The uncovered set in spatial voting games

In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set.     

Contingent on Context? Social Work and the State in Australia, Britain, and the USA

Correspondence to John Harris, School of Health and Social Studies, University of Warwick, Coventry CV4 7AL, UK. E-mail: j.harris{at}warwick.ac.uk Summary The notion that social work is an international profession,operating with generally similar goals, methodologies, and commonvalues is considered critically. Examining the political andsocial contexts of three countries with liberal democratic governments—Australia,Britain and the United States—the role of social workwithin the welfare processes of each country is compared. Whilesocial work as an identifiable professional activity sharessome features, it is argued that the idea of its having a coreessence needs to be tempered with a realistic assessment ofthe importance of contextually created difference. Recent andrapid developments in the institutional context, such as thoseexperienced in these three countries, further underscore thelimited utility of the notion of a common professional project.     

Alexithymia and Gambling: A Risk Factor for All Gamblers?

The purpose of this study was to investigate alexithymia (in relation with depression) in three groups of French gamblers (n = 186) recruited in their gambling location: at the racetracks (n = 80 males; mean age 28.1 years), in the slot machine rooms (n = 65; 29 males, 36 females; mean age 34.6 years), and in the traditional gaming rooms (n = 41 males; mean age 36 years). Gambling behavior was measured by the South Oaks Gambling Screen and DSM-IV criteria for pathological gambling, Alexithymia by the Toronto Alexithymia Scale (TAS-20) and depression with the Beck Depression Inventory (BDI-13). For racetracks and slot machine gambling, pathological gamblers differed from non-pathological gamblers, regarding their alexithymia scores. These results remained stable after controlling for depression scores among the racetracks gamblers only. The relationship between alexithymia and depression depends on the type of pathological gambler. These findings are consistent with the idea of identifying clinically distinct subgroups of gamblers.     

Backward Induction Is Not Robust: The Parity Problem and the Uncertainty Problem

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no known endpoint in the latter case, an extension of the idea of backward induction is used to determine the possible outcomes. The parity problem highlights the lack of robustness of backward induction, but it poses no conflict between foundational principles. On the other hand, two conflicting views of the future underlie the uncertainty problem, depending on whether the number of rounds is bounded (the players invariably shoot from the start) or unbounded (they may all cooperate and never shoot, despite the fact that the truel will end with certainty and therefore be effectively bounded). Some real-life examples, in which destructive behavior sometimes occurred and sometimes did not, are used to illustrate these differences, and some ethical implications of the analysis are discussed.