When Choosing the Social Welfare Function Really Matters: A Quantitative Analysis

Abstract

This paper proposes a quantitative approach to study two methodological problems arising when alternative legal rules are compared: a) aggregating individual into social preferences and b) choosing the object of maximization. We consider a redistribution policy that reduces inequality but diminishes total wealth and we specify a set of social welfare functions combining different preferences aggregation methods and maximands. For each social welfare function, we calculate its “price of equity”, defined as the maximum fraction of total wealth that a society is willing to sacrifice in order to implement the redistribution. Comparing the prices for equity across different social welfare function specifications, we identify systematic relationships and we rank them according to the efficiency-equity orientation. Results show that social welfare functions characterized by aggregation methods conventionally considered equity-oriented may reject redistribution policies that are evaluated as welfare-improving by social welfare functions using efficiency-oriented aggregation methods. Similarly, social welfare functions considered equity-oriented because using utility as object of maximization may reject distributive policies that are evaluated as welfare-improving by social welfare functions using wealth as maximand.We argue that a quantitative approach, by expounding the trade-off between equity and efficiency connected to different social welfare functions, may prove useful for rule-makers engaging in the choice of a normative criterion for the evaluation of social welfare.