Category-theoretic basis for social decision-making theory

Abstract

The paper develops a basis for social welfare functions using mathematical general systems theory. Although research on social welfare functions has a long history, most of it has tried to devise a new condition for social welfare functions. This paper, on the contrary, views social welfare functions from a different angle, i.e. it applies to social decision-making a unified framework which the authors originally proposed for decision principles of decision-making under uncertainty or of multiple-objective decision-making. The framework claims basically that a ‘rational” decision principle should satisfy Pareto consistency and the similarity condition. Since the similarity condition requires recognition of the structural similarity explicitly among the social profiles, it naturally leads to a category-theoretic formulation of a social welfare function. Basic properties of social welfare functions are first represented in categorical terms, and then the validity of the framework is demonstrated by discussing Arrow's ‘impossible theorem” as well as Sen's ‘liberalism condition” in it. Furthermore, this categorical treatment reveals isomorphy among the ‘rational” decision principles of decision-making under uncertainty, of decision-making with multiple objectives and of social decision-making.