Fuzzy preferences and Arrow-type problems in social choice

There are alternative ways of decomposing a given fuzzy weak preference relation into its antisymmetric and symmetric components. In this paper I have provided support to one among these alternative specifications. It is shown that on this specification the fuzzy analogue of the General Possibility Theorem is valid even when the transitivity restrictions on the individual and the social preference relations are relatively weak. In the special case where the individual preference relations are exact but the social preference relation is permitted to be fuzzy it is possible to distinguish between different degrees of power of the dictator. This power increases with the strength of the transitivity requirement.For comments on an earlier version of the paper I am indebted to an anonymous referee, an anonymous member of the Board of Editors and to participants in the 1991 Annual Conference of the Indian Econometric Society at North Bengal University, India. However, I retain sole responsibility for any error(s) that the paper may contain.     

Egalitarian-equivalence and the Pareto principle for social preferences

The Pareto principle is often in conflict with the equity criteria in construction of social preferences: there exist two allocations x and y such that x Pareto dominates y, but y is an equitable allocation whereas x is not. The efficiency-first principle requires to rank an allocation x higher than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal elements of the social preference relations in the set of feasible allocations. The results are contrasted with those in the case where no-envy is the notion of equity.This paper is a much extended version of a part of Tadenuma (1998). The author is grateful to Marc Fleurbaey, Serge-Chiristophe Kolm, Kotaro Suzumura, and William Thomson for helpful comments on the earlier version of the paper. ‘‘Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan for the 21st Century Center of Excellence Project on the Normative Evaluation and Social Choice of Contemporary Economic Systems is gratefully acknowledged’’.     

Dichotomous preferences and the possibility of Arrovian social choice

Consider an individual whose judgments are always based on a fundamental criterion such as a political ideology or a religious doctrine. In a choice situation, he always prefers any alternative that is compatible with the criterion to any that is not. When individuals are allowed to have preference spaces restricted in this manner, we investigate Arrow-consistent domains. We observe that a diversity of attitudes is essential in order to escape an Arrovian impossibility.This paper received the Kanematsu Fellowship from RIEB, Kobe University in May 2002. We are much indebted to two anonymous referees of this journal, three anonymous referees of the Kanematsu Fellowship, Jun Iritani, William Thomson, and John Weymark for helpful comments. We also thank Takashi Kamihigashi, Tetsuya Kishimoto, Ryo-ichi Nagahisa, Hiroaki Nagatani, Tadashi Sekiguchi, Koji Shimomura, Tomoichi Shinotsuka, Koichi Suga, Makoto Tanaka, Ken Urai, and participants at the Kobe-Osaka Joint Seminar in Mathematical Economics at Osaka University in March 2001, the meeting of the Japanese Economic Association at Hiroshima Syudo University in May 2001, the Far Eastern Meeting of the Econometric Society in Kobe in July 2001, the Seventh Decentralization Conference at Waseda University in October 2001, the Sixth International Meeting of the Society for Social Choice and Welfare at Caltech in July 2002 for valuable suggestions. The first version was written while we were graduate students in Economics at Kobe University.

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Individual, household and gender preferences for social transfers

This paper reports the results of a nationally representative survey that explored willingness to pay extra taxes for increased levels of social transfers in Ireland. Respondents differ in their interpretation of willingness-to-pay questions with respect to the relevant income constraint being the individual’s budget or the individual’s household budget, with an important explanatory variable in this interpretation being the level of financial management integration within the household. Respondents are also shown to take intra-household bargaining considerations into account when stating preferences for specific redistributive policies; a significant gender difference emerges for a specific fiscal policy (child benefit) which alters the intra-household entitlement to income.     

Arrow's theorem for economic environments and effective social preferences

Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper proves the impossibility theorem for the entire allocation space and the classical domain of economic preferences by adding effectiveness to Arrow's hypothesis. Social preference is effective if every nonempty compact set contains at least one socially optimal allocation.Financial support from the Social Sciences and Humanities Research Council (Canada) is gratefully acknowledged. The comments of an anonymous referee were much appreciated. The author assumes responsibility for any errors.     

Wilson's theorem for economic environments and continuous social preferences

Wilson's generalization of Arrow's impossibility theorem has been proved for the realm of private goods and economic preferences by Border and by Bordes and Le Breton. However, their proofs require the exclusion of the zero vector from the commodity space. This paper assumes continuity of social preference to obtain the impossibility theorem for the entire allocation space, even if the society is infinite. A simple corollary reveals that there is some individual who is assigned the zero consumption vector at every social optimum whenever the social welfare function is nonnull and nonimposed, and satisfies Arrow's independence axiom and continuity and transitivity of social preference.Financial support from the Social Sciences and Humanities Research Council is gratefully acknowledged, as are the suggestions of Charles Plott and an anonymous referee. The author assumes responsibility for any errors.     

Interpersonal risk assessment and social preferences: An experimental study

We investigate interpersonal risk assessment, that is how individuals use either their own or their partner’s monetary resources to offset the risk that affects them or their partner. The observed behavior is in line with the predictions of a simple piecewise linear model of social preferences. Overall, individuals opportunistically draw from others’ resources to offset risk; furthermore, they display higher levels of risk aversion when delegated to choose for others rather than when choosing for themselves. However, different social types differ in the assessment of interpersonal risk. Considering our results, we suggest that studies dealing with interpersonal risk assessment should not only focus on risk preferences, but also take into account social preferences.     

Inching toward interdependence: Social work and social policy affecting infants,toddlers and their families

Conclusion Social policy that affects infants, toddlers and their families also affects individual social workers, the arenas in which we practice, and the opportunities for our profession as a whole to work effectively. Since social policy is created and implemented at many levels and in a process that is an ongoing one, social workers at every stage of experience and in any setting can participate. With our twin commitment to the development of the individual and to a society based on interdependence, social workers have much to offer. And there is much to do.The profession of social work has the broad purpose of trying to make it possible that every individual have the most productive life of which he is capable.Charlotte Towle,Common Human Needs, 1945, p.10     

Invariance axioms for preferences: applications to social choice theory

I investigate the role played by the combination of two invariance axioms for preferences in utility theory; namely, those of zero-independence and scale-independence, respectively. I provide a characterization of the preference relations on ${\mathbb{R}^{n}}$ that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on ${\mathbb{R}^{n}}$ . This result is then applied in social choice theory to characterize those social welfare functions that satisfy IIA and PI. Other characterizations involving the usual Pareto concepts are also provided.     

The core of social choice problems with monotone preferences and a feasibility constraint

We consider collective choice with agents possessing strictly monotone, strictly convex and continuous preferences over a compact and convex constraint set contained in ₊^k . If it is non-empty the core will lie on the efficient boundary of the constraint set and any policy not in the core is beaten by some policy on the efficient boundary. It is possible to translate the collective choice problem on this efficient boundary to another social choice problem on a compact and convex subset of ₊^c (c<k) with strictly convex and continuous preferences. In this setting the dimensionality results in Banks (1995) and Saari (1997) apply to the dimensionality of the boundary of the constraint set (which is lower than the dimensionality of the choice space by at least one). If the constraint set is not convex then the translated lower dimensional problem does not necessarily involve strict convexity of preferences but the dimensionality of the problem is still lower. Broadly, the results show that the homogeneity afforded by strict monotonicity of preferences and a compact constraint set makes generic core emptyness slightly less common. One example of the results is that if preferences are strictly monotone and convex on ² then choice on a compact and convex constraint exhibits a version of the median voter theorem.I thank Donald Saari for helpful comments on an earlier version of this paper.     

The vulnerability of four social choice functions to coalitional manipulation of preferences

The vulnerability of a social choice function to coalitional manipulation of preferences is defined as the proportion of voting situations in which the social choice function can be manipulated by a coalition of individuals. In this paper, we provide exact relations giving the vulnerability of four specific social choice functions (plurality rule, anti-plurality rule, plurality with runoff, anti-plurality with runoff) in three-alternative elections. Plurality with runoff appears to be less vulnerable than the other three rules.     

The impact of self-control depletion on social preferences in the ultimatum game

We study the interaction of different motives and decision processes in determining behavior in the ultimatum game. We rely on an ego-depletion manipulation which consumes self-control resources, thereby enhancing the influence of default reactions, or in psychological terms, automatic processes. Experimental results provide evidence that proposers make higher offers under ego depletion. Based on findings from a closely related dictator game study, which shows that depleted dictators give less than non-depleted ones, we discard the possibility that other-regarding concerns are the default mode. Instead, we conclude that depleted proposers offer more because of a strategic ‘fear of rejection’ of low offers, consistent with self-centered monetary concerns. For responders, ego depletion increases the likelihood to accept offers, in line with unconditional monetary concerns being more automatic than affect-influenced reactions to reject unfair offers.     

Inter-group contact and out-group altruism after violence

Altruism among humans is common. It is especially prominent among in-group members. However, we are struck by results from laboratory-in-the-field experiments with out-group members of different ethnic or religious backgrounds. In all instances, the groups were rivals in civil wars. While we find almost no altruistic behavior among groups that were engaged in fighting, out-group altruism emerges with the passage of time. To address the underlying mechanism that might explain this puzzling result, we use a laboratory experiment that sorts between a norms revision explanation and a contact hypothesis explanation. Our findings show that contact with out-group members, in a mutually beneficial task, results in a reversion to prior levels of out-group altruism following conflict. Our findings reinforce the idea that deeply held attitudes toward a stigmatized out-group change following productive interactions with those out-group members. It is clear that hostility between groups need not persist over time.     

Can preferences for catastrophe avoidance reconcile social discounting with intergenerational equity?

A social welfare function treating all generations equally is derived from a set of axioms that allow for preferences for catastrophe avoidance or risk equity. Implications for the case where there is a risk of world extinction are studied. We show that substantial time discounting can arise from the planner’s taste for catastrophe avoidance, even if the probability of the world ending is infinitesimally small. We wish to thank Marc Fleurbaey, Thibault Gajdos, two anonymous referees and an associate editor for many valuable comments.     

A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives

I prove that under each strategy-proof and unanimous social choice correspondence, there is at least one agent who is decisive. Because the result is established on a weak requirement on preferences over sets, the existence of a decisive agent is an underlying feature of most strategy-proof and unanimous social choice correspondences. Moreover, I consider a restriction on the space of preferences over alternatives. I prove that circular sets of preferences over alternatives are sufficient for the existence of a decisive agent.