Preference Relativity, Ambiguity and Social Welfare Evaluation

In the real world many social and economic decisions have to be made with imperfect information and uncertainty. In the past two decades, economists and mathematicians have devoted a great deal of time and effort into the study of ambiguity and much progress has been made in modeling ambiguity. Decision models under ambiguity have been widely used in portfolio selection, asset pricing, and risk measurement. However, few studies have been done on linking ambiguity to the social welfare function, although social welfare evaluation also faces a scarcity of information and ambiguity of income distribution. In this paper I set up a framework with policy relevance for social welfare evaluation, with the help of a model that is developed to handle income distribution ambiguity. Under some reasonable conditions the relation of income distribution to social preference is identified and the social welfare function is clearly expressed. It is shown that the social welfare functions derived from the framework are robust in form and invariant up to a monotonous increasing transformation. The framework is also flexible enough to contain many thoughtful ideas about the social welfare function.