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)

In this article I aim to counter Jason Brennan’s principled objection to the Representativeness Argument for compulsory voting, and to criticize the case in favour of voting lotteries, on which this challenge is predicated. In brief, Brennan claims that compulsory voting should be rejected because there is an alternative system, i.e. a voting lottery, which is able to ensure demographic proportionality in electoral turnouts without diminishing the freedom of citizens. But even on the most favourable (...) conception of freedom which the argument can employ, voting lotteries raise a number of serious concerns in respect to this value. Furthermore, while comparing voting lotteries and compulsory voting on the basis of freedom cannot provide any generalizable support for the former, a plausible case can instead be offered in support of the opposite idea, namely that compulsory voting outperforms voting lotteries with respect to freedom. (shrink)

This article compares the ‘enfranchisement lottery’, a novel method for allocating the right to vote, with universal suffrage. The comparison is conducted exclusively on the basis of the expected consequences of the two systems. Each scheme seems to have a relative advantage. On the one hand, the enfranchisement lottery would create a better informed electorate and thus improve the quality of electoral outcomes. On the other hand, universal suffrage is more likely to ensure that elections are seen to (...) be fair, which is important for political stability. This article concludes that, on balance, universal suffrage is prima facie superior to the enfranchisement lottery. Yet the analysis shows that the instrumental case for the ‘one person, one vote’ principle is less conclusive than democratic theorists usually suppose. (shrink)

This article compares the ‘enfranchisement lottery’, a novel method for allocating the right to vote, with universal suffrage. The comparison is conducted exclusively on the basis of the expected consequences of the two systems. Each scheme seems to have a relative advantage. On the one hand, the enfranchisement lottery would create a better informed electorate and thus improve the quality of electoral outcomes. On the other hand, universal suffrage is more likely to ensure that elections are seen to (...) be fair, which is important for political stability. This article concludes that, on balance, universal suffrage is prima facie superior to the enfranchisement lottery. Yet the analysis shows that the instrumental case for the ‘one person, one vote’ principle is less conclusive than democratic theorists usually suppose. (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.

Au xviiie siècle, la figure insistante de la «femme philosophe» s'articule à un imaginaire ambivalent de la différence des sexes, entre hantise d'une confusion délétère et quête d'un modèle d'harmonie. La femme travestit-elle la philosophie? Les Lumières ont-elles un genre?

Democracy is commonly associated with political equality and/or majority rule. This essay shows that these three ideas are conceptually separate, so the transition from any one to another stands in need of further substantive argument, which is not always adequately given. It does this by offering an alternative decision-making mechanism, called lottery voting, in which all individuals cast votes for their preferred options but, instead of these being counted, one is randomly selected and that vote determines the outcome. (...) This procedure is democratic and egalitarian, since all have an equal chance to influence outcomes, but obviously not majoritarian. (shrink)

Recently, political models which employ lottery-selection instead of ballot voting have been proposed. Proponents argue that such lottocratic models can improve the representation of the population and reduce undemocratic influences. In this paper, I argue that these proposals also satisfy the egalitarian requirement of democracy. I claim that having an equal chance to be selected by lot is equally egalitarian as having an equally weighed vote for two reasons: first, having a chance to be selected by lot satisfies (...) the requirement for political justice better than electoral democracy, and second, it provides citizens with equal political influence and not merely equal impact. (shrink)

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (shrink)

Democratic institutions are appealing means of making publicly justified social choices. By allowing participation by all citizens, democracy can accommodate diversity among citizens, and by considering the perspectives of all, via ballots or debate, democratic results can approximate what the balance of reasons favors. I consider whether, and under what conditions, democratic institutions might reliably make publicly justified social decisions. I argue that conventional accounts of democracy, constituted by voting or deliberation, are unlikely to be effective public justification mechanisms. (...) I conclude that the limitations of conventional mechanisms can be ameliorated through the use of lotteries instead of elections. (shrink)

After centuries of oblivion, the idea of using civic lotteries to select citizens to participate in major decision-making bodies has started gaining popularity among certain democratic theorists. Undoubtedly, this is an idea worth exploring, given the constantly rising dissatisfaction with the operation of major representative institutions. One should not, however, infer from this fact that any proposed sortition-based institutional arrangement is compatible with basic democratic principles. This article critically examines two such proposals: (a) that we should establish fully powered legislative (...) bodies consisting entirely of allotted citizens and (b) López-Guerra’s enfranchisement lottery, the gist of which is that voting rights should be granted only to a very small random sample of current electors, who will be subjected to a “competence-building process.” The article argues that both proposals run counter to the idea of rule by the people conceived as equally valuable and fully participating memb ers of a self-governing political entity. (shrink)

Landmark Supreme Court rulings determine American law by adjudicating among competing reasonable interpretations of basic political rights. Jeremy Waldron argues that this practice is democratically illegitimate because what determines the content of basic rights is a bare majority vote of an unelected, democratically unaccountable, elitist body of nine judges. I argue that Waldron's democratic critique of judicial review has implications for real-world reform, but not the implications he thinks it has. He argues that systems of legislative supremacy over the judiciary (...) are democratically preferable to the American one. I provide reasons why his argument is unsound and explain that, properly construed, Waldron's premises support implementing a system where ordinary citizens chosen by lottery participate in a deliberative mini-public to vote on which reasonable interpretation of a basic political right will become the law of the land. (shrink)

Before an election, two candidates choose policies which are lotteries over electionday distributive positions. I find conditions under which there exist mixed-strategy probabilistic-voting equilibria which are independent, treating voter groups independently.

One way to evaluate electoral rules is instrumental: we ask what effects they tend to produce. A second way is constitutive: we ask what kinds of values they embody, or whether the procedures they effect respect people's rights or moral status. A third way is genetic: we ask by what procedure the electoral rules were adopted. I shall argue that in judging the value or the legitimacy of electoral rules, we must consider not only (1) the values they serve instrumentally (...) and (2) the values, rights, or statuses they embody or respect, but also (3) the procedure by which they were chosen. I argue, moreover, that the best way to choose electoral rules in representative governments is on an ongoing basis via a randomly selected citizen assembly whose decisions are binding independently of any appeal to referenda. (shrink)

The lottery paradox can be solved if epistemic justification is assumed to be a species of permissibility. Given this assumption, the starting point of the paradox can be formulated as the claim that, for each lottery ticket, I am permitted to believe that it will lose. This claim is ambiguous between two readings, depending on the scope of ‘permitted’. On one reading, the claim is false; on another, it is true, but, owing to the general failure of permissibility (...) to agglomerate, does not generate the paradox. The solution generalizes to formulations of the paradox in terms of rational acceptability and doxastic rationality. (shrink)

In a recent article, Douven and Williamson offer both (i) a rebuttal of various recent suggested sufficient conditions for rational acceptability and (ii) an alleged ‘generalization’ of this rebuttal, which, they claim, tells against a much broader class of potential suggestions. However, not only is the result mentioned in (ii) not a generalization of the findings referred to in (i), but in contrast to the latter, it fails to have the probative force advertised. Their paper does however, if unwittingly, bring (...) us a step closer to a precise characterization of an important class of rationally unacceptable propositions—the class of lottery propositions for equiprobable lotteries. This helps pave the way to the construction of a genuinely lottery-paradox-proof alternative to the suggestions criticized in (i). (shrink)

The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties (...) encountered by those approaches. (shrink)

The lottery paradox plays an important role in arguments for various norms of assertion. Why is it that, prior to information on the results of a draw, assertions such as, “My ticket lost,” seem inappropriate? This paper is composed of two projects. First, I articulate a number of problems arising from Timothy Williamson’s analysis of the lottery paradox. Second, I propose a relevant alternatives theory, which I call the Non-Destabilizing Alternatives Theory , that better explains the pathology of (...) asserting lottery propositions, while permitting assertions of what I call fallible propositions such as, “My car is in the driveway.” Le paradoxe de la loterie joue un rôle important dans l’argumentation visant à défendre diverses normes de l’assertion. Comment se fait-il que, avant que les résultats d’un tirage soient connus, des assertions comme «Mon billet a perdu» semblent inappropriées? Cet article se compose de deux projets. Premièrement, je relève certains problèmes issus de l’analyse du paradoxe de la loterie par Timothy Williamson. Deuxièmement, je propose une théorie des alternatives pertinentes que j’appelle la «théorie des alternatives non-déstabilisantes» , et qui explique d’une meilleure façon la pathologie de l’assertion de propositions concernant la loterie, tout en permettant des assertions faillibles, telles que «Ma voiture est dans l’entrée». (shrink)

The lottery paradox shows that the following three individually highly plausible theses are jointly incompatible: highly probable propositions are justifiably believable, justified believability is closed under conjunction introduction, known contradictions are not justifiably believable. This paper argues that a satisfactory solution to the lottery paradox must reject as versions of the paradox can be generated without appeal to either or and proposes a new solution to the paradox in terms of a novel account of justified believability.

Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in (...) its chances of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (shrink)

The lottery paradox shows seemingly plausible principles of rational acceptance to be incompatible. It has been argued that we shouldn’t be concerned by this clash, since the concept of (categorical) belief is otiose, to be supplanted by a quantitative notion of partial belief, in terms of which the paradox cannot even be formulated. I reject this eliminativist view of belief, arguing that the ordinary concept of (categorical) belief has a useful function which the quantitative notion does not serve. I (...) then propose a solution to the paradox it engenders. (shrink)

This paper defends the permissibility solution to the lottery paradox against an objection by Anna-Maria Asunta Eder. Eder argues that the permissibility solution should also be applicable to the preface paradox, but conflicts with a plausible principle about epistemic permissions when so applied. This paper replies by first criticizing Eder’s considerations in defense of her principle; in particular, it argues that the plausibility of her principle is to a large extent parasitic on the spurious plausibility of the principle of (...) factual detachment. The paper then presents a direct argument against Eder’s principle, which shows that her principle conflicts with a Pareto-style condition on permissible belief. (shrink)

The opportunities to become a good person are not the same for everyone. Modern European ethical theory, especially Kantian ethics, assumes the same virtues are accessible to all who are capable of rational choice. Character development, however, is affected by circumstances, such as those of wealth and socially constructed categories of gender, race, and sexual orientation, which introduce factors beyond the control of individuals. Implications of these influences for morality have, since the work of Williams and Nagel in the seventies, (...) raised questions in philosophy about the concept of moral luck. In The Unnatural Lottery, Claudia Card examines how luck enters into moral character and considers how some of those who are oppressed can develop responsibility. Luck is often best appreciated by those who have known relatively bad luck and have been unable to escape steady comparison of their lot with those of others. The author takes as her paradigms the luck of middle and lower classes of women who face violence and exploitation, of lesbians who face continuing pressure to hide or self-destruct, of culturally Christian whites who have ethnic privilege, and of adult survivors of child abuse. How have such people been affected by luck in who they are and can become, the good lives available to them, the evils they may be liable to embody? Other philosophers have explored the luck of those who begin from privileged positions and then suffer reversals of fortune. Claudia Card focuses on the more common cases of those who begin from socially disadvantaged positions, and she considers some who find their good luck troubling when its source is the unnatural lottery of social injustice. (shrink)

In this paper, we present the results of two surveys that investigate subjects’ judgments about what can be known or justifiably believed about lottery outcomes on the basis of statistical evidence, testimonial evidence, and “mixed” evidence, while considering possible anchoring and priming effects. We discuss these results in light of seven distinct hypotheses that capture various claims made by philosophers about lay people’s lottery judgments. We conclude by summarizing the main findings, pointing to future research, and comparing our (...) findings to recent studies by Turri and Friedman. (shrink)

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some "lottery proposition" which we think we do not know but to which we assign a high probability of being true (for instance: “I will never be a multi-millionaire” entails “I will not win this lottery”). How is this possible - given that some closure principle is true? This problem, also known as “the Lottery puzzle”, has recently provoked a lot of discussion. In (...) this paper I discuss one of the most promising answers to the problem: Stewart Cohen’s contextualist solution which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)

One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...) the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event. (shrink)

One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters requires (...) a nonconstructive axiom like AC. (shrink)

What limits should there be on the areas of life that are governed by market forces? For many years, no one seriously defended the buying and selling votes for political elections. In recent years, however, this situation has changed, with a number of authors defending the permissibility of vote markets. One popular objection to such markets is that they would lead to a tyranny of wealth, where the poor are politically dominated by the rich. In a recent paper, Taylor :313–328, (...) 2017. doi: 10.1007/s11158-016-9327-0) has argued that this objection can be avoided if certain restrictions are placed on vote markets. In this paper we will argue that this attempt to rebut an argument against vote markets is unsuccessful. Either vote markets secure their purported benefits but then they inevitably lead to a tyranny of wealth, or they are restricted so heavily that they lack the features that have been claimed to make vote markets attractive in the first place. Using Taylor’s proposal as a test case, we make the more general claim that vote markets cannot avoid the tyranny of wealth objection and bring about their supposed benefits at the same time. (shrink)

Thomas Kroedel argues that we can solve a version of the lottery paradox if we identify justified beliefs with permissible beliefs. Since permissions do not agglomerate, we might grant that someone could justifiably believe any ticket in a large and fair lottery is a loser without being permitted to believe that all the tickets will lose. I shall argue that Kroedel’s solution fails. While permissions do not agglomerate, we would have too many permissions if we characterized justified belief (...) as sufficiently probable belief. If we reject the idea that justified beliefs can be characterized as sufficiently probably beliefs, Kroedel’s solution is otiose because the paradox can be dissolved at the outset. (shrink)

To resolve the lottery paradox, the “no-justification account” proposes that one is not justified in believing that one's lottery ticket is a loser. The no-justification account commits to what I call “the Harman-style skepticism”. In reply, proponents of the no-justification account typically downplay the Harman-style skepticism. In this paper, I argue that the no-justification reply to the Harman-style skepticism is untenable. Moreover, I argue that the no-justification account is epistemically ad hoc. My arguments are based on a rather (...) surprising finding that the no-justification account implies that people living in Taiwan typically suffer from the Harman-style skepticism. (shrink)

A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that (...) is intrinsically vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness. (shrink)

Self-interest voting is irrational when it has even a small cost, but it can be rational for those who care about others; its expected utility (EU) may exceed its cost. For cosmopolitan voters (those who care about outsiders), the EU of voting increases with the number of affected others. The EU of voting for the good of the world now and in the future can thus be large. In some cases, the EU of parochial voting (e.g., (...) considering only one's nation) may not cross the cost threshold, but cosmopolitan voting can cross it. I apply these principles to various kinds of voting. And I compare voting to charity. Voting has the advantage of enlisting the coercive power of the state, but charity can be more focused on effective policies. I discuss campaign contributions, and I conclude with a discussion of the existence of utilitarian voters. (shrink)

It can often be heard in the hallways, and occasionally read in print, that reliabilism runs into special trouble regarding lottery cases. My main aim in this paper is to argue that this is not so. Nevertheless, lottery cases do force us to pay close attention to the relation between justification and probability.

Voting Advice Applications (VAAs) are interactive online tools designed to assist voters by improving the basis on which they decide how to vote. In recent years, they have been widely adopted, but their design is the subject of ongoing and often heated criticism. Most of these debates focus on whether VAAs accurately measure the standpoints of political parties and the preferences of users and on whether they report valid results while avoiding political bias. It is generally assumed that if (...) their methodology is sound, then VAAs can be seen as strengthening the democratic process. But as we argue in this chapter, the setup of VAAs raises basic questions of normative democratic theory as well. Insofar as VAAs are supposed to improve the functioning of the democratic process, it must be clarified in what sense they aim to make a contribution, before it even makes sense to discuss their effectiveness at doing so. -/- VAAs are often intended to enhance the democratic process by one or all of the following: (I) informing voters about the policy standpoints of political parties (or individual candidates), (2) increasing voter turnout, and (3) ensuring that the composition of parliaments more accurately reflects the political attitudes of the electorate. In the next three sections, we discuss three central bones of contention in current democratic theory that are crucial to these ways in which VAAs typically take themselves to contribute to strengthening the democratic process: -/- 1. Questions about citizen competence: What forms of competence do citizens need to have, and to what extent, for a democracy to function properly? -/- 2. Questions about political participation: What forms and extent of participation are vital to democracy? -/- 3. Questions about democratic representation: How should the relation between the elected and the electorate be understood? -/- For each issue we aim to show, first, how the design and setup of mainstream VAAs are tacitly structured by a specific conception of the democratic aim at issue and, second, what some alternative positions on these questions are within contemporary political theory. In the final section, we will discuss some of the implications of this analysis for the responsibilities of VAA developers, and particularly for the procedural neutrality to which they are typically committed. Our conclusion will be that once these issues are identified, developers of VAAs should either argue in favour of their views on democratic competence, participation and representation, or they should rethink the design of VA As in ways that move beyond their current assumptions, or both. (shrink)

Suppose that I hold a ticket in a fair lottery and that I believe that my ticket will lose [L] on the basis of its extremely high probability of losing. What is the appropriate epistemic appraisal of me and my belief that L? Am I justified in believing that L? Do I know that L? While there is disagreement among epistemologists over whether or not I am justified in believing that L, there is widespread agreement that I do not (...) know that L. I defend the two-pronged view that I am justified in believing that my ticket will lose and that I know that it will lose. Along the way, I discuss four different but related versions of the lottery paradox—The Paradox for Rationality, The Paradox for Knowledge, The Paradox for Fallibilism, and The Paradox for Epistemic Closure—and offer a unified resolution of each of them. (shrink)

We analyze the results from three different risk attitude elicitation methods. First, the broadly used test by Holt and Laury, HL, second, the lottery-panel task by Sabater-Grande and Georgantzis, SG, and third, responses to a survey question on self-assessment of general attitude towards risk. The first and the second task are implemented with real monetary incentives, while the third concerns all domains in life in general. Like in previous studies, the correlation of decisions across tasks is low and usually (...) statistically non-significant. However, when we consider only subjects whose behavior across the panels of the SG task is compatible with constant relative risk aversion, the correlation between HL and self-assessed risk attitude becomes significant. Furthermore, the correlation between HL and SG also increases for CRRA-compatible subjects, although it remains statistically non-significant. (shrink)

The allocation of vaccines and therapeutics for Covid‐19 obviously raises ethical questions, and physicians and ethicists have begun to address them. Writers have identified various criteria that should guide allocation decisions, but the criteria often conflict and need to be balanced against one another. This article proposes a model for thinking about how different considerations that are relevant to the distribution of vaccines and scarce treatments for Covid‐19 could be integrated into an allocation procedure. The model employs the construct of (...) a weighted lottery, which is a construct that has been employed in other contexts that involve the distribution of scarce resources. The article highlights the advantages of applying a weighted lottery to the Covid‐19 context and offers an illustration for how it might work in practice. The primary aim of the article is to articulate the structural features of a weighted lottery for this context and to bring out its advantages over other methods for allocating Covid‐19 medications. (shrink)

In this imaginative and provocative book, Barbara Goodwin explores the question of how lottery systems can achieve egalitarian social justice in societies with seemingly ineradicable inequalities. She begins with the utopian fable of Aleatoria, a country not unlike our own in the not-too-distant-future, where most goods are distributed by lottery--even the right to have children. She then analyzes the philosophical arguments for and against lottery distribution and a comparison of "justice by lottery" with other contemporary theories (...) of justice. Goodwin also applies her theory to practical problems in the real world which could be--or have been--justly resolved by the use of lotteries, such as military drafts, jury duty, and immigration eligibility. She demonstrates that in many areas, including that of political power, a regular and random reallocation of goods would be a fairer and more democratic method than the distributive systems found in liberal democracies today. (shrink)

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible by <κ-directed closed forcing; a strong cardinal κ becomes indestructible by κ-strategically closed forcing; and a strongly compact cardinal κ becomes indestructible by, among others, the (...) forcing to add a Cohen subset to κ, the forcing to shoot a club Cκ avoiding the measurable cardinals and the forcing to add various long Prikry sequences. The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laver function concept from the supercompact cardinal context. (shrink)

We talk and think about our beliefs both in a categorical and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How to (...) resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate. (shrink)

We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei–Shelah model or in saturated models. We argue that some of the objections to hyperreal probabilities arise from hidden biases that favor Archimedean models. We discuss the advantage of the hyperreals over transferless fields with infinitesimals. In Paper II we analyze two underdetermination theorems by Pruss and (...) show that they hinge upon parasitic external hyperreal-valued measures, whereas internal hyperfinite measures are not underdetermined. (shrink)

As John Rawls makes clear in A Theory of Justice, there is a popular and influential strand of political thought for which brute luck – that is, being lucky in the so-called “lottery of life” – ought to have no place in a theory of distributive justice. Yet the debate about luck, desert, and fairness in contemporary political philosophy has recently been rekindled by a handful of philosophers who claim that desert should play a bigger role in theories of (...) distributive justice. In the present paper, we present the results of our attempts to fill in some of the missing empirical details of this debate. Our findings provide some preliminary evidence that, contrary to what most contemporary political philosophers have assumed, people are not as worried by natural luck as previously thought. Instead, people’s worries seem to be focused exclusively on inequalities generated by social luck. (shrink)

Prevailing opinion—defended by Jason Brennan and others—is that voting to change the outcome is irrational, since although the payoffs of tipping an election can be quite large, the probability of doing so is extraordinarily small. This paper argues that prevailing opinion is incorrect. Voting is shown to be rational so long as two conditions are satisfied: First, the average social benefit of electing the better candidate must be at least twice as great as the individual cost of (...) class='Hi'>voting, and second, the chance of casting the decisive vote must be at least 1/N, where N stands for the number of citizens. It is argued that both of these conditions are often true in the real world. (shrink)

Two prominent relational egalitarians, Elizabeth Anderson and Niko Kolodny, object to giving people in a democratic community differential voting weights on the grounds that doing so would lead to unequal relations between them. Their claim is that deviating from a “one-person, one-vote” scheme is incompatible with realizing relational egalitarian justice. In this article, I argue that they are wrong. I do so by showing that people can relate as moral, epistemic, social, and empirical equals in a scheme with differential (...) voting weights. I end the article by showing that from the perspective of relational egalitarianism, it is sometimes true that differential voting weights are more just than equal voting weights. (shrink)