Public policy recommendation by optimizing an unknown social welfare function

A classical utilitarian perspective on public decision-making is that the public should choose an alternative that maximizes some function over the utilities of individuals, called a social welfare function. If the utility function for each decision-maker is cardinal and comparable with other decision-makers, then there are many valid social welfare functions. We examine the problem of finding a social welfare function that implicitly best fits society’s values, where we assume that a group's decision problem is the same as maximizing an unknown social welfare function implicitly held by the group. While there is a wealth of literature on possible social welfare functional forms based on different assumptions about the preferences of individuals, we propose a new empirical approach that approximates a group's social welfare function based on both individual preferences and group voting behavior. We test the approach's ability to promote compromise on climate-related energy policy among Pittsburgh residents who are plan to vote in the 2020 Democratic Primary. Our three-stage research design first elicits individual preferences, then uses a mean-variance algorithm to approximate a welfare function that fits group voting behavior, then finally makes a recommendation for the group based on that function. In addition to testing whether a group's social welfare function can be learned from individual choices, this study provides a roadmap for solving group recommendation problems more broadly.