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)

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)

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.

I aim to explain why majority voting can be assumed to have an epistemic edge over lottery voting. This would provide support for majority voting as the appropriate decision mechanism for deliberative epistemic accounts of democracy. To argue my point, I first recall the usual arguments for majority voting: maximal decisiveness, fairness as anonymity, and minimal decisiveness. I then show how these arguments are over inclusive as they also support lottery voting. I (...) then present a framework to measure accuracy so as to compare the two decision mechanisms. I go over four arguments for lottery voting and three arguments for majority voting that support their respective accuracy. Lottery voting is then shown to have, compared to majority voting, a decreased probability of discrimination. That is, I argue that with lottery voting it is less probable under conditions of normal politics that if the procedure selects X, X is reasonable. I then provide two case scenarios for each voting mechanism that illustrate my point. (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 (...) class='Hi'>majority 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)

I am grateful to Geoffrey Brennan, Campbell Brown, Franz Dietrich, Christian Elsholtz, Robert Goodin, Frank Jackson and David Soskice for very helpful comments and suggestions; and to the participants of a Social and Political Theory seminar at the ANU in February 2003 and the participants of a conference panel of the Australasian Association of Philosophy at the University of Adelaide in July 2003 for comments and discussion.

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)

This study investigates how adoption of advisory governance policy encourages firms to become more responsive to their shareholders over time. Although shareholder activism is costly and often viewed as unable to drive meaningful change, we identify increasing shareholder voice as an underlying mechanism to explain how advisory policy adoption ultimately reshapes board–shareholder relations. Drawing on signaling theory and behavioral views of board–shareholder dynamics, we test our predictions following the broad shift in corporate board voting policies from plurality to (...) class='Hi'>majority vote standards. While prior research shows that majority vote adoption has little to no direct impact on director elections, empirical results from 2,390 firm-year observations provide support for our hypotheses that adoption of this advisory electoral standard signals a willingness to hear shareholder concerns, leading to increased shareholder activism and, in turn, board responsiveness to shareholder proposals. Overall, our results help explain why some firms continue to fight the purely advisory policy and why an era of shareholder empowerment followed the majority vote campaign. (shrink)

The Condorcet Jury Theorem, along with empirical results, establishes the accuracy of majority voting in a broad range of conditions. Here we investigate whether naïve participants (in the U.S. and...

Voters satisfy maximin or maximax in their choices between sets of alternatives and secure a Pareto improvement by all voting strategically under simple majority voting for particular sincere preferences. Thus the assumption that strategic voting is a bad thing is challenged and the idea that we should reject voting because of the possibility of misrepresentation dismissed.

Scientists are often asked to advise political institutions on pressing risk-related questions, like climate change or the authorization of medical drugs. Given that deliberation will often not eliminate all disagreements between scientists, how should their risk assessments be aggregated? I argue that this problem is distinct from two familiar and well-studied problems in the literature: judgment aggregation and probability aggregation. I introduce a novel decision-theoretic model where risk assessments are compared with acceptability thresholds. Majority voting is then defended (...) by means of robustness considerations. (shrink)

I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some (...) related results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative’ means that policy or law that will best promote the public good. I also explicate a Convincing Majorities Theorem, which shows the extent to which the majority vote should provide evidence that the better policy has been selected. Finally, I show how to extend all of these results to judgments among multiple alternatives through the kind of sequential balloting typical of the legislative amendment process. (shrink)

Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate (...) the outcome of the election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states. (shrink)

The strengths and weaknesses of federalism have been debated for centuries. But one major possible advantage of building decentralization and limited government into a constitution has been largely ignored in the debate so far: its potential for reducing the costs of widespread political ignorance. The argument of this paper is simple, but has potentially important implications: Constitutional federalism enables citizens to “vote with their feet,” and foot voters have much stronger incentives to make well-informed decisions than more conventional ballot box (...) voters. The informational advantage of foot voting over ballot box voting suggests that decentralized federalism can increase citizen welfare and democratic accountability relative to policymaking in a centralized unitary state.Ballot box voters have strong incentives to be “rationally ignorant” about the candidates and policies they vote on because the chance that any one vote will have a decisive impact on an electoral outcome is vanishingly small. For the same reason, they also have little or no incentive to make good use of the information they do possess. By contrast, “foot voters” choosing a jurisdiction in which to reside have much stronger incentives to acquire information and use it rationally; the decisions they make are individually decisive. (shrink)

The main criticism to the aggregation of individual preferences under majority rules refers to the possibility of reaching inconsistent collective decisions from the election process. In these cases, the collective preference includes cycles and even could prevent the election of any alternative as the collective choice. The likelihood of consistent outcomes under a class of majority rules constitutes the aim of this paper. Specifically, we focus on majority rules that require certain consensus in individual preferences to declare (...) an alternative as the winner. Under majorities based on difference of votes, the requirement asks to the winner alternative to obtain a difference in votes with respect to the loser alternative taking into account that individuals are endowed with weak preference orderings. Same requirement is asked to the restriction of these rules to individual linear preferences. (shrink)

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high (...) mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College. (shrink)

There are various ways to reach a group decision on a factual yes–no question. One way is to vote and decide what the majority votes for. This procedure receives some epistemological support from the Condorcet Jury Theorem. Alternatively, the group members may prefer to deliberate and will eventually reach a decision that everybody endorses—a consensus. While the latter procedure has the advantage that it makes everybody happy, it has the disadvantage that it is difficult to implement, especially for larger (...) groups. Besides, the resulting consensus may be far away from the truth. And so we ask: Is deliberation truth-conducive in the sense that majority voting is? To address this question, we construct a highly idealized model of a particular deliberation process, inspired by the movie Twelve Angry Men, and show that the answer is ‘yes’. Deliberation procedures can be truth-conducive just as the voting procedure is. We then explore, again on the basis of our model and using agent-based simulations, under which conditions it is better epistemically to deliberate than to vote. Our analysis shows that there are contexts in which deliberation is epistemically preferable and we will provide reasons for why this is so. (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)

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)

We propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head majority comparison, then A should still win in the election with B included (unless there is another candidate A' who has the same kind of claim to winning, in which case a tiebreaker may choose between such (...) candidates). We call this principle Stability for Winners (with Tiebreaking). Stable Voting satisfies this principle while also having a remarkable ability to avoid tied outcomes in elections even with small numbers of voters. (shrink)

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...

This paper explores ethical issues raised by quadratic voting. We compare quadratic voting to majority voting from two ethical perspectives: the perspective of utilitarianism and that of democratic theory. From a utilitarian standpoint, the comparison is ambiguous: if voter preferences are independent of wealth, then quadratic voting out- performs majority voting, but if voter preferences are polarized by wealth, then majority voting may be superior. From the standpoint of democratic theory, we (...) argue that assess- ments in terms of efficiency are too narrow. Voting institutions and political institutions more generally face a legitimacy requirement. We argue that in the presence of inequalities of wealth, any vote buying mechanism, including quadratic voting, will have a difficult time meeting this requirement. (shrink)

Suppose a committee or a jury confronts a complex question, the answer to which requires attending to several sub-questions. Two different voting procedures can be used. On one, the committee members vote on each sub-question and the voting results are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based approach, which requires the members to directly vote on the conclusion, with the vote of each member being guided (...) by her views on the relevant sub-questions. The two procedures are not equivalent: There may be a majority of voters supporting each of the premises, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with the discussion of deliberative democracy. The problem we want to examine instead concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. Which of them is better when it comes to tracking truth? As it turns out, the answer is not univocal. On the basis of Condorcet’s jury theorem, the premise-based procedure can be shown to be superior if the objective is reach truth for the right reasons, without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority. (shrink)

In representative democracies, referendum voting and parliamentary elections provide two fundamentally different methods for determining the majority opinion. We use three mathematical paradoxes – so-called majority voting paradoxes – to show that referendum voting can reverse the outcome of a parliamentary election, even if the same group of voters have expressed the same preferences on the issues considered in the referendums and the parliamentary election. This insight about the systemic contrarieties between referendum voting and (...) parliamentary elections sheds a new light on the debate about the supplementary value of referendums in representative democracies. Using this insight, we will suggest legal conditions for the implementation of referendums in representative democracies that can pre-empt the conflict between the two methods for determining the majority opinion. (shrink)

How to handle vagueness? One way is to introduce the machinery of acceptable sharpenings, and reinterpret truth as truth-in-all-sharpenings or truth-in-some-sharpenings. A major selling point has been the conservativism of the resulting systems with respect to classical theoremhood and inference. Supervaluationism and subvaluationism possess interesting formal symmetries, a fact that has been used to argue for the subvaluationist approach. However, the philosophical motivation behind each is a different matter. Subvaluationism comes with a standard story that is difficult to sign up (...) to. In this paper, I make use of a variant of Putnam’s well-known idea of linguistic deference, and some results in voting theory, to answer this criticism of subvaluationism. The acceptability intuitions of each member of a linguistic community amount to their voting for one or more acceptable sharpenings, with truth then characterised as truth-in-a--sufficiency-of-sharpenings. This produces a family of logical systems that are close relations of subvaluationism, share its conservatism results, yet have stronger philosophical foundations in the workings of externalist content. (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.

Complaints are common about the arbitrary and conservative bias of special-majority rules. Such complaints, however, apply to asymmetrical versions of those rules alone. Symmetrical special-majority rules remedy that defect, albeit at the cost of often rendering no determinate verdict. Here what is formally at stake, both procedurally and epistemically, is explored in the choice between those two forms of special-majority rule and simple-majority rule; and practical ways are suggested of resolving matters left open by symmetrical special- (...) class='Hi'>majority rules – such as ‘judicial extrapolation’ or ‘subsidiarity’ in a federal system. (shrink)

We consider scenarios with distributed decision processes, e.g., coupled majorities and personal union in parliament chambers, supranational decisions and supervisory boards. When computing the adoption rate for reaching a decision in these scenarios, multiple linear inequality restrictions in combinatorial countings are present. These rates cannot be computed in closed form. We introduce a general method for incorporating multiple inequality conditions in multiple majority decisions, which significantly reduces the number of involved summations and removes restrictions on the summation indices. Exact (...) solutions are provided through integral representations which can be evaluated numerically, and unrestricted, contracted sums over discrete events. Further, we provide methods to reduce the number of necessary summations by splitting or recurring the original problem to easier sub-problems. For five dedicated scenarios, full results are given which indeed require a single unrestricted summation only. (shrink)

Anglophone political theorists regard democracy as an electoral system. The moral character of citizens in a democracy is of no interest to them. But electoral systems that disregard the virtue of citizens yield racist governmental systems and major injustices. Democracy requires citizens distinguished by virtues.

The majority of research on human rights focuses on the consequences of regime-type for human rights violations, and overwhelming evidence suggests that democracies are less likely to violate human rights of their citizens as compared to non-democracies. However, a regime-type perspective is unable to account for disparities in human rights violations within democratic and non-democratic regimes. This paper disaggregates regime-type and analyzes the relationship between citizens’ participation and human rights violations. I argue that a participative citizenry, as captured by (...) high voter turnout, is indicative of an active and vigilant populace who are more likely to hold governments accountable and ensure better human rights protections. The paper tests the relationship between human rights and voter turnout among 89 democratic countries from 1976 to 2008. The findings demonstrate that a participative citizenry enhances governmental respect for human rights. (shrink)

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any (...) preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways. (shrink)

Panels, boards, and committees throughout society evaluate all manner of things by grading them, first individually and then collectively. Thus risks are prioritized, research proposals are funded, and candidates are shortlisted for jobs. It is not usual to pick winners in political elections by grading the candidates, but there are examples in history. This article takes up a question about the quality of judgments and decisions made by grading: under which conditions are they likely to be right? An answer comes (...) in the form of a jury theorem for median grading. Here, the collective grade for a thing is the median of its individually assigned grades—the one in the middle, when all of them are listed from "top" to "bottom." A second objective of this article is to suggest a solution to problems of voter ignorance in democracies. The idea is for democratic assemblies to use voting methods that make more of people's limited knowledge than do commonly used methods, such as majority voting. It turns out that in theory anyway, and perhaps also in practice, median grading can enable unenlightened assemblies to “track the truth”—even as majority voting would run them off the rails. (shrink)

A standard objection to a market in political votes is that it will enable the rich politically to dominate the poor. If a market in votes was allowed then the poor would be the most likely sellers and the rich the most likely buyers. The rich would thus accumulate the votes of the poor, and so the candidates elected and the policies passed would represent only their interests and not those of the electorate as a whole. To ensure that the (...) poor do not become de facto disenfranchised, then, markets in votes should be disallowed. This objection seems so straightforward and compelling that it has received almost no critical scrutiny. This is unfortunate, for close examination reveals that this argument is not as straightforward as it initially appears. Indeed, there are four different ways of understanding this objection. It could be understood as expressing: the concern that markets in votes would enable candidates to win elections who would otherwise lose them; the concern that they would enable the election of candidates opposed by the majority of the electorate; the concern that they would lead to the poor having disproportionately low political influence; and the concern that they would lead to the rich having disproportionately high political influence. I will argue in this paper that only and could plausibly ground objections to markets in votes. Moreover, these will only plausibly ground objections to unrestricted markets in votes; they will not ground objections to markets in votes per se. Thus, if we are to continue to object to markets in political votes we will have to do this on grounds other than that were they to be allowed the rich will politically dominate the poor. (shrink)

A familiar debate in first-past-the-post democracies is whether ideologically disenfranchised voters should cast their vote for minor party candidates. We argue that voting for minor party candidates will sometimes be the best strategic option for voters with non-mainstream ideologies. Major parties, as rational agents, will be ideologically responsive to genuine threats of defection. By voting for a minor party, voters can simultaneously punish major parties for unfairly “bargaining” with their voting bloc and also signal their ideological reasons (...) for defecting. (shrink)

According to the expressive view of voting, a voter derives expressive utility from casting a vote. We present two possible sources of expressive utility: social interaction with voters having the same political preferences, and interestingness of the election. First, it has been suggested that a voter's expressive utility may increase when there are more voters having the same political preference. We extend this line of study and test the hypothesis that a voter's expressive utility increases as the number of (...) voters having the same political preferences increases in the local community, where interaction occurs more frequently with others than it does with others in distant communities. Second, we propose and test the other hypothesis, that voters’ expressive utility is larger when the election is more interesting. Using 2008 parliamentary election data from Korea, where the election consists of both 245 single-member districts and only one nationwide district for proportional representatives, we find supporting evidence for these two arguments: the turnout rate is significantly and positively related to the share of proportional representation votes for the largest party in each single-member district; the turnout rate is also significantly and positively related to the number of polls for single-member district election conducted by major broadcasting companies, which we use as a proxy variable for interestingness of the election. (shrink)

We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review 58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.

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 present thesis is intended as a contribution toward a Rousseauean theory of democracy. The central problem discussed is how the act of voting must be interpreted in democratic theory. The notion of a theoretical interpretation of voting is discussed in Chapter One. A theory of democracy must include an interpretation of the act of voting if any praise or criticism of democracy is to be possible. The theoretical interpretation is distinct from an empirical account of (...) class='Hi'>voting behavior, and also distinct from a moral or prudential imperative. It is left as an open question whether one ought, morally or prudentially, to vote in the way that democratic theory interprets voting, or indeed whether one ought to vote at all. ;Social choice theory typically assumes that votes are expressions of individual preferences--that each individual expresses his or her narrowly self-interested preferences, and a proper aggregation of these will yield a utility maximizing result. In Chapter Two it is argued that, for reasons stemming from analysis of the concept of democratic voting, no understanding of "preference" is acceptable as a theoretical interpretation of voting. Six such understandings are disqualified, and the interpretation of votes as statements on the common interest is argued to succeed where these fail. In Chapter Three Richard Wollheim's puzzle of the minority democrat is discussed in relation to several closely related puzzles which apply to both democracy and utilitarianism. All three puzzles are argued to be dissolved if votes are interpreted as statements on the common interest. The solution to Wollheim's paradox, called the Correction Solution, gives rise to the disturbing possibility that the minority is interpreted as simply deferring to the majority. This danger is discussed in detail in Chapter Four, and again the interpretation of votes as statements on the common interest is argued to be uniquely qualified to avoid it. (shrink)

This paper examines the Quranic perspective on Muslim voting for non-Muslim candidate leader in the election. It discusses the position of non-Muslim in a majority Muslim and democratic Indonesia and serves as a response to contemporary political rallies against the candidacy of non-Muslim. The Jakarta Governor election in 2017 clearly demonstrated how Muslim politics define non-Muslim in democracy. Examining important concepts on leadership, mainly the doctrine of khali>fah, uli al-amr, ima>m, and awliya>’, explained in the Qur’an, this article (...) further argues that this holy scripture has defined criteria of leader for the Muslim. Faith and competencies of leadership candidate serve as main references when Muslim send their vote in the election. In political affairs or nashb al-ima>mah, Muslim is supposed to vote for Muslim candidate while also having obligation to guarantee the fulfillment of civic rights, particularly for non-Muslim. (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)

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)

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their “ability”, the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states. We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} (...) jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when n=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=3$$\end{document}, the probability of a correct verdict is maximized when the agent of median ability has the casting vote. (shrink)

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet methods, (...) namely that the choice of winners depends only on the ordering of majority margins by size. (shrink)

Can we hold citizens causally responsible for the outcomes of their voting decisions? They could stand in the causal relationship required for such responsibility either collectively or individually. Recent accounts ascribing responsibility to citizens have primarily taken the collective route because of a major obstacle to using an individualistic approach, namely, the problem of overdetermination: the actions of each citizen do not make an individual difference to, and therefore cannot be a cause of, the overall political outcome. I suggest, (...) drawing on Parfit (1984) and Wright (1985), that we should allow for the idea that individuals can be causally responsible in virtue of making a difference to an outcome not only as an individual, but also as part of a set of agents. I conclude that we therefore can overcome the problem of overdetermination for the individualistic approach and that it merits further investigation. (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)