On Kolm’s Use of Epistemic Counterfactuals in Social Choice Theory

In a series of writings, Serge Kolm has examined the conceptual foundations of Arrovian social choice theory (see Kolm, 1993, 1994, 1995, 1996, 1997). In its choice-theoretic formulation, an Arrovian social choice correspondence specifies the socially best alternatives from each admissible feasible set of alternatives as a function of the individual preferences over the universal set of alternatives. An issue that needs to be addressed when constructing a social choice correspondence is: For what feasible sets of alternatives and for what preference profiles are social decisions required? The rationale for the choice of this domain is one of the issues that Kolm discusses at some length. When considering resource allocation problems, social alternatives are meant to be complete descriptions of all the features of a social state relevant to choice, including future allocations of resources. It would then seem to follow that there is only one choice situation for which a social choice is required, the situation characterized by the actual feasible set and the actual preference profile. However, Arrow’s famous impossibility theorem (see Arrow 1951, 1963) requires the domain of a social choice correspondence to be reasonably rich. Indeed, many of Arrow’s axioms are vacuous if there is only one feasible set and one preference profile. Arrow (1951, p.24) appeals to uncertainty about what the actual choice environment is at the time social decisions are being made to justify having a non-singleton domain. Kolm (1996), however, believes that it is difficult to reconcile this rationale for the choice of domain with the adoption of the axioms Arrow proposes for relating choices in different choice environments.