The voting paradox occurs when a democratic society seeking to aggregate individual preferences into asocialpreference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for anindividualaggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of (...) philosophical and economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. (shrink)

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)

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 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)

Schwartz [A Procedural Condition Necessary and Sufficient for Cyclic Social Preference, J. Econ. Theory 137 (2007), 688–695] provides a generalization of the voting paradox by using the impotence‐partition condition. This paper aims to clarify his result by providing several remarks. We show that a main result of Schwartz can be strengthened by replacing strong Pareto by weak Pareto. We also discuss how the impotence partition is related to the standard concept of decisiveness, which is widely employed in the literature (...) on social choice. (shrink)

This book deals with 18 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid paradoxical outcomes. Together with a companion volume by the same authors, Monotonicity Failures Afflicting Procedures for Electing a Single Candidate, published by Springer in 2017, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of procedures thereby assisting decision makers in (...) the choice of a voting procedure that would best suit their purposes. (shrink)

This paper connects the question of the rationality of voting to the question of what it is morally permissible for elected representatives to do. In particular, the paper argues that it is rational to vote to increase the strength of the manifest normative mandate of one's favored candidate. I argue that, due to norms of political legitimacy, how representatives ought to act while in office is tied to how much support they have from their constituents, where a representative’s “support” (...) is a function of the percentage of adults living in the political jurisdiction who voted for her. In a representative system, whether a particular law or policy is legitimate is in part a function of how much support the particular representative government has, rather than simply being a function of the governmental structure or the normative content of the law or policy. Representatives with more support can permissibly act more like trustees (doing what they think is best) and less like delegates (doing what their constituents presently prefer). I argue that this fact provides a reason for individuals to vote, even given the incredibly small chance an individual voter has of casting a pivotal vote. (shrink)

This book deals with 20 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid five important paradoxes in a restricted domain, viz., when a Condorcet winner exists and is elected in the initial profile. Together with the two companion volumes by the same authors, published by Springer in 2017 and 2018, this book aims at giving a comprehensive overview of (...) the most important advantages and disadvantages of voting procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes. (shrink)

The renowned paradox of voting arises when one tries to explain the decision to go out and vote in an exclusively instrumental framework. Instead of postulating that voters always derive utility from the act of voting, I want to search for the reasons that underlie the absence or presence of a preference for voting. In my noninstrumental account of expressive rationality, citizens want to express who they are and what they care about. Whether or not one votes (...) therefore depends on the force of one’s commitments to principles, norms, ideologies or particular persons. This has been confirmed by empirical research showing that citizens vote because they feel they have to, not because they like doing so. Complementing instrumental rationality, this concept of expressive rationality gives a fuller, deeper and more adequate view of the way citizens make political decisions, thereby solving the paradox of voting. (shrink)

In his 2007 Ethics article, “Responsibility Incorporated,” Philip Pettit argued that corporations qualify as morally responsible agents because they possess autonomy, normative judgment, and the capacity for self-control. Although there is ongoing debate over whether corporations have these capacities, both proponents and opponents of corporate moral agency appear to agree that Pettit correctly identified the requirements for moral agency. In this article, I do not take issue with either the claim that autonomy, normative judgment, and self-control are the requirements for (...) moral agency or the claim that corporations possess them. I claim that if both of these claims are correct, then corporate moral agency entails that, in a liberal democracy, corporations should have the right to vote. I show that under the conception of democracy supported by most liberal political theorists, all parties subject to the law are entitled to the right to vote, and all parties that possess autonomy, normative judgment, and self-control are subject to the law. Therefore, if the proponents of corporate moral agency are correct, then corporations satisfy the requirements for the right to vote. I then consider potential objections to this argument. I show that the strongest objection to the corporate right to vote is undermined by Pettit’s own argument for corporate autonomy. I then show that objections derived from other arguments for limiting the rights of corporations are equally unavailing. I conclude with some observations about the implications of my argument for the question of corporate speech rights. (shrink)

In this paper, I examine the view that, surprisingly, the more citizens deliberate about politics, the less likely they are to participate in the realm of the political, and vice versa. In the first part of the paper, I approach the problem from the perspective of the paradox of voting, the claim that voting itself is instrumentally irrational because of the very low probability that a single vote will make any difference at the elections. In the second part (...) of the paper, I argue that rather than analyzing voting instrumentally, it is better to view it as part of the civic commitments that constitute what it means to be a citizen in a democratic society. The act of voting is not primarily an individual?s attempt to decisively influence any particular outcome, but an affirmation of the key practice that upholds the democratic society in which citizens play a part. This reveals a meta-paradox of voting. Namely, to not vote is to exhibit a type of behavior that implies acceptance of democracy simultaneously with rejecting its defining component. Because of that, I will claim, not voting is itself irrational. In light of that conclusion, in the third part of the paper, I explore the extant divide between deliberation and participation by referring back to the analysis of civic commitments. Whereas participation without deliberating reveals ideological bias, deliberation without participation expresses a lack of understanding of what it means to be a citizen. The way to connect them is to engage in a process of attaining reflective equilibrium between the two, starting from the practice of deliberation that would be fully informed by the awareness of our democratic commitments and disconnected from ideologically motivated participation. (shrink)

In his recent article in Philosophy and Public Affairs, 'The Paradox of Voting and Ethics of Political Representation', Alexander A. Guerrero argues it is rational to vote because each voter should want candidates they support to have the strongest public mandate possible if elected to office, and because every vote contributes to that mandate. The present paper argues that two of Guerrero's premises require correction, and that when those premises are corrected several provocative but compelling conclusions follow about the (...) rationality of voting and duties of elected officials: (A) Voting is typically rational for the members of a political party’s base; (B) Voting is often (but not always) irrational for “swing” voters (i.e. independent voters who are not affiliated with any political party, as well as “undecided” voters who are considering voting across party lines); and (C) Elected officials have a moral duty to respond to changing levels of popular support once in office, as indicated by properly monitored and corroborated public opinion polls of constituents, functioning more as delegates the lower their level of popular support. Finally, I suggest that the last of these conclusions has wide-ranging implications for political ethics. I illustrate these implications by focusing on the questions -- under debate in the 2016 US Presidential election cycle -- of whether a sitting President has a moral duty to nominate or not nominate a new Supreme Court justice during his or her final year in office, and similarly, whether US Senators have a moral duty to obstruct, or not obstruct, confirmation of the President’s eventual nominee. (shrink)

Weighted voting involves weighting representatives’ votes by the populations that they represent. Such systems have been adopted in some legislative bodies as a remedy for malapportionment, and are sometimes used to elect candidates for the executive branch of government. But they receive little attention. This note observes the neglected vices of weighted voting systems: they violate intuitive conditions of monotonicity and participation. These vices count significantly against the use of weighted voting, and reflecting on why they arise (...) improves our understanding of axioms in social choice theory. (shrink)

In explaining the outcome of the 2016 EU referendum in the United Kingdom, can theories emphasizing the importance of economic factors be reconciled with the fact that many people appeared to vote against their economic self-interest? This article approaches this puzzle through case study research that draws on fieldwork and a process of reciprocal knowledge exchange with local communities in five local authorities in England and Wales. It argues that the Leave vote can be attributed partly to political discontent associated (...) with trajectories of relative economic decline and deindustrialization. Building on the growing literature about the role of narratives and discourses in navigating uncertainty, it contends that these localized economic experiences, interpreted through local-level narratives, paved the way for local-level discourses of resilience and nationwide optimistic messaging about the economic impacts of Brexit to resonate. Local and national-level discourses discounting the potential economic costs of leaving the European Union played a crucial role in giving precise, somewhat paradoxical, political content to the sense of discontent. The article contributes to the growing focus on place and community in understanding political behavior and invites further research on local discourses linking macro-level trajectories and micro-level voting decisions. (shrink)

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on (...) smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections. (shrink)

The phenomenon of the paradoxes of the largest remainders methods has been studied by numerous authors. Nevertheless, the examples presented in their studies do not deal with the case where a party’s possible additional votes can directly lead to a loss in the party’s number of representatives. This paradox, which can be called the no-show apportionment paradox, has not previously been mentioned in the literature. It is based on the assumption that a voter’s favourite party may lose a seat (...) if the voter votes honestly but get more seats if he or she abstains. The article gives simple examples illustrating the no-show paradox in a party-list proportional representation electoral system using the quota method of apportionment. In these situations it would be better for the party if some of their voters abstained, otherwise it would lose one or more seats. (shrink)

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can (...) occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity. (shrink)

In referendum elections, voters are often required to register simultaneous votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on one proposal depends on the outcomes of other proposals. This type of interdependence can lead to unsatisfactory or even paradoxical election outcomes, such as a winning outcome that is the last choice of every voter. Here we propose an iterative voting scheme that allows voters to revise their voting strategies based on the outcomes of (...) previous iterations. Using a robust computer simulation, we investigate the potential of this approach to solve the separability problem. (shrink)

In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we (...) investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected. (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)

We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates (...) both “spoiler effects” and “strong no show paradoxes.”. (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)

In his thoughtful Commentary on my article, “Should Corporations Have the Right to Vote? A Paradox in the Theory of Corporate Moral Agency,” Kenneth Silver incorrectly asserts that I endorse Robert Dahl’s Principle of Affected Interests and social contract theory. To the extent that Silver’s criticism of my argument is based on the claim that I appeal to either theory as the ground for my claim that corporate moral agency entails a corporate right to vote, it is misguided. I rely (...) only on the Rawlsian equal participation principle that invests those subject to the law with the right to vote. To the extent Silver’s criticism is directed to that assertion, it is on 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 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 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)

There are two seemingly unrelated paradoxes of democracy. The older one is the doctrinal paradox or the discursive dilemma. or a comprehensive bibliography, see List 1995. The younger one is the mixed motivation problem introduced by Jonathan Wolff (1994) in this journal. In the mixed motivation problem, we have voters with mixed Benthamite and Rousseauian motivations who reach a majority on an issue that is neither in the self-interest of a majority of the voters, nor considered to be conducive (...) to the common good by a majority of the voters. What has gone unnoticed so far is that both of these paradoxes share a common structure. (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)

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is (...) to be used as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). (shrink)

The combination of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion in which the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set (...) of propositions (the conclusion). This problem is known as the doctrinal paradox. The doctrinal paradox is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox - the so-called premise-based procedure and the conclusion-based procedure - are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge knowledge bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

L'histoire n'est pas avare de paradoxe. C'est à Alger qu'est signée l'ordonnance du 21 avril 1944 qui accorde aux femmes françaises le droit de vote, mais c'est aussi à Alger, ou plus exactement en Algérie, que son champ d'application fut le plus restreint : si les Algériennes de souche européenne ont bénéficié des dispositions nouvelles, les Algériennes musulmanes, soit environ un million et demi de femmes, ont été privées du droit de vote. Si l'ordonnance du 7 mars 1944 qui proclam...

L'histoire n'est pas avare de paradoxe. C'est à Alger qu'est signée l'ordonnance du 21 avril 1944 qui accorde aux femmes françaises le droit de vote, mais c'est aussi à Alger, ou plus exactement en Algérie, que son champ d'application fut le plus restreint : si les Algériennes de souche européenne ont bénéficié des dispositions nouvelles, les Algériennes musulmanes, soit environ un million et demi de femmes, ont été privées du droit de vote. Si l'ordonnance du 7 mars 1944 qui proclam...

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of (...) propositions (the conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the proposition-wise independence of votes.

We consider two no-show paradoxes, in which a voter obtains a preferable outcome by abstaining from a vote. One arises when the casting of a ballot that ranks a candidate in first place causes that candidate to lose the election, superseded by a lower-ranked candidate. The other arises when a ballot that ranks a candidate in last place causes that candidate to win, superseding a higher-ranked candidate. We show that when there are at least four candidates and when voters (...) may express indifference, every voting rule satisfying Condorcet’s principle must generate both of these paradoxes. (shrink)

This paper presents the conditions required for a profile in order to never exhibit either the strong or the strict Borda paradoxes under all weighted scoring rules in three-candidate elections. The main particularity of our paper is that all the conclusions are deduced from the differences of votes between candidates in pairwise majority elections. This way allows us to answer new questions and provide an organized knowledge of the conditions under which a given profile never shows one or the (...) other of the two paradoxes. (shrink)

In this paper I start by briefly presenting an analysis of token cause and of token causal relevance that I developed elsewhere, and then apply it to the famous thirsty traveler riddle. One general outcome of the analysis of causal relevance employed here is that in preemption cases (early or late) the preempted cause is not a cause since it is causally irrelevant to the effect. I consider several variations of the thirsty traveler riddle. In the first variation the first (...) enemy emptied the canteen and the second enemy threw it away. On this variation, the act of neither enemy comes out, on the analysis employed here, as causally relevant to, and thus not as a cause of, the fact that the traveler died, but the conjunction of the two acts is a cause of it. This version is a case of mutual preemption. I argue that it has the same structure as the voting paradox, which thus has an analogous solution. In the standard version, in which the first enemy added poison to the water in the traveler's canteen, the act of the second enemy (who threw the canteen away) comes out, on the analysis used here, as causally relevant to and as a cause of the fact that the traveler died, but the act of the first enemy comes out as neither. I also make a comparison with Lewis' accounts, and discuss alternative treatments of the puzzle such as those of Hart and Honore and of Gavison, Margalit, and Ullmann-Margalit. (shrink)

Condorcet’s voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, Sen identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen’s result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen’s condition. We discuss how Sen’s condition is logically related to a number of (...) precursors. Finally, we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen’s sufficient condition, Sen’s condition cannot be further generalized in an appealing way. (shrink)