Public goods and Arrovian social choice (Q1196707)

Consider a social welfare function (SWF) generating continuous and transitive social preferences over the space of allocations when there are private and public goods and when individual preferences have the classical economic properties. According to the analysis of \textit{G. Bordes} and \textit{M. Le Breton} [ibid. 7, No. 1,1-17 (1990; Zbl 0696.90003)] dictatorship results if social choice is required to satisfy the Pareto criterion (P) and Arrow's independence axiom (I). In this paper it is shown that little is gained by dropping P and by retaining I. Imposing I suffices to make the SWF be either constant or dictatorial or inversely dictatorial. ``(An inversely dictatorial rule selects a particular individual, the inverse dictator, and defines social preference by turning his preference relation upside down.) A constant SWF is completely unresponsive to individual preferences. It maps all profiles into the same social ordering. Therefore the independence axiom implies that the SWF has either zero efficiency content (it is constant) or zero equity content (it is dictatorial or inversely dictatorial).'' (quoted from the introduction).