Abstract
Ramsey famously condemned discounting “future enjoyments” as “ethically indefensible”. Suppes enunciated an equity criterion which, when social choice is utilitarian, implies giving equal weight to all individuals’ utilities. By contrast, Arrow (Contemporary economic issues. International Economic Association Series. Palgrave Macmillan, London, 1999a; Discounting and Intergenerational Effects, Resources for the Future Press, Washington DC, 1999b) accepted, perhaps reluctantly, what he called Koopmans’ (Econometrica 28(2):287–309, 1960) “strong argument” implying that no equitable preference ordering exists for a sufficiently unrestricted domain of infinite utility streams. Here we derive an equitable utilitarian objective for a finite population based on a version of the Vickrey–Harsanyi original position, where there is an equal probability of becoming each person. For a potentially infinite population facing an exogenous stochastic process of extinction, an equitable extinction biased original position requires equal conditional probabilities, given that the individual’s generation survives the extinction process. Such a position is well-defined if and only if survival probabilities decline fast enough for the expected total number of individuals who can ever live to be finite. Then, provided that each individual’s utility is bounded both above and below, maximizing expected “extinction discounted” total utility—as advocated, inter alia, by the Stern Review on climate change—provides a coherent and dynamically consistent equitable objective, even when the population size of each generation can be chosen.
Highlights
1.1 The discounting issue: weighting future generationsThe question of whether and how to discount the welfare of future generations has played a critical role in discussing the ethical and economic foundations of longrun policy analysis
This, is precisely the form that Vickrey (1945, 1960) and Harsanyi (1953, 1955, 1977, 1978, 1979) advocated, taking the view that ethical decisions are those that would be made by an impartial benefactor who, by definition, acts as if facing an original position in which there is an equal probability of becoming any of the n individuals i ∈ I
With a potential infinite set of individuals as well as infinite time, we are confronted with what Arrow (1999a, b) called the “strong argument” for discounting the welfare of future generations
Summary
The question of whether and how to discount the welfare of future generations has played a critical role in discussing the ethical and economic foundations of longrun policy analysis. This is especially true in the case of climate change which, if managed badly enough, could even accelerate the possibility of human extinction. It seems quite likely that carefully and attentively reading the Stern Review led KA to have some doubts about his own earlier articles.2 This helps explain why he appeared so keen to make discounting the subject of one-on-one discussions with one of us (PH) over at at least two lunches at Stanford during the approximate period 2014–2015.3 It seems quite likely that carefully and attentively reading the Stern Review led KA to have some doubts about his own earlier articles. This helps explain why he appeared so keen to make discounting the subject of one-on-one discussions with one of us (PH) over at at least two lunches at Stanford during the approximate period 2014–2015.3
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