discounting while treating generations equally


Geir Bjarne Asheim

date de sortie



Économie et finance

There are about 7 billion people currently alive. About 100 billion people have ever lived. Hence, the ratio of people who have ever lived in the past to people living today is about 14 to 1. With 500 million years left of the earth as acceptable habitat for humans, population being stable at 10 billion with an average length of life equal to 71 years, the ratio of people who will potentially live in the future to people living now is about 10 million to 1. These observations indicate that there are many people that may potentially live in the future.

There are clear conflicts of interest between generations, in the sense that the wellbeing of future generation may be undermined unless we take costly action today. Examples of such costly current action with future benefits include:

- abating greenhouse gas emissions, which mitigates future climate change;

- preserving biodiversity, which widens options for future generations;

- exploiting soil and water resources with caution, which increases the potential for future food production;

- using antibiotics with care, which reduces future health problems.


If we adopt a purely consequentialist position (by abstracting from entitlements and procedural issues) and seek to evaluate such current action from an impartial perspective, what criteria should be used? Does equal treatment of generations rule out that future generations’ wellbeing are discounted? Such questions can be posed within the axiomatically based field of intertemporal social choice1.


Equal treatment is often—e.g., in the debate following the publication of the Stern Review Report on the Economics of Climate Change—associated with utilitarianism, where a cardinal index (utility) of wellbeing is summed over all generations. However, if we model the many potential people in the future by assuming that there infinitely many generations, then this criterion assigns zero relative weight to the present generation’s interest; in fact, to the interest of any finite number of generations. It leads to the unappealing prescription that the present generation should endure heavy sacrifices even if it contributes to only a tiny gain for all future generations.


The criterion of maximizing the wellbeing of the worst-off generation (maximin) also treats generations equally, but assigns zero relative weight to all generations but the worst-off. It leads to the unappealing prescription that the present generations should not do an even negligible sacrifice for the benefit of better off future generations.


This dilemma—that the ethical commendable requirement of equal treatment seems to lead to unappealing prescription when applied in actual criteria of intergenerational equity—has been a main motivation for my own research during the last few years, leading to the criteria of sustainable discounted utilitarianism (SDU) and rank-discounted utilitarianism (RDU)2.


According to both these criteria, discounting future utility is OK as long as the future is better off than the present, thereby trading-off current sacrifice and future gain. Hence, in this case, future’s higher wellbeing is discounted for two reasons: (i) at a higher level, its wellbeing contributes less to utility, and (ii) being better off, its utility is assigned less weight. Hence, if wellbeing is perfectly correlated with time, these criteria work as the ordinary time-discounted utilitarian criterion economists usually promote. The important difference is that, in the criteria of SDU and RDU, the future is discounted because priority is given to the worse off earlier generations.


However, if the present is better off than the future, then priority shifts to the future. Hence, in this case, future utility is not discounted, implying that zero relative weight is assigned to present wellbeing. As shown formally in the case of RDU, such rank-dependent utility discounting is compatible with equal treatment of generations. Moreover, both SDU and RDU yield seemingly appealing consequences in economic models (also where natural resources are important) and provides a resolution of the above mentioned dilemma.


A first effort in combining such recent advances within the field of intertemporal social choice with empirical evaluation of climate-change policies has already been done3. However, applying criteria for intergenerational equity to a distributional problem like climate change requires that the criteria explicitly take into account that population size changes over time and that the effects of present policy have uncertain future consequences. The main research question during my stay at Paris IAS is to consider how to extend analyses of intergenerational equity, in particular RDU, to variable population and uncertainty.


It appears relatively straightforward to extend criteria to the case where population size changes exogenously over time. RDU can be generalized to such a situation, by letting individuals rather than generations be the object of analysis.


It is more challenging to analyze a situation where population changes endogenously, e.g., as a consequence of climate change. Climate change may prevent the existence of a great many people who would otherwise have existed. One cannot simply ignore the loss of such potential lives. Rather, it seems natural to assume that there exists a critical level of well-being which, if experienced by an added individual without changing the well-being levels of the existing population, leads to an alternative which is as good as the original. This raises the question of how to merge such critical-level population ethics with RDU.


To handle uncertainty, one can in principle think of two polar approaches. An ex post approach is first to value each realization and then assign probability weights to the different realizations. An ex ante approach is first to determine a certainty equivalent for each individual/generation and then value the stream of certainty equivalents. When applying SDU and RDU to uncertainty, the choice between these approaches matters for policy evaluation: in the context of climate change, the possibility for catastrophic consequences is assigned more weight if the ex post approach is adopted. This raises the problem of how to determine what axiomatic basis exists for each of these positions and thereby shed light on which one fits more naturally with SDU and RDU.

Finally, the issues of population and uncertainty might be interrelated. In particular, the Stern Review argued that the probability that the human race will be extinguished is the primary justification for utility discounting. This raises the question of how SDU and RDU can take into account this concern.


1. Geir B. Asheim, « Intergenerational equity », Annual Review of Economics 2, 2010, p. 197–222.
2. Geir B. Asheim & Tapan Mitra « Sustainability and discounted utilitarianism in models of economic growth », Mathematical Social Sciences 59, 2010, p. 148–169; Geir B. Asheim, Tapan Mitra & Bertil Tungodden, « Sustainable recursive social welfare functions », Economic Theory 49, 2012, p. 267–292; Geir B. Asheim & Stéphane Zuber, « Justifying social discounting: the rank-discounted utilitarian approach », Journal of Economic Theory, 147, 2012, p. 1572–1601.
3. Geir B. Asheim & Simon Dietz, « Climate policy under sustainable discounted utilitarianism », Journal of Environmental Economics and Management 63, 2012, p. 321–335.

Licencié en mathématiques et en économie de l’université de Bergen, Norvège, et docteur en économie de l’université de Californie, à Santa Barbara, il est également professeur d’économie à l’université d’Oslo depuis 1994 et a occupé des postes de professeur invité dans de nombreuses universités américaines incluant Cornell, Harvard, Northwestern et Stanford. Ses principaux domaines de recherche sont la théorie des jeux et l’équité intergénérationnelle, au sujet de laquelle il publie depuis plus de vingt-cinq ans.


01/04/2012 - 31/08/2012


Économie et finance
16/01/2012 - 15/06/2012