Social welfare and electoral competition in democratic societies

Abstract

With the model of the electoral process described in Section 1, and a social welfare function defined by symmetrically weighting and summing individual utility functions, two factors, in addition to the density of preferences and the form of the weighting function, affect the performance of the electoral process as a mechanism for policy selection. These factors are: (1) the form of the individual loss functions, ∅, (i.e., convexity vs. quasi-convexity), and; (2) the causes of abstentions from voting. If ∅ is strictly convex, a social welfare optimum is achieved except when abstentions are caused by alientation — in which case there is no general solution. If, however, ∅ is quasi-convex, the conditions for achieving a social welfare optimum (presented in Table 2) are more restrictive, requiring at least that w (x) f (x) be unimodal. Finally, if f (x) is a symmetric multimodal density, if ∅ is quasi-convex, and if abstentions are caused by alientation, social welfare optima are achieved only in fortuituous circumstances.