عدالت-بهره وری تجارت کردن در یک روش هندسی به انتخاب کمیته

The trade-off between equity and efficiency is analyzed in a geometric framework for the problem of committee selection, which has recently attracted interest in the social choice literature. It is shown that this trade-off can be maximal in the precise sense of the antipodality of the outcomes corresponding to the rules implementing the two normative principles. Following an approach in location theory, the minimization of the convex combination of the two criteria is presented as a compromise solution.

The equity-efficiency trade-off is one of the major puzzles in the ethical evaluation of economic outcomes and the diverse mechanisms—such as markets or voting rules—supporting those outcomes. This trade-off is also related to the conflict between the two most prominent welfare criteria in welfare economics and social choice theory, Rawlsian egalitarianism and utilitarianism à la Harsanyi.1 Following the seminal work of Saari (1995), a geometric approach has been introduced into social choice theory. In particular such an approach provides a framework for the comparison of voting rules with the help of the distance between their respective outcomes (for such comparisons of voting rules see Eckert & Klamler, 2008 and Klamler, 2004, and Ratliff (2002)). A geometric approach is particularly natural if the preferences can be assumed to be induced by the topology of the space of alternatives. In this case, complete preferences can be derived from exclusive information about a voter's most preferred (“ideal”) alternative. Typically this is done in spatial voting, where Euclidean preferences are obtained by identifying alternatives with a point in the d-dimensional Euclidean space ℜd and ranking them according to their distance to an individual's ideal point. Similar issues being analyzed in location theory, where costs are derived from distances (see Nickel and Puerto (2005) and Daskin (1995)), we will adapt an approach from location theory to distance-based voting. As an application, we use the problem of committee selection which has recently been analyzed in a distance-based framework. In Brams et al. (2007) a committee selection rule is a function that assigns to each profile of voters' ideal committees a committee that minimizes a distance-based objective function. In particular they have introduced a minimax procedure and compared it with the application of majority voting to the election of committee members. Their finding, that these two rules can lead to antipodal results is all the more disturbing as these rules can be considered to incorporate the principles of equity and of efficiency respectively. We extend their approach and suggest the use of a classical solution from location theory to deal with this problem.

A geometric approach to social choice problems allows to operationalize principles of justice through distance-based objective functions and to analyze their trade-off in a common framework. If the trade-off between efficiency and equity is measured by the distance between the outcomes corresponding to the different principles, their antipodality indicates that this trade-off can be maximal in certain situations. This suggests to look for a compromise based on the convex combination of the corresponding distance-based objective functions, as done in location theory. Given the difference between the framework of social choice and location theory, further studies on the properties of such compromises and an analysis of such rules are required.