Group for Research in Decision Analysis

A mixed Bentham-Rawls criterion for intergenerational equity

Ngo Van Long

The practical implications of ranking time-paths of utilities on the sole basis of comparing the values of the associated integrals of discounted utilities can be quite drastic, yielding consequences that offend our sense of justice. New alternative social welfare criteria should be considered.

A welfare criterion with an extreme form of egalitarianism has been proposed: the maximin criterion. Another type of reaction to discounted utilitarianism is to moderate its effects by adding to the social welfare function a second term that takes seriously the welfare of the generations that live in the far distant future. Chichilnisky proposes a social welfare function that has two desirable properties: (i) non-dictorship of the present, and (ii) non-dictatorship of the future. However, in many economic models of interest, there exists no time path that is optimal under the Chichilnisky criterion.

In this paper, we introduce a third desideratum: "non-dictatorship of the least advantaged," and we propose a new welfare criterion which we argue to be morally compelling. Our criterion is a weighted average of two terms. The first term is the conventional sum of discounted utilities, and the second term is the utility level of the least advantaged generation. We call this new criterion the Mixed Bentham-Rawls criterion (MBR). We present arguments that justify this criterion and develop a set of necessary conditions to characterize growth paths that satisfy the MBR criterion. We show that in some models with familiar dynamic specifications, an optimal path under MBR exists and displays appealing characteristics. Some numerical calibrations are also provided for sensitivity analysis.