Ranking sets additively in decisional contexts: an axiomatic characterization

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.      

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

Comparison and choice

This paper develops the idea of a choice as a mapping of subsets of a set X into their respective subsets and the idea of the comparison, as a relation between elements of X, that is determined or revealed by a choice. It then studies how certain properties of a choice imply or are implied by certain properties, such as acyclicity, quasi-transitivity, pseudo-transitivity and transitivity, of the comparison revealed, finally giving a complete logical diagram of all the implications between these latter properties of the comparison.     

The essential ranking of decision rules in small panels of experts

For small panels of experts (e.g., boards of managers, courts, specialized committees), n 5, this paper provides an algorithm for ranking the seven efficient and commonly used weighted majority rules by their respective performance. These rules are terned efficient since they constitute the set of potentially optimal decision rules in uncertain, symmetric, pairwise choice situations. The main contribution of this study is the discovery of an essential ordering of six of these rules which entails that the set of possible ranking of the seven rules is almost single peaked.The essential ordering significantly reduces the number of possible rankings of the rules, and thus, simplifies the development of the ranking algorithm. The essential ordering has important applications when the available information on the experts' decisional skills is incomplete.     

An experimental investigation of transitivity in set ranking

A decision under ‘complete uncertainty’ is one where the decision maker knows the set of possible outcomes for each decision, but cannot assign probabilities to those outcomes. This way, the problem of ranking decisions is reduced to a problem of ranking sets of outcomes. All rankings that have emerged in the literature in this domain imply transitivity. In the current study, transitivity is subjected to an empirical evaluation in two experiments, where subjects are asked to choose between sets of monetary consequences. After analysis with a Bayes Factor, very few violations of transitivity were found. It can be concluded that transitivity seems a plausible condition for the ranking of sets of monetary consequences.     

Comparison of the Polar Decision Rules for Various Types of Distributions

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns.     

On the emptiness of the stability set of order d

We know from Li's theorem (1993) that the stability set of order d may be empty for some preference profiles. However, one may wonder whether such situations are just rare oddities or not. In this paper, we partially answer this question by considering the restrictive case where the number of alternatives is the smallest compatible with an empty stability set. More precisely, we provide an upper bound on the probability for having an empty stability set of order d for the majority game under the Impartial Weak Ordering Culture assumption. This upper bound is already extremely low for small population and tends to zero as the number of individuals goes to infinity.     

On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity

The Condorcet efficiency of a social choice procedure is usually defined as the probability that this procedure coincides with the majority winner (or majority ordering) in random samples, given a majority winner exists (or given the majority ordering is transitive). Consequently, it is in effect a conditional probability that two sample statistics coincide, given certain side conditions. We raise a different issue of Condorcet efficiencies: What is the probability that a social choice procedure applied to a sample matches with the majority preferences of the population from which the sample was drawn? We investigate the canonical case where the sample statistic is itself also majority rule and the samples are drawn from real world distributions gathered from national election surveys in Germany, France, and the United States. We relate the results to the existing literature on majority cycles and social homogeneity. We find that these samples rarely display majority cycles, whereas the probability that a sample misrepresents the majority preferences of the underlying population varies dramatically and always exceeds the probability that the sample displays cyclic majority preferences. Social homogeneity plays a fundamental role in the type of Condorcet efficiency investigated here.

     

Signed orders in linear and nonlinear utility theory

Self-reflecting signed orders on a set A and its anti-set A ^* were introduced previously as a way to account for negative as well as positive feelings about the inclusion of items in A in potential subsets of choice. The present paper extends the notion of signed orders to lotteries on A A ^*, describes reflection axioms for the lottery context, and shows how these axioms simplify utility representations for preference between lotteries. The simplified representations are then used to guide procedures for extending preferences from A A ^* and its lotteries to preferences between subsets of items.     

Inferring a linear ordering over a power set

An observer attempts to infer the unobserved ranking of two ideal objects, A and B, from observed rankings in which these objects are `accompanied' by `noise' components, C and D. In the first ranking, A is accompanied by C and B is accompanied by D, while in the second ranking, A is accompanied by D and B is accompanied by C. In both rankings, noisy-A is ranked above noisy-B. The observer infers that ideal-A is ranked above ideal-B. This commonly used inference rule is formalized for the case in which A,B,C,D are sets. Let X be a finite set and let be a linear ordering on 2^X. The following condition is imposed on . For every quadruple (A,B,C,D)Y, where Y is some domain in (2^X)⁴, if and , then . The implications and interpretation of this condition for various domains Y are discussed.     

Order extensions,budget correspondences,and rational choice

This article is concerned with extensions of a continuous ordering R on a set X to a subset P(X) of the power set of X. The underlying topology will be the Hausdorff metric topology. We will see that continuous extensions of R do not require that P(X) contain every nonempty finite subset of X. Therefore, the analysis can be applied to consumer theory and inverse choice functions. In analogy to these functions budget correspondences are established which relate alternatives x with certain subsets of X, according to the extended ordering.     

Discriminating Between Preference Functionals: A Monte Carlo Study

This paper reports on the results of a Monte Carlo investigation into the power of commonly employed procedures for identifying the ‘correct’ preference functional of individuals, and hence for discriminating between the large number of preference functionals now advocated in the theoretical literature. The paper also asks which of two commonly employed experimental procedures might be the most efficient in this respect. The results show that several of the ‘newer’ preference functionals are difficult to distinguish empirically-at least on the basis of conventional experimental tests-and that the Complete ranking experimental design might be better than the Pairwise Choice design. The conclusion of the paper is that more thought should therefore be given to the question of the experimental design.     

Echelons in Incomplete Relations

An efficient method of value assessment of a set of exchangeable alternatives A = {a ₁,a ₂, ,a _n} is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is transformed into an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation.     

Guy with a Gun - Condemned Man,Rebel, Writer: "War" Prose by Young Authors

Spirit breathes where it pleases. But literature lives where it can—or, rather, where it is allowed to live. Literature's life in thick literary-artistic journals is a difficult one, but no more difficult than the life of any regular person in this era of changes; in other words, the difficulties are natural. In recent years, literature has begun to "live" in publications of an entirely different type: "glossy" journals and newspapers, including dailies. How is its life there, in, for instance, Playboy magazine? Or Cosmopolitan? Or on the newspaper pages, next to the horrors of our everyday life? We asked some very different people from some very different "nonliterary" publications to tell us about it. These people have one thing in common: all of them, directly or indirectly, are helping literature to expand its habitat.     

A Rule For Updating Ambiguous Beliefs

When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on event E happening, do not depend on lotteries received on E ^c, obey axioms which lead to maxmin expected utility representation with multiple priors, and have common induced preferences over lotteries. The paper shows that when all priors give positive probability to an event E, a certain coherence property between conditional and unconditional preferences is satisfied if and only if the set of subjective probability measures considered by the agent given E is obtained by updating all subjective prior probability measures using Bayes rule.     

Weak covering relations

This paper proposes and justifies a natural way to weaken the concept of covering relation defined on a finite tournament. Various weak covering relations, calledk-covering relations, are introduced. To eachk-covering relation corresponds a strong uncovered set containing all nonk-covered outcomes. It is proved that those strong uncovered sets may be empty. Moreover, the set of all tournaments having an empty strong uncovered set is characterized within two rather large classes of tournaments. Finally, we offer a complete study of the cases where the directed graph defined by ak-covering relation coincides with the initial tournament.     

Giving money to strangers: European welfare states and social trust

Jensen C, Svendsen GT. Giving money to strangers: European welfare states and social trust Int J Soc Welfare 2011: 20: 3–9 © 2009 The Author, Journal compilation © 2009 Blackwell Publishing Ltd and the International Journal of Social Welfare. Why would you give money to strangers? That is the fundamental question posed by a new body of research into the relationship between social trust and willingness to accept high taxes and extensive welfare states. The literature argues that generalised trust causes and upholds universal welfare state institutions, an entirely plausible explanation of the Scandinavian social democratic welfare states. However, it cannot explain the presence of very large welfare states in Continental Europe, where the level of generalised trust is much lower than in Scandinavia. The article adds to the existing literature by arguing that the ‘bumblebee’ of conservative welfare states is characterised by particularistic trust and familiaristic welfare institutions, which are functional equivalents to the mechanisms found in Scandinavia. Future research into the trust–welfare state relationship should therefore focus on the trust profile of a country to understand how the welfare state provides its citizens with benefits.     

Finite Alternating-Move Arbitration Schemes and the Equal Area Solution

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72.     

Expectations and Practice in Social Citizenship: Some Insights from an Attitude Survey in a Chinese Society

This paper draws on empirical evidence from an attitude survey in a Chinese society to show that the universal ideals of social citizenship have strong appeal among the Chinese in Hong Kong, even though the latter are conventionally seen as having low expectations in the area of social rights. It is also shown that high expectations of social responsibilities do not imply low expectations of social citizenship. However, this does not mean that cultural context or tradition does not matter. Findings of strong support for the responsibility of parents to care for children, but in a westernized and modern context, suggest that cultural variations in beliefs about social citizenship and practice continue, but framed by an understanding of, and moral commitment to, more universal values of social citizenship.     

Shedding Some (More) Light in Bourdieu's Habitus and Doxa: A Socio-Phenomenological Approach

In this paper, I attempt to shed more light in Bourdieu's habitus and doxa, by drawing on phenomenological and Bourdieusian-based literature, social theory and some findings from sociological research. Despite the fact that there is a vast work concerning the examination of these two concepts, there are still some misunderstandings about them. For that reason, I have tried to draw a clearer picture of habitus, by linking it with phenomenological “being-in-the-world” and describing its elements. As for doxa, I discuss its conceptual relation with habitus and phenomenology's natural attitude. Also, attention is given to some aspects of both habitus and doxa, which have not addressed in detailed fashion yet, but they are nevertheless theoretically useful for empirical qualitative research.