Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings

The aim of the present paper is to provide an axiomatic analysis of incomplete social judgments. In particular, we clarify the underlying power structure of Arrovian collective choice rules when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness and investigate the properties of the collection of quasi-decisive sets associated with an Arrovian collective choice rule. In the course of this, we offer a series of applications.     

Consequences,opportunities, and Arrovian impossibility theorems with consequentialist domains

We examine the possibility of Arrovian social choice when alternatives consist of outcomes and opportunity sets from which they are chosen. Consequentialism is a choice attitude towards outcomes and opportunities for choice and prioritizes outcomes rather than opportunities for choice. We first propose a sufficient condition for a restricted domain on which Arrow’s impossibility theorem holds. A domain such that there exists a similarity of choice attitudes within consequentialism satisfies the proposed domain condition. We observe that a diversity of choice attitudes within consequentialism is crucial to resolve an Arrovian impossibility, but this resolution is restricted in plausibility.     

On the separability of assembly preferences

Analyses of assembly elections often assume that voters have well-defined preferences over candidates, even though preferences over assemblies are the natural analytic starting point. This candidate-based approach is usually justified by an assumption that preferences over assemblies are separable. We show, however, that if preferences over assemblies are themselves derived from underlying preferences over legislative or economic outcomes, then preferences over assemblies will not in general be separable. Received: 23 June 1997/Accepted: 3 March 1998     

Social choice with analytic preferences

Arrow's axioms for social welfare functions are shown to be inconsistent when the set of alternatives is the nonnegative orthant in a multidimensional Euclidean space and preferences are assumed to be either the set of analytic classical economic preferences or the set of Euclidean spatial preferences. When either of these preference domains is combined with an agenda domain consisting of compact sets with nonempty interiors, strengthened versions of the Arrovian social choice correspondence axioms are shown to be consistent. To help establish the economic possibility theorem, an ordinal version of the Analytic Continuation Principle is developed. Received: 4 July 2000/Accepted: 2 April 2001     

‘One and a Half Dimensional’ Preferences and Majority Rule

I examine a model of majority rule in which alternatives are described by two characteristics: (1) their position in a standard, left-right dimension, and (2) their position in a good-bad dimension, over which voters have identical preferences. I show that when voters’ preferences are single-peaked and concave over the first dimension, majority rule is transitive, and the majority’s preferences are identical to the median voter’s. Thus, Black’s (The theory of committees and elections, 1958) theorem extends to such a “one and a half” dimensional framework. Meanwhile, another well-known result of majority rule, Downs’ (An economic theory of democracy, 1957) electoral competition model, does not extend to the framework. The condition that preferences can be represented in a one-and-a-half-dimensional framework is strictly weaker than the condition that preferences be single-peaked and symmetric. The condition is strictly stronger than the condition that preferences be order-restricted, as defined by Rothstein (Soc Choice Welf 7:331–342;1990).     

Gender and Organizational Justice Preferences

Despite evidence that women and men possess similar workplace values, debate continues regarding gendered preferences for justice in the workplace. In particular, some have argued that women and men have fundamentally different justice orientations, which lead men to value fair outcomes and women to value fair procedures. Recent research finds that such beliefs may influence managers to reward men with greater monetary rewards than those provided to women. Here, we review this literature and argue that men and women do not have fundamentally different justice orientations. Instead, the few findings of gender difference in preferences for procedural vs. distributive justice in the workplace are a function of status differences between men and women.     

On continuity of Arrovian social welfare functions

We study continuity properties of Arrovian social welfare functions in the infinite population framework. We show that continuous welfare functions satisfying unanimity and independence of irrelevant alternatives are dictatorial. Weak anonymity is shown to be incompatible with continuity and unanimity: every continuous weakly anonymous social welfare function must be a constant function.     

Topological manipulators form an ultrafilter

Consider the problem of aggregating preferences. A coalition is manipulative if it is able to force the outcome of the aggregation process. In the framework of topological aggregation (due to Chichilnisky) the family of manipulative coalitions constitutes an ultrafilter. This result holds for finite and for infinite populations, and supports the analogy between the Chichilnisky and the Arrovian aggregation model.This text presents research results of the Belgian Programme of Interuniversity Poles of Attraction initiated under the Science Policy Programmes of the Prime Ministers Office, Belgium. The scientific responsibility is assumed by its authors. I thank the referee for her/his constructive comments.     

From Arrow to cycles, instability, and chaos by untying alternatives

From remarkably general assumptions, Arrow's Theorem concludes that a social intransitivity must afflict some profile of transitive individual preferences. It need not be a cycle, but all others have ties. If we add a modest tie-limit, we get a chaotic cycle, one comprising all alternatives, and a tight one to boot: a short path connects any two alternatives. For this we need naught but (1) linear preference orderings devoid of infinite ascent, (2) profiles that unanimously order a set of all but two alternatives, and with a slightly fortified tie-limit, (3) profiles that deviate ever so little from singlepeakedness. With a weaker tie-limit but not (2) or (3), we still get a chaotic cycle, not necessarily tight. With an even weaker one, we still get a dominant cycle, not necessarily chaotic (every member beats every outside alternative), and with it global instability (every alternative beaten). That tie-limit is necessary for a cycle of any sort, and for global instability too (which does not require a cycle unless alternatives are finite in number). Earlier Arrovian cycle theorems are quite limited by comparison with these. Received: 31 July 1999/Accepted: 15 October 1999     

Is abstention an escape from Arrow’s theorem?

In a society of variable size, Quesada (Soc Choice Welfare 25(1): 221–226, 2005) establishes the existence of Arrovian social welfare functions which are not dictatorial. We show that this escape from the Arrovian impossibility collapses when a very mild monotonicity condition is introduced.     

Arrovian impossibilities in aggregating preferences over non-resolute outcomes

Let A be a set of alternatives whose power set is . Elements of are interpreted as non-resolute outcomes. We consider the aggregation of preference profiles over into a (social) preference over . In case we allow individuals to have any complete and transitive preference over , Arrow’s impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over is severely restricted. In fact, we identify a mild “regularity” condition which ensures the dictatoriality of a domain. Regularity is compatible with almost all standard extension axioms of the literature. Thus, we interpret our results as the strong prevalence of Arrow’s impossibility theorem in aggregating preferences over non-resolute outcomes. This paper is part of a project entitled “Social Perception—A Social Choice Perspective”, supported by Istanbul Bilgi University Research Fund. It has been completed while Remzi Sanver was visiting Ecole Polytechnique, Paris. We are grateful to both institutions. We thank Nick Baigent, two anonymous referees and an anonymous associate editor for their valuable comments.     

The influence of tax authorities on the employment of tax practitioners: Empirical evidence from a survey and interview study

Tax practitioners play a crucial role in the degree of taxpayers’ compliance – a role that has increased as tax systems worldwide have become more complex. However, little is known about tax authorities’ impact on taxpayers’ decisions to employ tax practitioners. Based on earlier research on motivations to employ a tax practitioner and the extended slippery slope framework of tax compliance, we conducted two studies which provide some answers. A survey study – comprising a representative sample of 500 Austrian self-employed taxpayers – revealed that financial gain is not the most important reason to employ a tax practitioner but instead the motivation to avoid problems with the tax authorities. Related to that, we also find that taxpayers’ perception of tax authorities wielding coercive power motivates them to employ tax practitioners. In the interview study with 33 self-employed taxpayers and 30 tax auditors, taxpayers indicated that they sought to avoid contact with tax officers by employing tax practitioners. This finding was supported by tax officers who reported preferring interaction with tax practitioners over direct contact with taxpayers. The two studies point to the complex relationship between taxpayers, tax authorities and tax practitioners, and allow the drawing of theoretical and practical implications.     

No-envy and Arrow's conditions

This paper analyzes the concept of envy-freeness in the framework of Arrovian social choice theory. We define various no-envy conditions and study their relationships with Arrow's condition of independence of irrelevant alternatives. We also propose a new condition, called Minimal Equity, that says that each individual must have the conditional power to veto at least one social state (for instance, a social state which is particularly unfair to him). We show that, under unrestricted domain, Pareto Optimality and a weak independence condition, Minimal Equity leads to an impossibility result. Received: 9 October 1997/Accepted: 27 May 1998     

Libertarian collective decision-making: A new framework

A model of collective decision-making is presented which enables us to analyze the allocation of individual rights and liberties. The model broadens the traditional social choice framework. In social choice theory it is usually assumed that individuals have preferences over a set of feasible alternatives and that society reaches a decision on the basis of those preferences only. In the model presented in this paper, decision procedures do not only take information about individual preferences as input, but also information about individual freedom. The specific decision procedures we present and analyze can be characterized as libertarian.This paper was written while I was a visitor at the University of California, Riverside. The visit was made possible by financial support of the Netherlands Organization of Scientific Research (NWO). I am extremely grateful to Prasanta Pattanaik for many stimulating discussions on the subject. For helpful comments I also thank Ad van Deemen, Grahame Lock, Huib Pellikaan and Marcel Wissenburg. Finally, I express my thanks to Wulf Gaertner and two anonymous referees.     

Impulsivity traits and gambling cognitions associated with gambling preferences and clinical status

Impulsivity (and related traits reward/punishment sensitivity and tolerance to delayed rewards) and gambling cognitions have been linked to gambling. However, their independent associations with gambling preferences and clinical status have never been dissociated. The current study applied a data-driven strategy to identify gambling preferences, based on gambling frequency in several modalities. The two resulting factors were used to classify gambling disorder patients (GDPs) and non-problem recreational gamblers (RGs) into Type I (preferring cards, casino games and skill-based bets) and Type II (preferring slot machines, lotteries/pools and bingo). Participants were assessed in impulsivity, delay discounting, reward/punishment sensitivity, gambling-related cognitions, gambling severity, gambling frequency and average amount gambled per episode. GDPs scored higher than RGs in positive and negative urgency, delay discounting, reward sensitivity and intensity of gambling-related cognitions, but less in lack of perseverance. Additionally, Type II gamblers had greater difficulties delaying gratification, whereas Type I gamblers showed higher cognitive distortion and reward sensitivity levels. In practical terms, the finding that some characteristics are equally pervasive in disordered gamblers independently of their preferences (affect-driven impulsivity), whereas others (distorted cognitions, reward sensitivity, delay discounting) are more prominent in one type or the other, provides a basis to establish targets’ priority in therapy.     

Parental substance misuse and statutory child protection in England: Risk factors and outcomes

Parental substance misuse is a significant child welfare issue and associated with increased risk of child maltreatment. The aim of the present study was to understand what social care outcomes children who live with parental substance misuse have, and to assess factors associated with those social care outcomes over a two-year period. The paper reports on a retrospective longitudinal study of 299 children all living with parental substance misuse and referred to one local authority in England. Data were collected from children's social work case files about procedural social care outcomes and factors which may be associated with those outcomes. Using cluster analysis, a new typology of children's longitudinal trajectories through the children's social care system was developed, consisting of five distinct types. Analysis indicated that some children received too little intervention from children's social care despite ongoing concerns, while other children were potentially unnecessarily caught up in the social care system. Factors associated with children having the poorest outcomes were: caregiver instability resulting from substance misuse, parenting capacity and household instability. The study's findings indicate that some children who live with parental substance misuse are at significant risk of harm, but others are not and may be better supported through non-statutory services such as early help.     

The Banks Set in Infinite Spaces

I provide a definition of the Banks set, or set of sophisticated voting outcomes, over an infinite policy space and when individual preferences are weak. I also show that the Banks set is a subset of one definition of the uncovered set, but not another. The interpretation of the Banks set in this setting differs from Banks’s original interpretation in the implicit role of the agenda setter. In addition, a characterization of the Banks set is provided for a three-player game of distributive politics. In this special setting, the Banks set and all definitions of the uncovered set have full measure over the space of alternatives.     

Axiomatic foundations for fairness-motivated preferences

Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight on each person’s payoff depends on a reference vector of how much each person deserves.