In mid-2019, the controversy regarding South African runner Caster Semenya’s eligibility to participate in competitions against other female runners culminated in a Court of Arbitration for Sport judgement. Semenya possessed high endogenous testosterone levels (arguably a performance advantage), secondary to a disorder of sexual development. In this commentary, Aristotelean teleology is used to defend the existence of ‘male’ and ‘female’ as discrete categories. It is argued that once the athlete’s sex is established, they should be allowed to compete in the (...) category of their sex without obligatory medical treatment. Indeed, other athletes who possess advantageous genetic or phenotypic traits that fall outside of the human norm have been allowed to compete as humans without restraint. In both cases, if an athlete possesses the essential attributes of being a human or being male or female they should be permitted to compete in those respective categories; athletes’ eligibilities should not be based upon accidental attributes. (shrink)

Don’t form beliefs on the basis of coin flips or random guesses. More generally, don’t take belief gambles: if a proposition is no more likely to be true than false given your total body of evidence, don’t go ahead and believe that proposition. Few would deny this seemingly innocuous piece of epistemic advice. But what, exactly, is wrong with taking belief gambles? Philosophers have debated versions of this question at least since the classic dispute between William Clifford and William James (...) near the end of the nineteenth century. Here I reassess the normative standing of belief gambles from the perspective of epistemic decision theory. The main lesson of the paper is a negative one: it turns out that we need to make some surprisingly strong and hard-to-motivate assumptions to establish a general norm against belief gambles within a decision-theoretic framework. I take this to pose a dilemma for epistemic decision theory: it forces us to either make seemingly unmotivated assumptions to secure a norm against belief gambles, or concede that belief gambles can be rational after all. (shrink)

With the previous technical reports, we presented the main insights from the qualitative analysis of the reflection of the mathematical dimension of gambling in gambling-related sites, in its structural, linguistic, epistemic, and informative aspects. In this report we will focus on the factors responsible for the patterns that the content of the gambling-related sites exhibit and the way that the mathematical dimension of gambling is reflected in this content, namely the factors that influence the content policies (...) of these sites. The report will also point to further directions of research-for both this project and for other investigators-for finding the appropriate balance and relation between the commercial policies on the one hand, and the adequacy and ethics of the content on the other hand. (shrink)

Randomness, a core concept of gambling, is seen in problem gambling as responsible for the formation of the math-related cognitive distortions, especially the Gambler’s Fallacy. In problem-gambling research, the concept of randomness was traditionally referred to as having a mathematical nature and categorized and approached as such. Randomness is not a mathematical concept, and I argue that its weak mathematical dimension is not decisive at all for the randomness-related issues in gambling and problem gambling, including (...) the correction of the misconceptions and fallacies about probability and statistical concepts applied in gambling. I distinguish between mathematical and nonmathematical dimensions of randomness (the epistemic, the theoretical-methodological, the functional, and the ethical) falling within the general concept, and I argue that both the studies having as object the math-related cognitive distortions among gamblers and the educational programs aiming at correcting them should employ this distinction in their design and content. (shrink)

The author proposes in this practical guide for both problem and non-problem gamblers a new pragmatic, conceptual approach of gambling mathematics. The primary aim of this guide is the adequate understanding of the essence and complexity of gambling through its mathematical dimension. The author starts from the premise that formal gambling mathematics, which is hardly even digestible for the non-math-inclined gamblers, is ineffective alone in correcting the specific cognitive distortions associated with gambling. By applying the latest (...) research results in this field, the author blends the gambling-mathematics concepts with the epistemology of applied mathematics and cognitive psychology for providing gamblers the knowledge required for rational and safe gambling. (shrink)

The desirable gambles framework offers the most comprehensive foundations for the theory of lower pre- visions, which in turn affords the most general ac- count of imprecise probabilities. Nevertheless, for all its generality, the theory of lower previsions rests on the notion of linear utility. This commitment to linearity is clearest in the coherence axioms for sets of desirable gambles. This paper considers two routes to relaxing this commitment. The first preserves the additive structure of the desirable gambles framework and (...) the machinery for coherent inference but detaches the interpretation of desirability from the multiplicative scale invariance axiom. The second strays from the additive combination axiom to accommodate repeated gambles that return rewards by a non-stationary processes that is not necessarily additive. Unlike the first approach, which is a conservative amendment to the desirable gambles framework, the second is a rad- ical departure. Yet, common to both is a method for describing rewards called discounted utility. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated (...) with this study describe the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

In light of the observations and research design presented in the previous reports, the current technical report is focused on the relationship between the quality and specificity of the content of the gambling sites and the site’s SEO and marketing policy. This relationship is dependent upon the category of the gambling site and the difference in content quality, and the degree to which the mathematical dimension of gambling is reflected in this content is explained by this dependence.

The current technical report of the research project investigating how the mathematical dimension of gambling is reflected in the communication and texts associated with the gambling industry raises the problem of the adequacy of sampling and proposes a new approach in this respect. The qualitative analysis of the reviewed websites is extended to a deeper analysis of language and also to the organization and structure of websites’ content. Although not stated as a goal of the initial project, the (...) research will also try to identify relationships between the specificity of content relative to the mathematical dimension of gambling, and the management and marketing of the website. An overview of the results of the statistical analysis of the current sample is also presented. (shrink)

The near-miss has been considered an important factor of reinforcement in gambling behavior, and previous research has focused more on its industry-related causes and effects and less on the gaming phenomenon itself. The near-miss has usually been associated with the games of slots and scratch cards, due to the special characteristics of these games, which include the possibility of pre-manipulation of award symbols in order to increase the frequency of these “engineered” near-misses. In this paper, we argue that starting (...) from an elementary mathematical description of the classical (by pure chance) near-miss, generalizable to any game, and focusing equally on the epistemology of its constitutive concepts and their mathematical description, we can identify more precisely the fallacious elements of the near-miss cognitive effects and the inadequate perception and representation of the observational-intentional “I was that close.” This approach further suggests a strategy of using non-standard mathematical knowledge of an epistemological type in problem-gambling prevention and cognitive therapies. (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)

It cannot be overstated that in recent times the gravity and complexity of irregular maritime migration have triggered concerns and debates in the academic domains of International Relations and International Law. The article examines how states’ compliance with, and enforcement of, international law and legal norms would tackle the challenges of irregular migration in the Indian Ocean region. The legislative and policy challenges regarding irregular migration can be analyzed under two segments. First, there is a lack of comprehensive discussion about (...) the sending and the receiving states’ commitments (regarding irregular migrants) to international law and legal norms. Secondly, deficit of comparative analysis to show how the littoral states comply with international law norms on migration and refugee influx. Such analysis from multiple perspectives would be helpful to get insights and make policy recommendations about how effectively international law norms could be enforced through national legislation and policy framework. (shrink)

One of John Paul II’s remarkable innovations was his embrace of the question of “the meaning of life.” The question of “the meaning of life” was never asked before the 19th century, and it was slow to be integrated into Catholic discourse. When the question of life’s meaning emerged, it effectively replaced a prior question, about the purpose or te-los of life, with a very different set of theoretical assumptions. From the traditional per-spective, the question of life’s meaning is highly (...) suspicious, and even Pope John Paul II’s unparalleled embrace of the question confirms that he framed his personalism in terms of the older question of life’s purpose or telos. (shrink)

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural (...) analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

Mindfulness is a form of meditation that derives from Buddhist practice and is one of the fastest growing areas of psychological research. Studies investigating the role of mindfulness in the treatment of behavioural addictions have – to date – primarily focused on gambling disorder. Recent pilot studies and clinical case studies have demonstrated that weekly mindfulness therapy sessions can lead to clinically significant change among individuals with gambling problems. Although preliminary findings indicate that there are applications for mindfulness (...) approaches in the treatment of gambling disorder, further empirical and clinical research utilizing larger-sample controlled study designs is clearly needed. (shrink)

This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of logical (...) soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by (...) providing the principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

There is a paucity of research on how psychopathy relates to decision-making. In this study, we assessed the relationship between affective decision-making and psychopathic personality. A sample of prisoners (n D 49) was characterized in terms of psychopathic traits using the Psychopathic Checklist: Screening Version (PCL:SV). Decision-making was assessed using the Iowa Gambling Task (IGT). Higher levels of psychopathy related to more advantageous choices (p D .003). Also counter-intuitively, higher levels of antisocial traits (facet 4) predicted advantageous choices during (...) the learning phase of the task (p D .004). Our findings suggest that some psychopathic facets may be more relevant to decisionmaking under risk, and highlight the importance of further investigations considering facet and trait-level relationships with decision-making. (shrink)

Some early phase clinical studies of candidate HIV cure and remission interventions appear to have adverse medical risk–benefit ratios for participants. Why, then, do people participate? And is it ethically permissible to allow them to participate? Recent work in decision theory sheds light on both of these questions, by casting doubt on the idea that rational individuals prefer choices that maximise expected utility, and therefore by casting doubt on the idea that researchers have an ethical obligation not to enrol participants (...) in studies with high risk–benefit ratios. This work supports the view that researchers should instead defer to the considered preferences of the participants themselves. This essay briefly explains this recent work, and then explores its application to these two questions in more detail. (shrink)

Since independence, at least 28 African countries have legalized some form of gambling. Yet a range of informal gambling activities have also flourished, often provoking widespread public concern about the negative social and economic impact of unregulated gambling on poor communities. This article addresses an illegal South African numbers game called fahfee. Drawing on interviews with players, operators, and regulatory officials, this article explores two aspects of this game. First, it explores the lives of both players and (...) runners, as well as the clandestine world of the Chinese operators who control the game. Second, the article examines the subjective motivations and aspirations of players, and asks why they continue to play, despite the fact that their aggregate losses easily outstrip their aggregate gains. In contrast with those who reduce its appeal simply to the pursuit of wealth, I conclude that, for the (mostly) black, elderly, working class women who play fahfee several times a week, the associated trade-off—regular, small losses, versus the social enjoyment of playing and the prospect of occasional but realistic windfalls—takes on a whole new meaning, and preferences for relatively lumpy rather than steady consumption streams help explain the continued attraction of fahfee. This reinforces the need to understand players’ own accounts of gambling utility rather than simply to moralistically condemn gambling or to dismiss gamblers behaviour as irrational. (shrink)

There have been several recent lawsuits in which problem gamblers (or those affected by problem gambling) have sued casinos or other gaming companies for damages relating to bankruptcies, suicides, and other negative consequences of compulsive gambling. Although the legal cases have been decided in favor of the gaming companies, it can seem as though there is a moral residue in some of these cases: perhaps some of the actions of the gaming companies, though legal, have been morally problematic. (...) This case invites students to explore this possibility by introducing them to the facts surrounding the lawsuits and highlighting some of the most salient moral considerations. Students will also be asked to reflect on the public policy implications, if any, of their findings. (shrink)

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) gave (...) an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware (...) of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

A surprisingly large number of scholars believe that (a) we are blameworthy, and therefore punishable, only for what we have control over; (b) we have control only over our actions and intentions, not the consequences of our actions; and therefore (c) if two agents perform the very same action (e.g., attempting to kill) with the very same intentions, then they are equally blameworthy and deserving of equal punishment – even if only one of them succeeds in killing. This paper argues (...) against these “equivalence theorists” that harmful consequences do make a moral difference, that the harm produced by the killer’s attempt retroactively makes her action more blameworthy, and therefore deserving of more punishment, than the failed attempter’s attempt. The primary argument for this “non-equivalence theory” is an analogy with gambling. Just as a gambler makes a deal with the casino to allow metaphysical luck to retroactively determine the “profit status” of her bet, so too the attempted killer makes a deal with “the casino of morality” to allow metaphysical luck to retroactively determine the moral status of her attempt. She makes the “moral deal” that if her attempt succeeds, her attempt was more blameworthy than if her attempt does not succeed. And it is the greater blameworthiness of the killer’s attempt that justifies our intuition that the killer should be punished more harshly than the failed attempter. (shrink)

In this paper, I examine two major challenges to epistemic theories of democracy: “the authority dilemma” and “the epistemic gamble.” The first is a conceptual challenge, suggesting that epistemic democracy is inherently self-undermining. The second is a normative challenge, asserting that the case for democracy should not rely on precarious epistemic grounds. I argue that both challenges fail. Thus, epistemic theories of democracy escape two of the most popular objections to this view.

Most accounts of cognitive scaffolding focus on ways that external structure can support or augment an agent’s cognitive capacities. We call cases where the interests of the user are served benign scaffolding and argue for the possibility and reality of hostile scaffolding. This is scaffolding which depends on the same capacities of an agent to make cognitive use of external structure as in benign cases, but that undermines or exploits the user while serving the interests of another agent. We develop (...) criteria for scaffolding being hostile and show by reference to examples including the design features of electronic gambling machines and casino management systems that hostile scaffolding exists and can be highly effective. In cases where the scaffolding is deep and permits the offloading of significant cognitive work, hostile scaffolding exploitatively manipulates cognitive processing itself. Given the extent of human reliance on scaffolding this is an important and neglected vulnerability. [This is an updated version of the paper, added in February 2023.]. (shrink)

I argue that in purely professional games of pure chance, such as slot machines, roulette, baccarat or pachinko, any instance of cheating that successfully deceives the judge can be ‘part of the game’. I examine, and reject, various proposals for the ‘ethos’ that determines how we ought to interpret the formal rules of games of pure chance, such as being a test of skill, a matter of entertainment, a display of aesthetic beauty, an opportunity for hedonistic pleasure, and a fraternal (...) activity. Ultimately, I argue that ‘winning the benefit’ is the only ethos that can apply in purely professional games of pure chance, and that if we interpret the formal rules according to this ethos, cheating that is undertaken with respect for the judge’s authority, but that attempts to cause the judge of the game to ‘voluntarily’ relinquish the benefit of the game by deceiving them into thinking that the formal rules of the game have been followed, is impermissible but acceptable cheating, and is therefore within, rather than outside, the game. Here, I define ‘games of pure chance’ as games in which chance is the only determinant of winning. (shrink)

The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demoting sets of probabilities from fundamental building blocks to secondary representations (...) that are derived or discarded as needed. (shrink)

Climate change mitigation has become a paradigm case both for externalities in general and for the game-theoretic model of the Tragedy of the Commons (ToC) in particular. This situation is worrying, as we have reasons to suspect that some models in the social sciences are apt to be performative to the extent that they can become self-fulfilling prophecies. Framing climate change mitigation as a hardly solvable coordination problem may force us into a worse situation, by changing real-world behaviour to fit (...) our model, rather than the other way around. But while this problem of the performativity of the ToC has been noted in a recent paper in this journal by Matthew Kopec, his proposed strategies for dealing with their self-fulfilling nature fall short of providing an adequate solution. Instead of relying on the idea that modelling assumptions are always strictly speaking false, this paper shows that the problem may be better framed as a problem of underdetermination between competing explanations. Our goal here is to provide a framework for choosing between this set of competing models that allows us to avoid a ‘Russian Roulette’-like situation in which we gamble with existential risk. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

4E approaches to affective technology tend to focus on how ‘users’ manage their situated affectivity, analogously to how they help themselves cognitively through epistemic actions or using artefacts and scaffolding. Here I focus on cases where the function of affective technology is to exploit or manipulate the agent engaging with it. My opening example is the cigarette, where technological refinements have harmfully transformed the affective process of consuming nicotine. I proceed to develop case studies of two very different but also (...) harmful affective technologies. Casinos and electronic gambling machines deploy computationally intensive scaffolding to shape the onset and continuation of gambling episodes. High-heeled shoes affectively engineer wearers’ relationships to their own embodied capacities and are predominantly expected to be worn by women. I conclude with a discussion of the need for study of affective technology to focus other-directed applications, some of which will serve competing or antagonistic interests. (shrink)

What is a game? What are we doing when we play a game? What is the value of playing games? Several different philosophical subdisciplines have attempted to answer these questions using very distinctive frameworks. Some have approached games as something like a text, deploying theoretical frameworks from the study of narrative, fiction, and rhetoric to interrogate games for their representational content. Others have approached games as artworks and asked questions about the authorship of games, about the ontology of the work (...) and its performance. Yet others, from the philosophy of sport, have focused on normative issues of fairness, rule application, and competition. The primary purpose of this article is to provide an overview of several different philosophical approaches to games and, hopefully, demonstrate the relevance and value of the different approaches to each other. Early academic attempts to cope with games tried to treat games as a subtype of narrative and to interpret games exactly as one might interpret a static, linear narrative. A faction of game studies, self-described as “ludologists,” argued that games were a substantially novel form and could not be treated with traditional tools for narrative analysis. In traditional narrative, an audience is told and interprets the story, where in a game, the player enacts and creates the story. Since that early debate, theorists have attempted to offer more nuanced accounts of how games might achieve similar ends to more traditional texts. For example, games might be seen as a novel type of fiction, which uses interactive techniques to achieve immersion in a fictional world. Alternately, games might be seen as a new way to represent causal systems, and so a new way to criticize social and political entities. Work from contemporary analytic philosophy of art has, on the other hand, asked questions whether games could be artworks and, if so, what kind. Much of this debate has concerned the precise nature of the artwork, and the relationship between the artist and the audience. Some have claimed that the audience is a cocreator of the artwork, and so games are a uniquely unfinished and cooperative art form. Others have claimed that, instead, the audience does not help create the artwork; rather, interacting with the artwork is how an audience member appreciates the artist's finished production. Other streams of work have focused less on the game as a text or work, and more on game play as a kind of activity. One common view is that game play occurs in a “magic circle.” Inside the magic circle, players take on new roles, follow different rules, and actions have different meanings. Actions inside the magic circle do not have their usual consequences for the rest of life. Enemies of the magic circle view have claimed that the view ignores the deep integration of game life from ordinary life and point to gambling, gold farming, and the status effects of sports. Philosophers of sport, on the other hand, have approached games with an entirely different framework. This has lead into investigations about the normative nature of games—what guides the applications of rules and how those rules might be applied, interpreted, or even changed. Furthermore, they have investigated games as social practices and as forms of life. (shrink)

In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...) the same type of causal interventions. When these categories do not evince such groupings, there is reason to revise existing classifications. The contributors all question current psychiatric classifications systems and the assumptions on which they are based. They differ, however, as to why and to what extent the categories are inadequate and how to address the problem. Topics discussed include taxometric methods for identifying natural kinds, the error and bias inherent in DSM categories, and the complexities involved in classifying such specific mental disorders as "oppositional defiance disorder" and pathological gambling. -/- Contributors George Graham, Nick Haslam, Allan Horwitz, Harold Kincaid, Dominic Murphy, Jeffrey Poland, Nancy Nyquist Potter, Don Ross, Dan Stein, Jacqueline Sullivan, Serife Tekin, Peter Zachar. (shrink)

According to all-luck egalitarianism, the differential distributive effects of both brute luck, which defines the outcome of risks which are not deliberately taken, and option luck, which defines the outcome of deliberate gambles, are unjust. Exactly how to correct the effects of option luck is, however, a complex issue. This article argues that (a) option luck should be neutralized not just by correcting luck among gamblers, but among the community as a whole, because it would be unfair for gamblers as (...) a group to be disadvantaged relative to non-gamblers by bad option luck; (b) individuals should receive the warranted expected results of their gambles, except insofar as individuals blamelessly lacked the ability to ascertain which expectations were warranted; and (c) where societal resources are insufficient to deliver expected results to gamblers, gamblers should receive a lesser distributive share which is in proportion to the expected results. Where all-luck egalitarianism is understood in this way, it allows risk-takers to impose externalities on non-risk-takers, which seems counterintuitive. This may, however, be an advantage as it provides a luck egalitarian rationale for assisting ‘negligent victims’. (shrink)

(This is one of the essays to be included in a book examining the causes of day-to-day strife in the populations of modern democracies vying to live and assert the freedoms promised to them by systems of governance supposed and expected to represent them.) -/- The emigrant / immigrant / migrant makes a conscious, relatively difficult decision to exchange what s/he knows for what is not known at all but in promise. The choice is often stark and carries with it (...) the imposition of restrictions on what will be possible in terms of existing customs, culture, and direct involvement with friends and family, and signifies a leap of faith into what appears to be a better, more prosperous, happier future. -/- At times, such choice is unavoidable, others it turns out to be a gamble of sorts, but, no matter what the cause, reason, or desire underlying an act of migration away from what the emigrant has known, it never turns out to be what was expected and no amount of preparation allows the emigrant to anticipate what will in fact occur. Migration is the founding of a new life in all the aspects of the emigrant’s existence. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for (...) testing scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...) about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

A moderately risk averse person may turn down a 50/50 gamble that either results in her winning $200 or losing $100. Such behaviour seems rational if, for instance, the pain of losing $100 is felt more strongly than the joy of winning $200. The aim of this paper is to examine an influential argument that some have interpreted as showing that such moderate risk aversion is irrational. After presenting an axiomatic argument that I take to be the strongest case for (...) the claim that moderate risk aversion is irrational, I show that it essentially depends on an assumption that those who think that risk aversion can be rational should be skeptical of. Hence, I conclude that risk aversion need not be irrational. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

The article addresses the necessity of increasing the role of mathematics in the psychological intervention in problem gambling, including cognitive therapies. It also calls for interdisciplinary research with the direct contribution of mathematics. The current contributions and limitations of the role of mathematics are analysed with an eye toward the professional profiles of the researchers. An enhanced collaboration between these two disciplines is suggested and predicted.

The orthodox theory of instrumental rationality, expected utility (EU) theory, severely restricts the way in which risk-considerations can figure into a rational individual's preferences. It is argued here that this is because EU theory neglects an important component of instrumental rationality. This paper presents a more general theory of decision-making, risk-weighted expected utility (REU) theory, of which expected utility maximization is a special case. According to REU theory, the weight that each outcome gets in decision-making is not the subjective probability (...) of that outcome; rather, the weight each outcome gets depends on both its subjective probability and its position in the gamble. Furthermore, the individual's utility function, her subjective probability function, and a function that measures her attitude towards risk can be separately derived from her preferences via a Representation Theorem. This theorem illuminates the role that each of these entities plays in preferences, and shows how REU theory explicates the components of instrumental rationality. (shrink)

This chapter focuses on the psychological mechanisms behind the construction of preference, especially the actual processes used by humans when they make decisions in their everyday lives or in business situations. The chapter uses cognitive psychological techniques to break down these processes and set them in their social context. When attributes are compatible with the response scale, they are assigned greater weight because they are most easily mapped onto the response. For instance, when subjects are asked to set a price (...) for a gamble this task is compatible with the information about the gamble payoff, which is also expressed in monetary values (e.g., dollars). Conversely, when the task requires a choice the payoff information is not easily mapped onto the response anymore and loses some of its salience. In fact, Slovic, Griffin, and Tversky (1990) could show that using non-monetary outcomes attenuates preference reversals when no compatibility between the pricing task and the outcome attribute was possible. An assumption of the compatibility effect is that response modes compatible with specific characteristics of the options (e.g., payoffs) draw attention to them. One of the main themes that has emerged from behavioral decision research during the past decades is the view that people's preferences are often constructed—not merely revealed—in the process of elicitation (see e.g. Slovic). This conception is derived in part from studies demonstrating that normatively equivalent methods of elicitation often give rise to systematically different responses. These "preference reversals" violate the principle of procedure invariance fundamental to theories of rational choice and raise difficult questions about the nature of human values. If different elicitation procedures produce different orderings of options, how can preferences be defined and in what sense do they exist? Describing and explaining such failures of invariance will require choice models of far greater complexity than the traditional models -/- . (shrink)

Investigation of neural and cognitive processes underlying individual variation in moral preferences is underway, with notable similarities emerging between moral- and risk-based decision-making. Here we specifically assessed moral distributive justice preferences and non-moral financial gambling preferences in the same individuals, and report an association between these seemingly disparate forms of decision-making. Moreover, we find this association between distributive justice and risky decision-making exists primarily when the latter is assessed with the Iowa Gambling Task. These findings are consistent with (...) neuroimaging studies of brain function during moral and risky decision-making. This research also constitutes the first replication of a novel experimental measure of distributive justice decision-making, for which individual variation in performance was found. Further examination of decision-making processes across different contexts may lead to an improved understanding of the factors affecting moral behaviour. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

In this paper we show that the coherence measures of Olsson (J Philos 94:246–272, 2002), Shogenji (Log Anal 59:338–345, 1999), and Fitelson (Log Anal 63:194–199, 2003) satisfy the two most important adequacy requirements for the purpose of assessing theories. Following Hempel (Synthese 12:439–469, 1960), Levi (Gambling with truth, New York, A. A. Knopf, 1967), and recently Huber (Synthese 161:89–118, 2008) we require, as minimal or necessary conditions, that adequate assessment functions favor true theories over false theories and true and (...) informative theories over true but uninformative theories. We then demonstrate that the coherence measures of Olsson, Shogenji, and Fitelson satisfy these minimal conditions if we confront the hypotheses with a separating sequence of observational statements. In the concluding remarks we set out the philosophical relevance, and limitations, of the formal results. Inter alia, we discuss the problematic implications of our precondition that competing hypotheses must be confronted with a separating sequence of observational statements, which also leads us to discuss theory assessment in the context of scientific antirealism. (shrink)

Research on preference reversals has demonstrated a disproportionate influence of outcome probability on choices between monetary gambles. The aim was to investigate the hypothesis that this is a prominence effect originally demonstrated for riskless choice. Another aim was to test the structure compatibility hypothesis as an explanation of the effect. The hypothesis implies that probability should be the prominent attribute when compared with value attributes both in a choice and a preference rating procedure. In Experiment 1, two groups of undergraduates (...) were presented with medical treatments described by two value attributes (effectiveness and pain-relief). All participants performed both a matching task and made preference ratings. In the latter task, outcome probabilities were added to the descriptions of the medical treatments for one of the groups. In line with the hypothesis, this reduced the prominence effect on the preference ratings observed for effectiveness. In Experiment 2, a matching task was used to demonstrate that probability was considered more important by a group of participating undergraduates than the value attributes. Furthermore, in both choices and preference ratings the expected prominence effect was found for probability. (shrink)

When you are indifferent between two options, it’s rationally permissible to take either. One way to decide between two such options is to flip a fair coin, taking one option if it lands heads and the other if it lands tails. Is it rationally permissible to employ such a tie-breaking procedure? Intuitively, yes. However, if you are genuinely risk-averse—in particular, if you adhere to risk-weighted expected utility theory (Buchak in Risk and rationality, Oxford University Press, 2013) and have a strictly (...) convex risk-function—the answer will often be no: the REU of deciding by coin-flip will be lower than the REU of choosing one of the options outright (so long as at least one of the options is a nondegenerate gamble). This turns out to be a significant worry for risk-weighted expected utility theory. I argue that it adds real bite to established worries about diachronic consistency afflicting views, like risk-weighted expected utility theory, that violate Independence. And that, while these worries might be surmountable, surmounting them comes at a price. (shrink)

Those who are risk averse with respect to money, and thus turn down some gambles with positive monetary expectations, are nevertheless often willing to accept bundles involving multiple such gambles. Therefore, it might seem that such people should become more willing to accept a risky but favourable gamble if they put it in context with the collection of gambles that they predict they will be faced with in the future. However, it turns out that when a risk averse person adopts (...) the long-term perspective, she faces a decision-problem that can be analysed as a noncooperative game between different “time-slices” of herself, where it is in the interest of each time-slice (given its prediction about other slices) to turn down the gamble with which it is faced. Hence, even if a risk averse but rational person manages to take the long-term perspective, she will, in the absence of what Hardin called “mutual coercion”, end up in a situation analogous to the “tragedy of the commons”. (shrink)

Utilitarian (U.) theories must be capable of being applied in practical reasoning, or they would have no value as a guide to rational conduct. However, I show that epistemic extensions to U. theories produce logical confusion. Basic questions about what one needs to know in order to apply a U. analysis embroil one in an infinite regress. And attempts to incrementally apply U. either are no help at all (leaving one entirely 'in the dark'), or in general constitute arbitrary gambles (...) which no practical reasoner could defend taking. These problems are serious enough to completely discredit U. theories as having any relevance to practical reasoning. (shrink)