On enforcing socially best alternatives of binary group decision rules

We consider a large class of group decision rules based on pairwise comparisons. We show that if a socially best alternative is defined by the group decision rule, then one can devise a game form such that at least one such alternative can be realized under the appropriate notion of equilibrium.We are extremely grateful to G. Chichilinsky, P. Coughlin and an anonymous referee for helpful comments on earlier drafts of this paper     

On some suggestions for having non-binary social choice functions

The various paradoxes of social choice uncovered by Arrow [1], Sen [10] and others have led some writers to question the basic assumption of a binary social choice function underlying most of these paradoxes. Schwartz [8], for example, proves an important theorem which may be considered to be a generalization of the famous paradox of Arrow, and then lays the blame for this paradox on the assumption of a binary social choice function. He then proceeds to define a type of choice functions which, like binary choice functions, define the best elements in sets of more than two alternatives on the basis of binary comparisons, but which, as he claims, have an advantage over binary choice functions, in so far as they always ensure the existence of best elements for sets of more than two alternatives irrespective of the results of binary comparisons. The purpose of this paper is to show that even a considerable weakening of the assumption of a binary social choice function does not go very far towards solving some of the paradoxes under consideration, and that if replacing the requirement of a binary social choice function by a Schwartz type social choice function solves these paradoxes, it does so only by violating the universally acceptable value judgment that in choosing from a set of alternatives, society should never choose an alternative which is Pareto inoptimal in that set (i.e., the socially best alternatives in a set should always be Pareto optimal). This argument is substantiated with the help of an extended version of Sen's [10] paradox of a Paretian liberal, and thus a by-product of our analysis is a generalization of the theorem of Sen [10]. The argument itself, however, is more general and applies also to the impossibility result proved by Schwartz [8].We are extremely grateful to Amartya Sen for his helpful comments.

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Binary data,hierarchy of attributes,and multidimensional deprivation

Empirical estimation of multidimensional deprivation measures has gained momentum in the last few years. Several existing measures assume that deprivation dimensions are cardinally measurable, when, in many instances, such data is not always available. In this paper, we propose a class of deprivation measures when the only information available is whether an individual is deprived in an attribute or not. The framework is then extended to a setting in which the multiple dimensions are grouped as basic attributes that are of fundamental importance for an individual’s quality of life and non-basic attributes which are at a much lower level of importance. Empirical illustrations of the proposed measures are provided based on the estimation of multidimensional deprivation among children in Ethiopia, India, Peru and Vietnam.     

On Preference and Freedom

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.