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 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 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)

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 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.

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)

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)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I (...) present two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (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)

Written not by a journalist or politician but rather by a theology professor with a Ph.D. in New Testament studies, Voting by the Bible: The Economic and Foreign Policy Issues begins with the assumption that God intended the Bible to give guidance to every area of life£including how governments should function. Derived from author Wayne Grudemþs magisterial Politics£According to the Bible, this book highlights those economic and foreign-policy issues that have dominated political debate recently. Throughout, author Wayne Grudem supports (...) political positions that would be called more 'conservative' than 'liberal.' However, 'it is important to understand that I see these positions as flowing out of the Bible's teachings rather than positions I hold prior to, or independently of, those biblical teachings,' he writes. 'My primary purpose in the book is not to be liberally or conservative, or Democrat or Republican, but to explain a biblical worldview and a biblical perspective on issues of politics, law, and government.' Concise yet carefully argued, this book is a must-read for any Christian concerned about current debates over the economy, the size and role of government, and the best way forward out of the current recession. Not every reader will agree with the book's conclusions. But by grounding his analysis deeply on Scripture, Grudem has equipped Christians to better understand and respond to some of today's key political debates wisely and in a manner consistent with their primary citizenship as members and ambassadors of the kingdom of God" -- Publisher description. (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)

In light of South Park's parody of the election process, this chapter engages with the questions such as How important was Stan's vote? Would the vote have been more valuable had the final margin of victory been closer? Also, how important is a vote that is between only two viable and equally unsavory options? by looking at how the power to vote has been extended in the United States over the past 200 years. The chapter discusses the voting irregularities (...) that arose in the 2000 and 2004 presidential elections. It considers the problem of choice within a two‐party system, given the South Park PETA member's comment that every election is “always between a Giant Douche and a Turd Sandwich.”. (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)

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.

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)

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)

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)

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)

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)

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)

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)

Recent political developments cast doubt on the wisdom of democratic decision-making. Brexit, the Colombian people's (initial) rejection of peace with the FARC, and the election of Donald Trump suggest that the time is right to explore alternatives to democracy. In this essay, I describe and defend the epistocratic system of government which is, given current theoretical and empirical knowledge, most likely to produce optimal political outcomes—or at least better outcomes than democracy produces. To wit, we should expand the suffrage as (...) wide as possible and weight citizens’ votes in accordance with their competence. As it turns out, the optimal system is closely related to J. S. Mill's plural voting proposal. I also explain how voters’ competences can be precisely determined, without reference to an objective standard of correctness and without generating invidious comparisons between voters. (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)

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)

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of (...) this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science. (shrink)

ABSTRACT In 1975 John Harris envisaged a survival lottery to redistribute organs from one to a greater number in order to reduce number of deaths as a consequence of organ failure. In this paper I reach a conclusion about when running a survival lottery is permissible by looking at the reason prospective participants have for allowing the procedure from a contractual perspective. I identify three versions of the survival lottery. In a National Lottery, everyone within a (...) jurisdiction is a candidate for being a donor for everyone else, disregarding all differences between individuals' eventual possibility of needing an organ. In a Group Specific Lottery, it is a question of running a lottery among members of a specific group who share the same probability of getting organ failure. In a Local Lottery one randomises among individuals who are already in need of a new organ but who happen to be compatible and in need of different organs. While the first is vulnerable to considerations of fairness, it is difficult to perceive a feasible way to implement the second option that does not come with a host of unwelcome consequences. I argue, however, that it is permissible to run Local Lotteries. (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)

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)

This paper addresses an argument offered by John Hawthorne gainst the propriety of an agent’s using propositions she does not know as premises in practical reasoning. I will argue that there are a number of potential structural confounds in Hawthorne’s use of his main example, a case of practical reasoning about a lottery. By drawing these confounds out more explicitly, we can get a better sense of how to make appropriate use of such examples in theorizing about norms, knowledge, (...) and practical reasoning. I will conclude by suggesting a prescription for properly using lottery propositions to do the sort of work that Hawthorne wants from them. (shrink)