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?

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 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)

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.

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)

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 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)

How should we make distributive decisions when there is not enough of the good to go around, or at least not enough of it right now? What does fairness require in such cases? In what follows, we distinguish between cases of scarcity and bottleneck cases, and we argue that both arguments for lotteries and arguments for queues have merit, albeit for different distributive scenarios. When dealing with scarcity not everyone can get the good. A secondary good that can be (...) distributed fairly is the chances of obtaining the good. In cases of scarcity, lotteries are the best way of allocating chances of obtaining the good fairly. When dealing with bottlenecks, the secondary good that can and ought to be distributed fairly is waiting time. Queues are best suited to distribute the good of waiting time fairly. (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)

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)

By exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. We solve the 'adding problems' that occur in these two contexts using a similar strategy, based on non-standard analysis.

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 article, I discuss three distinct but related puzzles involving lotteries: Kyburg’s lottery paradox, the statistical evidence problem, and the Harman-Vogel paradox. Kyburg’s lottery paradox is the following well-known problem: if we identify rational outright belief with a rational credence above a threshold, we seem to be forced to admit either that one can have inconsistent rational beliefs, or that one cannot rationally believe anything one is not certain of. The statistical evidence problem arises from the observation that (...) people seem to resist forming outright beliefs whenever the available evidence for the claim under consideration is purely statistical. We need explanations of whether it is in fact irrational to form such beliefs, and of whether a clear distinction can be drawn between statistical and non-statistical evidence. The Harman-Vogel paradox is usually presented as a paradox about knowledge: we tend to assume that we can know so-called ordinary propositions, such as the claim that I will be in Barcelona next spring. Yet, we hesitate to make knowledge claims regarding so-called lottery propositions, such as the claim that I won’t die in a car crash in the next few months, even if these lottery propositions are obviously entailed by the ordinary propositions we claim to know. Depending on one’s view about the relationship between rational belief and knowledge, the Harman-Vogel paradox has ramifications for a theory of rational outright belief. Formal theories of the relationship between rational credence and rational belief, such as Leitgeb’s stability theory, tend to focus mostly on handling Kyburg’s lottery paradox, but not the other two puzzles I mention. My aim in this article is to draw out relationships and differences between the puzzles, and to examine to what extent existing formal solutions to Kyburg’s lottery paradox help with answering the statistical evidence problem and the Harman-Vogel paradox. (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)

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)

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)

Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no (...) valid reason not to give preference to the derived accounts over the accounts from which they come. (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)

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)

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)

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)

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)

According to the safety principle, if one knows that p, one's belief that p could not easily have been false. One problem besetting this principle is the lottery problem – that of explaining why one does not seem to know that one will lose the lottery purely based on probabilistic considerations, prior to the announcement of the lottery result. As Greco points out, it is difficult for a safety theorist to solve this problem, without paying a heavy price. In this (...) paper, I first reject three existing safety-based solutions to the lottery problem, due to Pritchard, Sosa, and Broncano-Berrocal. Failure of these accounts reveals that there is something crucial missing in the safety principle. By way of remedying this, I propose to integrate a safety principle with a condition regarding one's own awareness of (nearby) error-possibilities. The resulting account, as I argue, enjoys a number of theoretical advantages, including its capacity to handle the lottery problem. (shrink)

As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models based (...) on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets. (shrink)

Faced with a choice between saving one stranger and saving a group of strangers, some people endorse weighted lotteries, which give a strictly greater chance of being saved to the group of strangers than the single stranger. In this paper I attempt to criticize this view. I first consider a particular version of the weighted lotteries, Frances Kamm's procedure of proportional chances, and point out two implausible implications of her proposal. Then, I consider weighted lotteries in general, (...) and claim (1) that the correct thing to distribute is not the chance of being saved but the good of being saved, (2) that assigning some chance to the single stranger is not the only way to give a positive (and equal) respect to the people concerned, and (3) that the weighted lottery appears to be deceptive since it would show the respect to the single stranger in a negligible way. (shrink)

The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.

The possibility to interpret expected and nonexpected utility theories in purely probabilistic terms has been recently investigated. Such interpretation proposes as guideline for the Decision Maker the comparison of random variables through their probability to outperform a stochastic benchmark. We apply this type of analysis to the model of Becker and Sarin, showing that their utility functional may be seen as the probability that an opportune random variable, depending on the one to be evaluated, does not outperform a non-random benchmark. (...) Further, the consequent choice criterion is equivalent to a sort of probability of ruin. Possible interpretations and financial examples are discussed. (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)

Safety accounts of knowledge intend to explain why certain true and intuitively justified beliefs fail to be knowledge in terms of such beliefs falling prey to a modal veritic type of luck. In particular, they explain why true and intuitively justified beliefs in “lottery propositions” (highly likely propositions reporting that a particular statistical outcome obtains) are not knowledge. In this paper, I argue that there is a type of case involving lottery propositions that inevitably lies beyond the scope of any (...) reasonable safety account of epistemic luck. I offer counterexamples to accounts of epistemic luck in terms of safety conditions that involve both “locally” and “globally” reliable ways of forming beliefs in nearby worlds. All such counterexamples present a lottery case illustrating the next possibility: the process of selecting the lottery winner might be such that any world in which it delivers a different outcome is extremely far away from the actual world. In addition to being a case of safe ignorance, this type of lottery case shows that, ultimately, either veritic epistemic luck is not unsafe true belief or beliefs in lottery propositions are not epistemically luckily true. (shrink)

Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of belief” or “high probability cores.” (...) In this paper, I examine whether the stability theory of belief can meet two further constraints that have been proposed in the literature: that it is irrational to outright believe lottery propositions, and that it is irrational to hold outright beliefs based on purely statistical evidence. I argue that these two further constraints create a dilemma for a proponent of the stability theory: she must either deny that her theory is meant to give an account of the common epistemic notion of outright belief, or supplement the theory with further constraints on rational belief that render the stability theory explanatorily idle. This result sheds light on the general prospects for a purely formal theory of the relationship between rational credence and belief, i.e. a theory that does not take into account belief content. I argue that it is doubtful that any such theory could properly account for these two constraints, and hence play an important role in characterizing our common epistemic notion of outright belief. (shrink)

Lottery puzzles involve an ordinary piece of knowledge which seems to imply knowledge of a so-called “lottery proposition,” which itself seems unknown: I might be said to know that I won’t be going on safari next year. But if I were to win the lottery, I would go, and I don’t know that I won’t win the lottery. Examples can be multiplied. Thus we seem left either with the paradoxical position of knowing certain ordinary propositions, but failing to know the (...) lottery propositions they imply, or else conceding to the skeptic. I present a version of reliabilism according to which empirical knowledge is true belief produced by a reliable process causally connecting belief and fact. According to this theory, if my ordinary belief and my belief in the lottery proposition are suitably connected to the facts that render them true, both count as knowledge. In cases where my ordinary belief and my belief in the lottery proposition are not suitably connected to the relevant facts, neither count as knowledge. Thus the paradoxical air of lottery puzzles is removed, and skepticism is avoided. (shrink)

Safety accounts of knowledge claim, roughly, that knowledge that p requires that one's belief that p could not have easily been false. Such accounts have been very popular in recent epistemology. However, one serious problem safety accounts have to confront is to explain why certain lottery‐related beliefs are not knowledge, without excluding obvious instances of inductive knowledge. We argue that the significance of this objection has hitherto been underappreciated by proponents of safety. We discuss Duncan Pritchard's recent solution to the (...) problem and argue that it fails. More importantly, the problem reaches deeper and poses a threat to any current safety accounts that require a belief's modal stability in close possibilities (as well as safety accounts that appeal to ‘normality’). We end by arguing that ways out of the problem require substantial reconstruction for a safety‐based account of knowledge. (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)

I seem to know that I won't experience spaceflight but also that if I win the lottery, then I will take a flight into space. Suppose I competently deduce from these propositions that I won't win the lottery. Competent deduction from known premises seems to yield knowledge of the deduced conclusion. So it seems that I know that I won't win the lottery; but it also seems clear that I don't know this, despite the minuscule probability of my winning (if (...) I have a lottery ticket). So we have a puzzle. It seems to generalize, for analogues of the lottery-proposition threaten almost all ordinary knowledge attributions. For example, my apparent knowledge that my bike is parked outside seems threatened by the possibility that it's been stolen since I parked it, a proposition with a low but non-zero probability; and it seems that I don't know this proposition to be false. Familiar solutions to this family of puzzles incur unacceptable costs—either by rejecting deductive closure for knowledge, or by yielding untenable consequences for ordinary attributions of knowledge or of ignorance. After canvassing and criticizing these solutions, I offer a new solution free of these costs. Knowledge that p requires an explanatory link between the fact that p and the belief that p. This necessary but insufficient condition on knowledge distinguishes actual lottery cases from typical, apparently analogous ‘quasi-lottery’ cases. It does yield scepticism about my not winning the lottery and not experiencing spaceflight, but the scepticism doesn't generalize to quasi-lottery cases such as that involving my bike. (shrink)

Weighted lottery proposals give guidance in rescue dilemma situations by balancing the demands of comparative and absolute fairness. While they do not advocate for saving the greater number outright, they are responsive to absolute fairness insofar as they show a certain sensitivity to the numbers involved. In this paper we investigate what criterion of absolute fairness we should demand weighted lotteries to fulfill. We do so by way of critically examining what is probably the most sophisticated weighted lottery on (...) the market: Gerard Vong's Exclusive Composition-Sensitive (EXCS) lottery. We find that both the standard that seems most common in the debate, and a different standard Vong uses to criticize Jens Timmermann's Individualist Lottery are in contradiction to basic demands placed upon weighted lotteries and are therefore unsuitable as necessary conditions for absolute fairness. We instead propose a purely gradual understanding of absolute fairness. (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)

Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is sufficient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent’s further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had event-independent risk-neutral utility and (...) a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities. (shrink)

Several philosophers have claimed that S knows p only if S’ s belief is safe, where S's belief is safe iff (roughly) in nearby possible worlds in which S believes p, p is true. One widely held intuition many people have is that one cannot know that one's lottery ticket will lose a fair lottery prior to an announcement of the winner, regardless of how probable it is that it will lose. Duncan Pritchard has claimed that a chief advantage of (...) safety theory is that it can explain the lottery intuition without succumbing to skepticism. I argue that Pritchard is wrong. If a version of safety theory can explain the lottery intuition, it will also lead to skepticism. Content Type Journal Article Category Original Article Pages 1-26 DOI 10.1007/s10670-011-9305-z Authors Dylan Dodd, Department of Philosophy, Northern Institute of Philosophy, University of Aberdeen, Aberdeen, UK Journal Erkenntnis Online ISSN 1572-8420 Print ISSN 0165-0106. (shrink)

Ever since Fred Dretske (1970) questioned closure, a denial of this principle has been among the standard options for a resolution of epistemological paradoxes such as the skeptical paradox (Cohen 1988) and the lottery paradox (Harman 1973). In this article, the author shall argue that all possible solutions of the latter paradox can only be defended if Multi-Premise Closure is rejected. These possible solutions are contextualism and both simple and sensitive moderate invariantism. It will be shown that skepticism and the (...) denial of Single-Premise Closure are not possible solutions of the lottery paradox. The upshot of the discussion here will be that while Single-Premise Closure is beyond reasonable doubt, resolving the lottery paradox forces one to abandon Multi-Premise Closure. (shrink)

Chance inevitably plays a role in law but it is not often that we consciously try to import an element of randomness into a legal process. Random Justice: On Lotteries and Legal Decision-Making explores the potential for the use of lotteries in social, and particularly legal, decision-making contexts. Utilizing a variety of disciplines and materials, Neil Duxbury considers in detail the history, advantages, and drawbacks of deciding issues of social significance by lot and argues that the value of (...) the lottery as a legal decision-making device has generally been underestimated. The very fact that there exists widespread resistance to the use of lotteries for legal decision-making purposes betrays a commonly held belief that legal processes are generally more important than are legal outcomes. Where, owing to the existence of indeterminacy, the process of reasoning is likely to be excessively protracted and the reasons provided strongly contestable, the most cost-efficient and impartial decision-making strategy may well be recourse to lot. Aversion to this strategy, while generally understandable, is not necessarily rational. Yet in law, as Professor Duxbury demonstrates, reason is generally valued more highly than is rationality. The lottery is often conceived to be a decision-making device that operates in isolation. Yet lotteries can frequently and profitably be incorporated into other decision-frameworks. The book concludes by controversially considering how lotteries might be so incorporated and also advances the thesis that it may sometimes be sensible to require that adjudication takes place in the shadow of a lottery. (shrink)

Is it unethical to advertise lotteries? Many citizens think that states should not be actively promoting and encouraging the public tospend hard-earned dollars on a bet that they are virtually guaranteed to lose. Perhaps more importantly, business ethicists are concerned that lottery advertising may be targeting the most vulnerable markets: households with the lowest income and education levels. If this were true, then it would increase the already disproportionately large burden of lottery taxes on the poor. Fortunately, our research (...) finds no evidence to support the contention that advertising is responsible for high rates of lottery participation and expenditures by lower income groups or that low-income groups are more affected by advertising than high-income groups. On the contrary, awareness of lottery advertising seems to be associated with a higher probability to play Lotto only for the middle income group. This means that lottery advertising may actually reduce the regressivity of lottery taxes. (shrink)

Knowledge and Lotteries is organized around an epistemological puzzle: in many cases, we seem consistently inclined to deny that we know a certain class of propositions, while crediting ourselves with knowledge of propositions that imply them. In its starkest form, the puzzle is this: we do not think we know that a given lottery ticket will be a loser, yet we normally count ourselves as knowing all sorts of ordinary things that entail that its holder will not suddenly acquire (...) a large fortune. After providing a number of specific and general characterizations of the puzzle, Hawthorne carefully examines the competing merits of candidate solutions. In so doing, he explores a number of central questions concerning the nature and importance of knowledge, including the relationship of knowledge to assertion and practical reasoning, the status of epistemic closure principles, the merits of various brands of scepticism, the prospects for a contextualist account of knowledge, and the potential for other sorts of salience-sensitive accounts. Along the way, he offers a careful treatment of pertinent issues at the foundations of semantics. His book will be of interest to anyone working in the field of epistemology, as well as to philosophers of language. (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)

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)

Objectivization forces the requirement of a high likelihood that an informant will be right if she is to be classified as a good one, but this does not, argues Craig, equal 1, for that figure has little basis in practical life. Nevertheless, the example of a lottery, and, in particular, the claim that one will not win, brings closer to our real experience the idea that one may not always be advised to act on information that has a chance of (...) less than 1 of being true. A similar push towards this stringent idea is sometimes exerted by the wish to draw inferences from multiple premises and to be able to rely on the result. However, though real situations can require a very high likelihood, they do not force us to set it at 1; that final push comes from reflection lying outside the framework of everyday practice. (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)

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)