variations of this model. (shrink)