Impossibility results in the axiomatic theory of intertemporal choice

Abstract

We have shown formally that for infinite generation, transitive, intertemporal choice procedures the familiar conditions of Pareto optimality and independence together with the equity condition of stationarity are incompatible unless one is willing to accept a dictatorship. As in the case of Arrow's impossibility theorem, the result is primarily conceptual rather than practical. Real world decisions are seldom made by a pre-specified rule that is broad enough to deal with a full domain of individual or generational preference profiles. Nevertheless, impossibility results give us important clues about inherent and surprising limitations in institutions we often accept unquestioningly. The appearance of stationarity, introduced in [2] and proposed as a social choice condition in [1], leads to broader and more practical questions involving discount rates. If we accept the full intertemporal choice model as presented, then we are led to question the validity of any debate about ‘fair’ discount rates. Indeed, no discount rate regardless of how close it may be to unity can be fair under the assumptions we have used. Such discounting implies stationarity and is tantamount to giving dictatorial power to the first generation. Since discount rates are in practice applied in much more specialized and varied ways, this criticism of discounting must be tempered somewhat. The results do suggest, however, that discounting should be employed discriminately and with caution. The dictatorship result of Arrow's theorem depends on the assumption that the social choice function is transitive. If transitivity is weakened to quasitransitivity or acyclicity, then one obtains, respectively, an oligarchy or a collegial polity (see [5] and [6]). It is not clear to what extent our results carry over to these situations, though it seems reasonable to conjecture that, in the quasitransitive case, the oligarchy must consist of consecutive initial segments of generations. In the acyclic case one would likewise expect the present generation to belong to the collegium (the intersection of all decisive sets) and thus to have, at least in the monotonic case, a power of veto.