On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.     

Contraction consistent stochastic choice correspondence

We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition, ‘contraction consistency’, subsumes earlier notions such as Chernoff’s Condition, Sen’s α and β, and regularity. We identify a restriction on the domain of the stochastic choice correspondence (SCC), under which contraction consistency is equivalent to the weak axiom of revealed preference in its most general form. When the universal set of alternatives is finite, this restriction is also necessary for such equivalence. Analogous domain restrictions are also identified for the special case where choice is deterministic but possibly multi-valued. Results due to Sen (Rev Econ Stud 38:307–317, 1971) and Dasgupta and Pattanaik (Econ Theory 31:35–50, 2007) fall out as corollaries. Thus, conditions are established, under which our notion of consistency, articulated only in reference to contractions of the feasible set, suffices as the axiomatic foundation for a general revealed preference theory of choice behaviour.     

Hansson’s theorem for generalized social welfare functions: an extension

 Hansson (1969) sets forth four conditions satisfied by no generalized social welfare function (GSWF), a mapping from profiles of individual preferences to arbitrary social preference relations. Though transitivity is not imposed on social preferences, one of Hansson’s conditions requires that socially maximal alternatives always exist. Of course, this condition is not satisfied by the majority GSWF. We prove a generalization of Hansson’s theorem that requires the existence of maximal alternatives only in very special cases. Our result applies to the majority GSWF and a large class of other GSWFs that sometimes produce no maximal alternatives. Received: 10 July 1995/Accepted: 4 March 1996     

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.     

Sociology’s <Emphasis Type="Italic">Suicide</Emphasis>: A Forensic Autopsy?

For decades Durkheim’s theory of suicide has been tested and found wanting. Yet, rather than being consigned to the dust-bin of history, it lives on and is pointed to as an exemplar of the powers of sociological theory and research. If this rationalizing and/or dismissal of so many falsifications of the theory were an isolated phenomenon, it might be evidence of some lemming-like propensity for suicide or a disciplinary death-wish, among a few sociologists. But it appears to be a much more widespread and common occurrence. In this paper we explore some possible explanations of this ‘falsification denial’—‘The Social Misconstruction of Reality’ (Hamilton 1996), ‘When Prophecy Fails’ (Festinger et al. 1956), ‘Underdetermination’ (Duhem 1954; Quine Journal of Philosophy 67:178–183, 1970, Erkenntnis 9:313–328, 1975; Lakatos 1970), and ‘Boundary Maintenance’ (Erikson 1966), and we outline some of the more important and pernicious consequences of this falsification denial for the discipline and future of sociology.     

Rational Choice and von Neumann– Morgenstern’s Stable Set: The Case of Path-dependent Procedures

Describing a procedure in which choice proceeds in a sequence, we propose two alternative ways of resolving the decision problem whenever the outcome is sequence sensitive. One way yields a rationalizable choice set, and the other way produces a weakly rationalizable choice set that is equivalent to von Neumann–Morgenstern’s stable set. It is shown that for quasi-transitive rationalization, the maximal set must coincide with its stable set.     

Examining Community Life “in the Making”: Emile Durkheim’s <Emphasis Type="Italic">Moral Education</Emphasis>

Although often overlooked in sociological circles, Emile Durkheim’s (1902–1903) Moral Education provides an important cornerstone in the quest to understand community life. Not only does Moral Education give a vibrant realism to the sociological venture in ways that Durkheim’s earlier works (1893, 1895, 1897) fail to achieve, but in addressing discipline, devotion, and informed reasoning as humanly engaged, collectively accomplished fields of activity Emile Durkheim also provides an exceptionally consequential baseline analysis of human knowing and acting. Notably as well, focusing on the organizational, intersubjectively achieved features of elementary education, Durkheim’s Moral Education lays bare the interactional nature of the moral order of community life. Indeed, as a sustained analysis of the way of life of a group of people collectively participating in the educational process, this text addresses the most basic features of people’s relations to one another and the broader society in which they find themselves. Much more than an account of childhood socialization, Durkheim’s Moral Education also presages the more thoroughly humanist sociology that Durkheim develops in The Evolution of Educational Thought (1904–1905), The Elementary Forms of the Religious Life (1912) and Pragmatism and Sociology (1913–1914).     

Condorcet choice and the Ostrogorski paradox

The Ostrogorski paradox refers to the fact that, facing finitely many dichotomous issues, choosing issue-wise according to the majority rule may lead to a majority defeated overall outcome. This paper investigates the possibility for a similar paradox to occur under alternative specifications of the collective preference relation. The generalized Ostrogorski paradox occurs when the issue-wise majority rule leads to an outcome which is not maximal according to some binary relation φ defined over pairs of alternatives. We focus on three possible definitions of φ, whose sets of maximal elements are respectively the Uncovered Set, the Top-Cycle, and the Pareto Set. We prove that a generalized paradox may prevail for the Uncovered Set. Moreover, it may be avoided for the same issue-wise majority margins as for the Ostrogorski paradox. However, the issue-wise majority rule always selects a Pareto-optimal alternative in the Top-Cycle. Gilbert Laffond and Jean Lainé are grateful to two anonymous referees for their helpful comments and suggestions.     

Why do larger families reduce parental investments in child quality, but not child quality per se?

Becker’s Quantity–Quality model (Becker in Demographic and economic change in developed countries, Princeton University Press, Princeton, pp 209–240, 1960; Becker and Lewis in J Polit Econ 81(2): S279–S288, 1973; Becker and Tomes in J Polit Econ 84(4): S143–S162, 1976) suggests a trade-off between family size and parental investments in children. To date, only Cáceras-Delpiano (J Hum Resour 41(4): 738–754, 2006) tests this theory by considering private school enrolment. This study extends this work by using a unique data set containing a broader range of parental investments that are arguably linked to parental intentions for producing higher quality children, such as overall and non-sectarian private school enrolment, the number of computers in the home per child, and saving for the child’s education. Both studies find that fertility reduces parental investments. However, the literature generally finds that fertility has no impact on child outcomes. The study offers three potential explanations for this ‘puzzle’.     

An Analysis of State–Civil Society Relations in Finland: A Case of Joensuu

Theoretical researches have argued that state–civil society relations differ from one country to another because of different economic, political, and socio-cultural factors. This article aims to show civil society’s role in the Finnish welfare state and how the state and the civil society affect each other in Joensuu, a 72,167 populated Finnish city. Joensuu case is analyzed from the theoretical perspectives of Esping-Andersen (The three worlds of welfare capitalism, 1990), Young (Nonprofit Volunt Sector Q 29:149–172, 2000), and Schofer and Fourcade-Gourinchas (Am Sociol Rev 66: 806–828, 2001) by taking into account interviews with 13 members of voluntary organizations in the city. In the light of the field work, the argument is based on the negative impact of welfare system’s transformation process on nongovernmental organizations in Joensuu, Finland.     

Coping with Guilt and Shame After Gambling Loss

In this study we examined the relations between guilt and shame and coping strategies in response to gambling loss. Based on H.B. Lewis’s (Shame & guilt in neurosis. New York: International Universities Press, 1971) account of guilt and shame, we proposed that unlike guilt, the experience of shame involves the attribution of gambling loss to stable and global internal factors (i.e., self-devaluation). We hypothesized that problem gambling severity would be more strongly associated with the intensity of shame than with the intensity of guilt following gambling loss. Further, we hypothesized that the intensity of shame would be positively associated with the use of avoidant coping strategies following gambling loss. Finally, we hypothesized that the intensity of shame would mediate the association between problem gambling severity and the use of avoidant coping. These hypotheses were supported by a retrospective survey of recent gambling losses. Our finding suggests that the experience of shame and the use of avoidant coping strategies to deal with this emotion are central to problem gambling severity.     

A distance measure for choice functions

This paper discusses and characterizes a distance function on the set of quasi choice functions. The derived distance function is in the spirit of the widely used Kemeny metric on binary relations but extends Kemeny’s use of the symmetric difference distance to set functions and hence to a more general model of choice.     

An extension of McGarvey’s theorem from the perspective of the plurality collective choice mechanism

In 1953, David McGarvey showed that if the number of voters is unrestricted, then the set of outputs obtained from majority rule is a very general class of binary relations. We will present an extension of McGarvey’s Theorem based on the plurality collective choice mechanism.     

Assessing the Reliability of the Gambling Functional Assessment: Revised

Dixon and Johnson (Anal Gambl Behav 1: 44–49, 2007) proposed the Gambling Functional Assessment as a tool to identify the consequences maintaining the respondent’s gambling behavior, but subsequent studies on its psychometric properties suggested that it could use improvement. The present study investigated the internal consistency of the Gambling Functional Assessment—Revised using the responses of 1,060 undergraduate students. Temporal reliability was assessed by a second administration of the measure four (n = 87) or twelve (n = 98) weeks after the first administration. Temporal reliability was also compared to the South Oaks Gambling Screen (Lesieur and Blume in Am J Psychiatry 144: 1184–1188, 1987), which was also administered at both time points. Internal consistency measures were good to excellent, even when potential non-gamblers were excluded from the analyses. Temporal stability was also very good, with the possible exception of the consequence of “escape” at 12 weeks. The Gambling Functional Assessment—Revised represents a potentially useful tool for researchers and therapists interested in why respondents are gambling.     

Children’s Deliberate Control of Facial Action Units Involved in Sad and Happy Expressions

Few attempts have been made since the pioneer work of Ekman et al. (1980) to examine the development of the deliberate control of facial action units in children. We are reporting here two studies concerned with this issue. In Study 1, we investigated children’s ability to activate facial action units involved in sadness and happiness expressions as well as combinations of these action units. In Study 2, we examined children’s ability to pose happiness and sadness with their face, without telling them which action unit to activate. The children who took part in this study were simply asked to portray happiness and sadness as convincingly as possible. The results of Study 1 indicate a strong developmental progression in children’s ability to produce elementary facial components of both emotions as well as in their ability to produce a combination of the elements in the case of happiness. In agreement with prior research in motor development, several non-target action units were also activated when children performed the task. Their occurrence persisted throughout childhood, indicating limitations in the finer motor control achieved by children across age. The results obtained in Study 2 paralleled those obtained in Study 1 in many respects, providing evidence that the children used the technique of deliberate action to pose the two target emotions.     

Measuring inequality of opportunity through between-group inequality components

Opportunity egalitarians support rich-to-poor redistribution whenever this allows for the compensation of income disparities due to non-responsible choices (circumstances). In this paper we focus on the measurement of opportunity inequality within Roemer’s (Philos Public Aff 22:146–166, 1993) pragmatic theory where a disjoint and exhaustive partition rule is assumed such that individuals within the same population can be grouped depending on the sole circumstances. Given entropy-based, deprivation-based and welfaristic inequality decomposition procedures, we show that the between-group Gini component from Dagum’s decomposition is the only well known between-group inequality index satisfying the Pigou-Dalton principle of transfer as reformulated for opportunity egalitarianism.     

A Social Choice Lemma on Voting Over Lotteries with Applications to a Class of Dynamic Games

We prove a lemma characterizing majority preferences over lotteries on a subset of Euclidean space. Assuming voters have quadratic von Neumann–Morgenstern utility representations, and assuming existence of a majority undominated (or “core”) point, the core voter is decisive: one lottery is majority-preferred to another if and only if this is the preference of the core voter. Several applications of this result to dynamic voting games are discussed.This paper was completed after Jeff Banks’s death. John Duggan is deeply indebted to him for his friendship and his collaboration on this and many other projects.     

Aggregation of binary evaluations for truth-functional agendas

In the problem of judgment aggregation, a panel of judges has to evaluate each proposition in a given agenda as true or false, based on their individual evaluations and subject to the constraint of logical consistency. We elaborate on the relation between this and the problem of aggregating abstract binary evaluations. For the special case of truth-functional agendas we have the following main contributions: (1) a syntactical characterization of agendas for which the analogs of Arrow’s aggregation conditions force dictatorship; (2) a complete classification of all aggregators that satisfy those conditions; (3) an analysis of the effect of weakening the Pareto condition to surjectivity. This is a sequel to the paper “Aggregation of binary evaluations.” The contents of both papers were presented, under the title “An Arrovian impossibility theorem for social truth functions,” at the Second World Congress of the Game Theory Society, Marseille, July 2004. The first version of “Aggregation of binary evaluations” was completed in June 2005. That working paper was subsequently split into two parts, of which this is the second. The comments of an anonymous referee are gratefully acknowledged. Part of R. Holzman’s work was done while he was a Fellow of the Institute for Advanced Studies at the Hebrew University of Jerusalem.     

Income inequality games

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, based on the Shapley value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that multiplicative inequality games provide dual results compared with Chantreuil and Trannoy’s ones. We also investigate the case of multiplicative poverty games for which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with, as in the Sen-Shorrocks-Thon poverty index. We finally show, in the case of additive poverty indices, that the Shapley value may be equivalent to traditional methods of decomposition such as subgroup consistency and additive decomposition.     

Asymmetric Preference and Inflation Bias in the Visegrad Four

This paper investigates the asymmetric preference of monetary policy in the Visegrad four (V-4). To this end, we estimate the nonlinear interest rate rule provided by Surico (2007). This enables us to estimate the central banker’s preference and to inference the average inflation bias. Empirical results provide some important evidence. First, the nonlinear rule and the preference are successfully estimated. This also imply that the average rates of inflation in the V-4 are set at a relatively high by their monetary policy. Second, After EU accession, the preferences of Slovakia and Poland become much lower than those in the full sample. This reflects the policy effort by these two to introduce the euro.