Optimal Social Design: Estimating a Social Welfare Function from Questionnaire Data

A social design x evokes a response y from a set of individuals. The value of the design is expressed in terms of a social welfare function which is derived from Arrow’s formulation of social choice. Making certain simplifying assumptions the social welfare function can be expressed in terms of individuals’ ideal designs. A method for estimating the social welfare function from quite limited empirical evidence is developed. The method is applied to an educational case study. There was considerable variation in individuals’ ideal designs. The components of the social welfare were estimated: the welfare ideal, the population sensitivity, the population variation, the deviation from the ideal and the welfare ceiling. Methodological problems are discussed.