Uncertainty in discount rate and aggregation of time preferences

This paper assumes that the individual discount rate is not deterministic but random, and investigates how to aggregate a finite number of individual probability distributions for the discount rate. We take an ex post approach by considering the individuals’ choice behavior after their random discount rates realize. Specifically, we propose a unanimity condition that if every individual in society adopts one discount rate with a higher probability than another, then so should society. We prove that when the probability distributions are countably additive, this condition implies the linear aggregation rule. We then demonstrate by way of examples that this is not true if the probability distributions are finitely additive. Finally, we show that one alternative way to recover the linear aggregation rule is to impose strong continuity on the distributions.