This article presents the question of the epistemology of disagreement, which can be discussed from two main points of view of conciliationism and of steadfastness. David Christensen and Thomas Kelly are chosen as the representatives. The main problem raised in the article is an epistemic peerhood. The paper aims to prove that it is not possible to identify two philosophers even specialized in the same discipline as peers in the strict sense. They can be treated as peers to a certain (...) extent only, and therefore their opinions cannot be treated as thoroughly equal. Accordingly, the article makes a point that the total evidence view seems to be the best solution in the epistemology of disagreement. (shrink)

The philosophical debate on paternalism is conducted as if the property of being paternalistic should be attributed to actions. Actions are typically deemed to be paternalistic if they amount to some kind of interference with a person and if the rationale for the action is the good of the person interfered with. This focus on actions obscures the normative issues involved. In particular, it makes it hard to provide an analysis of the traditional liberal resistance to paternalism. Given the fact (...) that actions most often have mixed rationales, it is not clear how we should categorize and evaluate interfering actions for which only part of the rationale is the good of the person. The preferable solution is to attribute the property of being paternalistic not to actions, but to compounds of reasons and actions. The framework of action–reasons provides the tools for distinguishing where exactly paternalism lies in the complex web of reasons and actions. (shrink)

I first distinguish four types of objection to paternalism and argue that only one – the principled objection – amounts to a substantive and distinct normative doctrine. I then argue that this doctrine should be understood as preventing certain facts from playing the role of reasons they would otherwise play. I explain how this filter approach makes antipaternalism independent of several philosophical controversies: On the role reasons play, on what reasons there are, and on how reasons are related to values. (...) I go on to contrast the filter approach with the competing and dominant action-focused approach, which understands objections to paternalism in terms of paternalistic action, behavior, law, policy and the like. Seana Shiffrin and Peter de Marneffe are singled out as prominent recent proponents of this approach. By engaging with their definitions of paternalism, I explain how the action-focused approach makes antipaternalism dependent on the sorting of actions into paternalistic and nonpaternalistic according to what reasons support them. Because one and the same action can be supported by many different reasons, and by different sorts of reasons, such sorting is very difficult. The upshot is that antipaternalism on the action-focused account fails to provide the precise normative implications of the filter approach that I favor. (shrink)

Paternalism means, roughly, benevolent interference: benevolent because it aims at promoting or protecting a person’s good; interference because it restricts his liberty without his consent. The paternalist believes herself superior in that she can secure some benefit for the person that he himself will not secure. Paternalism is opposed by the liberal tradition, at least when it targets sufficiently voluntary behavior. In legal contexts, policies may be paternalistic for some and not for others, forcing trade-offs. In medical contexts, paternalism can (...) be an open or hidden aspect of the relationship between caregiver and patient. (shrink)

This article first describes a dilemma for liberalism: On the one hand restricting their own options is an important means for groups of people to shape their lives. On the other hand, group members are typically divided over whether or not to accept option-restricting solutions or policies. Should we restrict the options of all members of a group even though some consent and some do not? This dilemma is particularly relevant to public health policy, which typically target groups of people (...) with no possibility for individuals to opt out. The article then goes on to propose and discuss a series of aggregation rules for individual into group consent. Consideration of a number of scenarios shows that such rules cannot be formulated only in terms of fractions of consenters and non-consenters, but must incorporate their motives and how much they stand to win or lose. This raises further questions, including what is the appropriate impact of altruistic consenters and non-consenters, what should be the impact of costs and benefits and whether these should be understood as gross or net. All these issues are dealt with in a liberal, anti-paternalistic spirit, in order to explore whether group consent can contribute to the justification of option-restricting public health policy. (shrink)

To nudge is to design choice contexts in order to improve choice outcomes. Richard Thaler and Cass Sunstein emphatically endorse nudging but reject more restrictive means. In contrast, I argue that the behavioral psychology that motivates nudging also motivates what may be called jolting — i.e. the design of choice content. I defend nudging and jolting by distinguishing them from the sometimes oppressive means with which they can be implemented, by responding to some common arguments against nudging, and by showing (...) how respect for preferences over option sets and their aggregate properties may require the trimming of option sets, as well as helpful choice contexts. (shrink)

Drink driving causes great suffering and material destruction. The alcohol interlock promises to eradicate this problem by technological design. Traditional counter-measures to drink driving such as policing and punishment and information campaigns have proven insufficient. Extensive policing is expensive and intrusive. Severe punishment is disproportionate to the risks created in most single cases. If the interlock becomes inexpensive and convenient enough, and if there are no convincing moral objections to the device, it may prove the only feasible as well as (...) the only justifiable solution to the problem of drink driving. A policy of universal alcohol interlocks, in all cars, has been proposed by several political parties in Sweden and is supported by the National Road Administration and the 2006 Alcohol Interlock Commission. This article assesses two possible moral objections to a policy of universal interlocks: (i) that it displaces the responsibility of individual drivers and (ii) that it constitutes a paternalistic interference with drivers. The first objection is found unconvincing, while the second has only limited bite and may be neutralized if paternalism is accepted for the sake of greater net liberty. Given the expected technological development, the proposed policy seems a commendable health promotion measure for the near future. (shrink)

Debates on the nature and justifiability of paternalism typically focus only on adults, sometimes presuming without argument that paternalism towards children is a non-issue or obviously justified. Debates on the moral and political status of children, in turn, rarely connect with the rich literature on paternalism. This chapter attempts to bridge this gap by exploring how issues that arise in the general debate on paternalism are relevant also for the benevolent interference with children. I survey and discuss various views and (...) argue for my own: that paternalism towards children is in most respects like paternalism towards adults and stands in the same need of justification, though such justification is more often forthcoming both because children are typically less prudent than adults and so benefit more from interference, and because, in some respects, interference is less harmful to them. (shrink)

In many or most instances of paternalism, more than one person acts paternalistically, or more than one person is treated paternalistically. This chapter discusses some complications that arise in such group cases, which are largely ignored in the conceptual debate. First, a group of people who together perform an action may do so for different reasons, which makes it more challenging to determine whether the action is paternalistic. This gives us some reason not to pin the property of being paternalistic (...) on actions, since we may alternatively pin it on reasons for actions and allow that these differ between members in the group. Second, the prevention of harmful consensual interactions is sometimes paternalism towards both or all involved, but only if all benefit from interference with themselves rather than with other members in the group, or if all want the harm or risk (more or less) for its own sake. Third, interrelations between three components of paternalism - interference, benevolence and consent - gives us reason to allow that an action can be paternalistic towards some but not others of those affected. This makes it even more difficult, and less relevant, to determine whether or not actions are paternalistic. (shrink)

This chapter concerns the normativity of the concepts of paternalism and libertarian paternalism. The first concept is central in evaluating public health policy, but its meaning is controversial. The second concept is equally controversial and has received much attention recently. It may or may not shape the future evaluation of public health policy. In order to facilitate honest and fruitful debate, I consider three approaches to these concepts, in terms of their normativity. Concepts, I claim, may be considered nonnormative, normatively (...) charged, or normative in that they involve more complex relationships between values or duties. While the last approach is often best, other approaches may be appropriate depending on the context and purpose of discussion. The chapter’s conceptual investigation is illustrated by application to two public health policies: a tax on the consumption of fat and the encouragement of health-promoting food displays in restaurants and supermarkets. (shrink)

As liberals, we would like each person to direct her own life in accordance with her will. However, because of the complexities of the human mind, it is very often not clear what a person wills. She may choose one thing though she prefers another, while having false beliefs the correction of which would cause her to prefer some third thing. I propose, against this background, that to respect a person’s will or self-direction is to respect both her choices and (...) her preferences, with some priority given to those preferences that are informed and coherent. This is a pluralist answer to the neglected question, “respect for what?”. (shrink)

Receiving information about threats to one’s health can contribute to anxiety and depression. In contemporary medical ethics there is considerable consensus that patient autonomy, or the patient’s right to know, in most cases outweighs these negative effects of information. Worry about the detrimental effects of information has, however, been voiced in relation to public health more generally. In particular, information about uncertain threats to public health, from—for example, chemicals—are said to entail social costs that have not been given due consideration. (...) This criticism implies a consequentialist argument for withholding such information from the public in their own best interest. In evaluating the argument for this kind of epistemic paternalism, the consequences of making information available must be compared to the consequences of withholding it. Consequences that should be considered include epistemic effects, psychological effects, effects on private decisions, and effects on political decisions. After giving due consideration to the possible uses of uncertain information and rebutting the claims that uncertainties imply small risks and that they are especially prone to entail misunderstandings and anxiety, it is concluded that there is a strong case against withholding of information about uncertain threats to public health. (shrink)

I first provide an analysis of Joel Feinberg’s anti-paternalism in terms of invalidation of reasons. Invalidation is the blocking of reasons from influencing the moral status of actions, in this case the blocking of personal good reasons from supporting liberty-limiting actions. Invalidation is shown to be distinct from moral side constraints and lexical ordering of values and reasons. I then go on to argue that anti-paternalism as invalidation is morally unreasonable on at least four grounds, none of which presuppose that (...) people can be mistaken about their own good: First, the doctrine entails that we should sometimes allow people to unintentionally severely harm or kill themselves though we could easily stop them. Second, it entails that we should sometimes allow perfectly informed and rational people to risk the lives of themselves and others, though they are in perfect agreement with us on what reasons we have to stop them for their own good. Third, the doctrine leaves unexplained why we may benevolently coerce less competent but substantially autonomous people, such as young teens, but not adults. Last, it entails that there are peculiar jumps in justifiability between very similar actions. I conclude that as liberals we should reject anti-paternalism and focus our efforts on explicating important liberal values, thereby showing why liberty reasons sometimes override strong personal good reasons, though never by making them invalid. (shrink)

Decisions in medical contexts have immediate and obvious consequences in terms of health and sometimes death or survival. Medical decisions also have less obvious and less immediate consequences, including effects on the long-term physical and mental well-being of patients, their families and of care-givers, as well as on the distribution of scarce medical resources. Some of these consequences are hard to measure and estimate. Even harder, perhaps, is the determination of the relative value of different consequences. How should consequences be (...) evaluated? How do uncertainties and biases affect our evaluations of consequences? What influence should our evaluations of consequences have on our actions? These questions are all philosophical in nature. (shrink)

Public health policy often limits people’s liberty for their own good. The very point of many types of public health measures is to restrict people’s options in order to stop them from doing unhealthy things, for example use harmful recreational drugs or drive without a seatbelt. While such restrictive public health policies enjoy widespread support, so does the traditional liberal idea that liberty (or autonomy) is a higher value, to be given priority in most, if not all, circumstances. In this (...) text, I will defend the thesis that liberty is an important value, but with no claim to priority. (shrink)

George Sher’s book Beyond Neutrality: Perfectionism and Politics has, he says, two main purposes. The first is to “defuse the main reasons to deny that the state may seek to promote the good”, the other is to “develop a conception of the good that is worth promoting” (1). In this article, I will not be concerned with either of these aims. Instead, I will focus on Sher’s preliminary discussion of the “scope and meaning” of neutralism (20). I consider Sher’s careful (...) analysis of the structure of neutralism one of the book’s virtues, alongside his original theory of the good and his comprehensive and convincing arguments against neutralism. This careful analysis inspires me to attempt some critique and development. I will defend an account of neutralism according to which this doctrine puts a constraint on what reasons should enter into political reasoning. What I defend is not neutralism per se, but only this account of neutralism relative to competing accounts. I believe this account is an improvement over Sher’s, in terms of conceptual precision and normative plausibility, both in general and from the perspective of the doctrine’s proponents in particular. (shrink)

Since ancient times, legal systems have held owners responsible for harm caused by their property. Across 4 experiments, we show that children aged 3–7 also hold owners responsible for such harm. Older children judge that owners should repair harm caused by property, and younger children may do this as well. Younger and older children judge that owners should apologize for harm, even when children do not believe the owners allowed the harm to occur. Children are also as likely to hold (...) owners responsible for harm caused by property as for harm caused by the owners themselves. The present findings contribute to psychological accounts of ownership by showing that ownership not only confers rights to control property, but also responsibility for harm caused by property. The findings also contribute to our understanding of the attribution of responsibility, and challenge accounts claiming that directly causing harm, or allowing it to happen, is a prerequisite for responsibility. The findings provide support for an account claiming that property is an extension of its owner, and likewise reveal that responsibility for harm caused by property is an early developing aspect of the psychology of ownership. 2018 APA, all rights reserved). (shrink)

Abstract: Lotteries have long been a source of fascination and intrigue, offering the tantalizing prospect of unexpected fortunes. In this research paper, we delve into the world of lottery predictions, employing cutting-edge AI techniques to unlock the secrets of lottery outcomes. Our dataset, obtained from Kaggle, comprises historical lottery draws, and our goal is to develop predictive models that can anticipate future winning numbers. This study explores the use of deep learning and time series analysis to achieve (...) this elusive feat. Through rigorous experimentation and data-driven approaches, we seek to determine the viability of AI in the realm of lottery predictions. Our findings reveal both the promise and limitations of AI in this context, shedding light on the complexities of lottery data and the potential need for quantum computing as a last resort. (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)

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)

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)

I review recent empirical findings on knowledge attributions in lottery cases and report a new experiment that advances our understanding of the topic. The main novel finding is that people deny knowledge in lottery cases because of an underlying qualitative difference in how they process probabilistic information. “Outside” information is generic and pertains to a base rate within a population. “Inside” information is specific and pertains to a particular item’s propensity. When an agent receives information that 99% of (...) all lottery tickets lose (outside information), people judge that she does not know that her ticket will lose. By contrast, when an agent receives information that her specific ticket is 99% likely to lose (inside information), people judge that she knows that her ticket will lose. Despite this difference in knowledge judgments, people rate the likelihood of her ticket losing the exact same in both cases (i.e. 99%). The results shed light on other factors affecting knowledge judgments in lottery cases, including formulaic expression and participants’ own estimation of whether it is true that the ticket will lose. The results also undermine previous hypotheses offered for knowledge denial in lottery cases, including the hypotheses that people deny knowledge because they either deny justification or acknowledge a chance for error. (shrink)

In some lottery situations, the probability that your ticket's a loser can get very close to 1. Suppose, for instance, that yours is one of 20 million tickets, only one of which is a winner. Still, it seems that (1) You don't know yours is a loser and (2) You're in no position to flat-out assert that your ticket is a loser. "It's probably a loser," "It's all but certain that it's a loser," or even, "It's quite certain that (...) it's a loser" seem quite alright to say, but, it seems, you're in no position to declare simply, "It's a loser." (1) and (2) are closely related phenomena. In fact, I'll take it as a working hypothesis that the reason "It's a loser" is unassertable is that (a) You don't seem to know that your ticket's a loser, and (b) In flat-out asserting some proposition, you represent yourself as knowing it.1 This working hypothesis will enable me to address these two phenomena together, moving back and forth freely between them. I leave it to those who reject the hypothesis to sort out those considerations which properly apply to the issue of knowledge from those germane to that of assertability. Things are quite different when you report the results of last night's basketball game. Suppose your only source is your morning newspaper, which did not carry a story about the 1 game, but simply listed the score, "Knicks 83, at Bulls 95," under "Yesterday's Results." Now, it doesn't happen very frequently, but, as we all should suspect, newspapers do misreport scores from time to time. On several occasions, my paper has transposed a result, attributing to each team the score of its opponent. In fact, that your paper's got the present result wrong seems quite a bit more probable than that you've won the lottery of the above paragraph. Still, when asked, "Did the Bulls win yesterday?", "Probably" and "In all likelihood" seem quite unnecessary. "Yes, they did," seems just fine.. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

In the first chapter of his Knowledge and Lotteries, John Hawthorne argues that thinkers do not ordinarily know lottery propositions. His arguments depend on claims about the intimate connections between knowledge and assertion, epistemic possibility, practical reasoning, and theoretical reasoning. In this paper, we cast doubt on the proposed connections. We also put forward an alternative picture of belief and reasoning. In particular, we argue that assertion is governed by a Gricean constraint that makes no reference to knowledge, and (...) that practical reasoning has more to do with rational degrees of belief than with states of knowledge. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. (...) In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about (...) our concept of knowledge. However, examining these shifts also raises interesting questions about how we ought to be thinking about possible outcomes in the first place. (shrink)

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical proposition (...) based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

Shortages of new therapeutics to treat coronavirus disease (COVID-19) have forced clinicians, public health officials, and health systems to grapple with difficult questions about how to fairly allocate potentially life-saving treatments when there are not enough for all patients in need (1). Shortages have occurred with remdesivir, tocilizumab, monoclonal antibodies, and the oral antiviral Paxlovid (2) -/- Ensuring equitable allocation is especially important in light of the disproportionate burden experienced during the COVID-19 pandemic by disadvantaged groups, including Black, Hispanic/Latino and (...) Indigenous communities, individuals with certain disabilities, and low-income persons. However, many health systems have resorted to first-come, first-served approaches to allocation, which tend to disadvantage individuals with barriers in access to care (3). There is mounting evidence of racial, ethnic, and socioeconomic disparities in access to medications for COVID-19 (4, 5). -/- One potential method to promote equitable allocation is to use a weighted lottery, which is an allocation strategy that gives all eligible patients a chance to receive the scarce treatment while also allowing the assignment of higher or lower chances according to other ethical considerations (6). We sought to assess the feasibility of implementing a weighted lottery to allocate scarce COVID-19 medications in a large U.S. health system and to determine whether the weighted lottery promotes equitable allocation. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox (...) as an argument against the second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

If someone disagrees with my moral views, or more generally if I’m in a group of n people who all disagree with each other, but I don’t have any special evidence or basis for my epistemic superiority, then it’s at best a 1-in-n chance that my views are correct. The skeptical threat from disagreement is thus a kind of moral lottery, to adapt a similar metaphor from Sharon Street. Her own genealogical debunking argument, as I discuss, relies on a (...) premise of such disagreement among evolutionary counterparts. -/- In this paper, I resist the threat from disagreement by showing that, on some of the most influential and most attractive theories of content determination, the premise of moral disagreement cannot serve any skeptical or revisionary purposes. I examine and criticize attempts, made by Gilbert Harman and Sharon Street, to argue from disagreement to relativism by relying on a theory of content determination that involves a principle that, within certain constraints, maximizes the attribution to us of true beliefs. And I examine and criticize Robert Williams’s attempt to show there is moral disagreement by relying on a theory of content determination that involves a principle that instead maximizes the attribution to us of rationality. My overall aim is to defend commonsense moral realism via a careful look at the theory of content and concepts. (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By (...) applying these data, one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

This article discusses Keith DeRose’s treatment of the lottery problem in Chapter 5 of his recent The Appearance of Ignorance. I agree with a lot of it but also raise some critical points and questions and make some friendly proposals. I discuss different ways to set up the problem, go into the difference between knowing and ending inquiry, propose to distinguish between two different kinds of lotteries, add to the defense of the idea that one can know lottery (...) propositions, give a critical discussion of DeRose’s contextualist solution to the problem, and support his defense against an absurdity objection with additional arguments. (shrink)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that (...) none of these strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

There are many conceivable circumstances in which some people have to be sacrificed in order to give others a chance to survive. The fair and rational method of selection is a lottery with equal chances. But why should losers comply, when they have nothing to lose in a war of all against all? A novel solution to this Compliance Problem is proposed. The lottery must be made self-enforcing by making the lots themselves the means of enforcement of the (...) outcome. This way no external authority is needed to make the losers’ compliance rational both ex ante and ex post. A fairly realistic concrete scenario is sketched to show that the solution could be made to work in practice, particularly since making it work is in everyone’s enlightened self-interest in the circumstances. (shrink)

We conducted five experiments that reveal some main contours of the folk epistemology of lotteries. The folk tend to think that you don't know that your lottery ticket lost, based on the long odds ("statistical cases"); by contrast, the folk tend to think that you do know that your lottery ticket lost, based on a news report ("testimonial cases"). We evaluate three previous explanations for why people deny knowledge in statistical cases: the justification account, the chance account, and (...) the statistical account. None of them seems to work. We then propose a new explanation of our own, the formulaic account, according to which some people deny knowledge in statistical cases due to formulaic expression. (shrink)

According to the permissibility solution to the lottery paradox, the paradox can be solved if we conceive of epistemic justification as a species of permissibility. Clayton Littlejohn has objected that the permissibility solution draws on a sufficient condition for permissible belief that has implausible consequences and that the solution conflicts with our lack of knowledge that a given lottery ticket will lose. The paper defends the permissibility solution against Littlejohn's objections.

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and (...) for risk-averse, certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (shrink)

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle.

In this paper it will be attempted to dissolve the lottery problem based on fallibilism, probabilism and the introduction of a so far widely neglected second context of knowledge. First, it will be argued that the lottery problem is actually an exemplification of the much wider Humean "future knowledge problem" (ch. 1). Two types of inferences and arguments will be examined, compared and evaluated in respect to their ability to fittingly describe the thought processes behind lottery/future knowledge (...) propositions (ch. 2). A second context of knowledge that underlines the importance of fallibilism and probabilism in a somewhat different manner will be introduced (ch. 3) and, based on that "two-context probabilism," the lottery/future knowledge problem will be dissolved (ch. 4). Lastly, it will be hinted at the necessity of adopting not just fallibilism including and two context minding probabilism, but, beyond that, also the even more encompassing position of both ontological and epistemological "gradualism" (ch. 5). (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Recent political theory has attempted to unbundle demos and ethnos, and thus citizenship from national identity. There are two possible ways to meet this challenge: by taming the relationship between citizenship and the nation, for example, by defending a form of liberal multicultural nationalism, or by transcending it with a postnational, cosmopolitan conception of citizenship. Both strategies run up against the boundedness of democratic authority. In this paper, I argue that Shachar adresses this issue in an innovative way, but remains (...) ultimately trapped by it. My argument has two parts. In the first one, I look at the analogy between property and citizenship on which Shachar rely to justify the obligations of wealthy states towards the global poor. I suggest that it does not work well to explain the rarity of citizenship and that the idea of taxing its value at the global level, however intuitive in liberal theory on property, could yield unexpected and non-liberal consequences. Nevertheless I also assess its merits. In the second part, I suggest that Shachar’s claim that her argument generates a legal obligation toward the global poor is not binding. It could only be so with the kind of cosmopolitan political institutions that she eschews. Thus we return where we begin. (shrink)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will (...) lose”… “ticket n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)