Differences in Cognitive Distortions Between Pathological and Non-Pathological Gamblers with Preferences for Chance or Skill Games

Cognitive distortions have been thought to play an important role in the development and maintenance of pathological gambling. The present study investigated whether severity of gambling problems and gamblers’ preference for chance or skill games were related to two sub-factors of cognitive distortions as measured by the Gamblers Belief Questionnaire: Luck/Perseverance, which reflects an individual’s perception that chance is favorable to him/her, and Illusion of Control, which reflects an individual’s perception that his/her behavior influences chance occurrences. Participants (N = 166) were recruited from a race track (n = 79), off-course betting facilities (n = 50) and from an online treatment program for problem gamblers (n = 49). Gambling severity was measured by the South Oaks Gambling Screen, and 73 were classified as pathological gamblers whereas 93 were classified as non-pathological gamblers. The present study supports previous proposals that cognitive distortions are core processes related to gambling behavior as pathological gamblers reported more cognitive distortions than did non-pathological gamblers. A preference for skill games was also associated with greater Illusion of Control compared to a preference for chance games. For gamblers preferring skill games there were no differences in Luck/Perseverance or Illusion of Control between pathological and non-pathological gamblers.     

Dividing Justly in Bargaining Problems with Claims

Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people’s impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environment. We measure people’s judgments on the normative attractiveness of solution concepts with the help of a survey and also observe actual agreements in a bargaining experiment with real money at stake. We find that the proportional solution is the normatively most attractive rule, whereas actual negotiation agreements are closest to the ‘constrained equal-award’ solution.     

On the adjudication of conflicting claims: an experimental study

This paper reports an experimental study on three well-known solutions for problems of adjudicating conflicting claims: the constrained equal awards, the proportional, and the constrained equal losses rules. We first let subjects play three games designed such that the unique equilibrium allocation coincides with the recommendation of one of these three rules. In addition, we let subjects play an additional game that has the property that all (and only) strategy profiles in which players coordinate on the same rule constitute a strict Nash equilibrium. While in the first three games subjects’ play easily converges to the unique equilibrium rule, in the last game the proportional rule overwhelmingly prevails as a coordination device, especially when we frame the game as an hypothetical bankruptcy situation. We also administered a questionnaire to a different group of students, asking them to act as impartial arbitrators to solve (among others) the same problems played in the lab. Also in this case, respondents were sensitive to the framing of the questions, but the proportional rule was selected by the vast majority of respondents.     

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting.     

The geometry of implementation: a necessary and sufficient condition for straightforward games

 We characterize games which induce truthful revelation of the players’ preferences, either as dominant strategies (straightforward games) or in Nash equilibria. Strategies are statements of individual preferences on R ⁿ . Outcomes are social preferences. Preferences over outcomes are defined by a distance from a bliss point. We prove that g is straightforward if and only if g is locally constant or dictatorial (LCD), i.e., coordinate-wise either a constant or a projection map locally for almost all strategy profiles. We also establish that: (i) If a game is straightforward and respects unanimity, then the map g must be continuous, (ii) Straightforwardness is a nowhere dense property, (iii) There exist differentiable straightforward games which are non-dictatorial. (iv) If a social choice rule is Nash implementable, then it is straightforward and locally constant or dictatorial. Received: 30 December 1994/Accepted: 22 April 1996     

Offspring of Parents with Gambling Problems: Adjustment Problems and Explanatory Mechanisms

We compared offspring of problem gamblers (n = 42) to offspring of parents without gambling problems (n = 100) to see (1) whether the two groups differed with respect to depressive feelings and conduct/antisociality problems and (2) whether ineffective parenting or the offspring’s own gambling problems played a mediating role in this context. Participants were drawn from a relatively large community-based study (N = 1,872). Parents rated their own gambling and other mental health problems when their children were in mid-adolescence. The children’s self-reports on depressive feelings and conduct/antisociality problems were assessed at two points in time: by mid-adolescence and again by early adulthood. Results showed that children of parents with gambling problems reported more depressive feelings and more conduct problems by mid-adolescence than children of parents without gambling problems. Children of problem gamblers also experienced an increase in their depressive symptoms from mid-adolescence to early adulthood. Importantly, ineffective parenting, but not children’s gambling problems, mediated almost all the links between parental problem gambling and children’s adjustment problems. These results add to a very small data base showing that children of problem gamblers are at risk for a variety of adjustment problems.

Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

Consistency in one-sided assignment problems

One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the division of payoffs to agents is flexible as part of the solution. We take a similar approach to one-sided assignment problems as Sasaki (Int J Game Theory 24:373–397, 1995) for two-sided assignment problems, and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [Pareto indifference and consistency] or [invariance with respect to unmatching dummy pairs, continuity, and consistency], then it coincides with the core (Theorems 1 and 2). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is non-empty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki’s (1995) characterizations of the core for two-sided assignment problems.     

Random conjugates of bankruptcy rules

This article introduces and analyzes random conjugates of bankruptcy rules. A random conjugate is a rule which is derived from the definition of the underlying rule for two-claimant problems. For example, the random conjugate of the Aumann–Maschler rule yields an extension of concede-and-divide: the basic solution for bankruptcy problems with two claimants. Using the concept of random conjugates an alternative characterization of the proportional rule is provided. It turns out that the procedural definition of a random conjugate extends several of the properties of the underlying rule for two-claimant problems to the general domain of problems with an arbitrary number of claimants.     

Objective measures of well-being and the cooperative production problem

 The concern for measuring well-being objectively (as opposed to subjectively, that is, relying only on preferences) is found in modern political philosophy, especially in J. Rawls’s, A. Sen’s and G. Cohen’s writings. This paper explains the implications of using an objective well-being index as equalisandum or, close to the so-called “safety net preoccupation”, to guarantee a well-being lower bound. In the simple production model studied here, five characterization results and two related theorems prove the convergence of both approaches. We come to the conclusion that the Proportional Solution is the dominant solution according to “objectivist” axioms. Received: 5 September 1994/Accepted: 29 June 1996     

On the equilibrium of voting games with abstention and several levels of approval

We study the core of “(j, k) simple games”, where voters choose one level of approval from among j possible levels, partitioning the society into j coalitions, and each possible partition facing k levels of approval in the output (Freixas and Zwicker in Soc Choice Welf 21:399–431, 2003). We consider the case of (j, 2) simple games, including voting games in which each voter may cast a “yes” or “no” vote, or abstain (j = 3). A necessary and sufficient condition for the non-emptiness of the core of such games is provided, with an important application to weighted symmetric (j, 2) simple games. These results generalize the literature, and provide a characterization of constitutions under which a society would allow a given number of candidates to compete for leadership without running the risk of political instability. We apply these results to well-known voting systems and social choice institutions including the relative majority rule, the two-thirds relative majority rule, the United States Senate, and the United Nations Security Council.     

Core concepts for share vectors

A value mapping for cooperative games with transferable utilities is a mapping that assigns to every game a set of vectors each representing a distribution of the payoffs. A value mapping is efficient if to every game it assigns a set of vectors which components all sum up to the worth that can be obtained by all players cooperating together.? An approach to efficiently allocate the worth of the ‘grand coalition’ is using share mappings which assign to every game a set of share vectors being vectors which components sum up to one. Every component of a share vector is the corresponding players' share in the total payoff that is to be distributed among the players. In this paper we discuss a class of share mappings containing the (Shapley) share-core, the Banzhaf share-core and the Large Banzhaf share-core, and provide characterizations of this class of share mappings. Received: 9 August 1999/Accepted: 25 April 2000     

Real Limits in the Virtual World: Self-Limiting Behavior of Internet Gamblers

The recent expansion of Internet gambling has stimulated debate, policy, and research on this relatively new phenomenon and its potential consequences. The current study focuses on bettors experiencing problems by sampling Internet gamblers who imposed limits on the amount they were allowed to deposit to a betting site. We analyzed the betting transactions over 18 months of all gamblers who subscribed to an online betting site in February, 2005 (N = 47,134), 567 of whom utilized the site’s self-limit feature. Self-limiting gamblers played a wider variety of games and placed more bets than others prior to imposing limits. After imposing limits, self-limiters reduced their activity, but did not reduce the amount they wagered per bet. Time spent gambling, not just money spent, appears to be an important indicator of gambling problems. Self-limit programs appear to be promising options for Internet gamblers at-risk for gambling problems.

Towards a Philosophy of Containment: Reading Goffman in the 21st Century

On the occasion of the re-publication of Erving Goffman’s Relations in Public: Microstudies of the Public Order, including the remarkable appendix, “Insanity of Place,” the authors propose new ways of reading Goffman’s work in order to highlight his attention to havoc and containment. Goffman’s “Insanity of Place,” explores the phenomenon of mental illness by asserting that it is an instance of havoc, a symbolic and practical condition that disrupts the social order of life, and one that must be contained. By situating this essay at the center of Goffman’s oeuvre they examine Goffman’s “philosophy of containment,” and trace its trajectory from Asylums, Stigma and “The Insanity of Place” to its full crystallization in Frame Analysis. The authors offer a generative reading of havoc and containment in order to understand the incoherence, irrationality, unreason, incomprehensibility and unbearableness of social life and the imperative to preserve social order from collapsing, dissolving or imploding. This reading enables us to see the cracks in the social order and understand containment as the constant effort exerted to recuperate transgressions and deviations back into that order. Goffman’s analysis becomes an opening into engagements with the work of Judith Butler and Michel Foucault around the notion of the normative order and the issues of containment and transgression. Thinking through Goffman’s philosophy of containment as the framework for an analysis of socialization, normalization, and social ordering affords an approach to thinking macro-micro linkages of order and instability that confront both our contemporary society and the discipline of sociology.     

Identifying habitat sinks: a case study of Cooper’s hawks in an urban environment

We studied a population of Cooper’s hawks (Accipiter cooperii) in Tucson, Arizona from 1994 to 2005. High rates of mortality of nestlings from an urban-related disease prompted speculation that the area represented an ecological trap and habitat sink for Cooper’s hawks. In this paper, we used estimates of survival and productivity from 11years of monitoring to develop an estimate of the rate of population change, λ, for Cooper’s hawks in the area. We used a Cormack–Jolly–Seber approach to estimate survival of breeding hawks, and a stochastic, stage-based matrix to estimate λ. Despite the urban-related disease, the estimate of λ indicated that the area does not function as a habitat sink for Cooper’s hawks (= 1.11 ± 0.047; P = 0.0073 for the null of λ ≤ 1). Because data required to reliably identify habitat sinks are extensive and difficult to acquire, we suggest that the concept of habitat sinks be applied cautiously until substantiated with reliable empirical evidence.     

Using Neural Networks to Model the Behavior and Decisions of Gamblers,in Particular,Cyber-Gamblers

This article describes the use of neural networks (a type of artificial intelligence) and an empirical data sample of, inter alia, the amounts of bets laid and the winnings/losses made in successive games by a number of cyber-gamblers to longitudinally model gamblers’ behavior and decisions as to such bet amounts and the temporal trajectory of winnings/losses. The data was collected by videoing Texas Holdem gamblers at a cyber-gambling website. Six “persistent” gamblers were identified, totaling 675 games. The neural networks on average were able to predict bet amounts and cumulative winnings/losses in successive games accurately to three decimal places of the dollar. A more important conclusion is that the influence of a gambler’s skills, strategies, and personality on his/her successive bet amounts and cumulative winnings/losses is almost totally reflected by the pattern(s) of his/her winnings/losses in the few initial games and his/her gambling account balance. This partially invalidates gamblers’ illusions and fallacies that they can outperform others or even bankers. For government policy-makers, gambling industry operators, economists, sociologists, psychiatrists, and psychologists, this article provides models for gamblers’ behavior and decisions. It also explores and exemplifies the usefulness of neural networks and artificial intelligence at large in the research on gambling.     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999     

Utilities,preferences, and substantive goods

 People’s utility levels are meant to be measures of their well-being. Early utilitarians defined them in terms of people’s happiness. Modern economics defines them in terms of people’s actual preferences. But in ethics they have to be defined in terms of people’s informed preferences. I shall discuss the relationship between people’s desires and preferences, and that between their reasoned and unreasoned preferences. I shall argue that people’s basic desires are much the same, whereas their preferences are often very different. Finally, I shall argue, contrary to Scanlon’s theory, that the things that are good for us are beneficial to us ultimately because they satisfy our biological and psychological needs and our personal interests. Received: 8 July 1996     

Social and Psychological Challenges of Poker

Poker is a competitive, social game of skill and luck, which presents players with numerous challenging strategic and interpersonal decisions. The adaptation of poker into a game played over the internet provides the unprecedented opportunity to quantitatively analyze extremely large numbers of hands and players. This paper analyzes roughly twenty-seven million hands played online in small-stakes, medium-stakes and high-stakes games. Using PokerTracker software, statistics are generated to (a) gauge the types of strategies utilized by players (i.e. the ‘strategic demography’) at each level and (b) examine the various payoffs associated with different strategies at varying levels of play. The results show that competitive edges attenuate as one moves up levels, and tight-aggressive strategies––which tend to be the most remunerative––become more prevalent. Further, payoffs for different combinations of cards, varies between levels, showing how strategic payoffs are derived from competitive interactions. Smaller-stakes players also have more difficulty appropriately weighting incentive structures with frequent small gains and occasional large losses. Consequently, the relationship between winning a large proportion of hands and profitability is negative, and is strongest in small-stakes games. These variations reveal a meta-game of rationality and psychology which underlies the card game. Adopting risk-neutrality to maximize expected value, aggression and appropriate mental accounting, are cognitive burdens on players, and underpin the rationality work––reconfiguring of personal preferences and goals––players engage into be competitive, and maximize their winning and profit chances.     

Acyclic sets of linear orders via the Bruhat orders

We describe Abello’s acyclic sets of linear orders [SIAM J Discr Math 4(1):1–16, 1991] as the permutations visited by commuting equivalence classes of maximal reduced decompositions. This allows us to strengthen Abello’s structural result: we show that acyclic sets arising from this construction are distributive sublattices of the weak Bruhat order. This, in turn, shows that Abello’s acyclic sets are, in fact, the same as Chameni-Nembua’s distributive covering sublattices (S.T.D.C s). Fishburn’s alternating scheme is shown to be a special case of the Abello/Chameni-Nembua acyclic sets. Any acyclic set that arises in this way can be represented by an arrangement of pseudolines, and we use this representation to derive a simple closed form for the cardinality of the alternating scheme. The higher Bruhat orders prove to be a natural mathematical framework for this approach to the acyclic sets problem. We would like to thank the Editor, Professor Bernard Monjardet, and two anonymous referees for their comments and additional references.