The Limit of Discounted Utilitarianism

Jonsson, Adam

doi:10.2139/ssrn.2305317

Cited by 11 publications

(15 citation statements)

References 30 publications

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“…. ) are comparable under the strong Pareto principle and stationarity, then the former stream is strictly preferred to the latter, thereby exhibiting a weak form of impatience (see also Jonsson and Voorneveld 2015, Proposition 1, not included in the published version Jonsson and Voorneveld 2018). In the present paper we show through our Proposition 2 how stationarity leads to impatience also in Koopmans' (1960) stronger sense even under conditions that would otherwise be consistent with anonymity.…”

Section: Introductionsupporting

confidence: 55%

How stationarity contradicts intergenerational equity

2020

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We show how the condition of stationarity may contradict intergenerational equity. By formalizing the intuition that less sensitivity remains for the continuation of the stream if sensitivity for the interests of the present is combined with stationarity, we point out conflicts (a) between stationarity and the requirement of not letting the present be dictatorial, and (b) between stationarity and equal treatment of generations. We use the results to interpret the non-stationarity of the Chichilnisky and Rank-discounted utilitarian social welfare functions. Non-stationarity combined with time invariance leads to time inconsistency. We illustrate how such non-stationary social welfare functions can be applied in the Ramsey model if time invariance is imposed.

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Section: Introductionsupporting

confidence: 55%

How stationarity contradicts intergenerational equity

2020

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“…Might discounting the future lead us to an arbitrarily bad absorbing state? Utility theory has considered several qualities two utilitiy streams, {r t } t≥1 , {r ′ t } t≥1 , may posses in forming binary relations used as orderings on value functions (utility streams) [8], including that of anonymity which essentially states that two utility streams are equal under an ordering if they are permutations of one another. Hence, anonymity can only be realized in the RL setting if γ = 1.…”

Section: Discussion and Related Workmentioning

confidence: 99%

Issues concerning realizability of Blackwell optimal policies in reinforcement learning

Denis

2019

Preprint

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N -discount optimality was introduced as a hierarchical form of policy-and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy [17,3]. We formalize notions of myopic discount factors, value functions and policies in terms of Blackwell optimality in MDPs, and we provide a novel concept of regret, called Blackwell regret, which measures the regret compared to a Blackwell optimal policy. Our main analysis focuses on long horizon MDPs with sparse rewards. We show that selecting the discount factor under which zero Blackwell regret can be achieved becomes arbitrarily hard. Moreover, even with oracle knowledge of such a discount factor that can realize a Blackwell regret-free value function, an ǫ-Blackwell optimal value function may not even be gain optimal. Difficulties associated with this class of problems is discussed, and the notion of a policy gap is defined as the difference in expected return between a given policy and any other policy that differs at that state; we prove certain properties related to this gap. Finally, we provide experimental results that further support our theoretical results. 1

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“…Given this, it is unsurprising that it is satisfied by every plausible stronger proposal so far proposed (e.g. Vallentyne and Kagan, 1997;Arntzenius, 2014;Jonsson and Voorneveld, 2018;Wilkinson, 2021;Bostrom, 2011, pp. 27-30).…”

Section: Separability Ofmentioning

confidence: 93%

Infinite Aggregation and Risk

Wilkinson

2022

Australasian Journal of Philosophy

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For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds-without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative-one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds.

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The Limit of Discounted Utilitarianism

Cited by 11 publications

References 30 publications

How stationarity contradicts intergenerational equity

How stationarity contradicts intergenerational equity

Issues concerning realizability of Blackwell optimal policies in reinforcement learning

Infinite Aggregation and Risk

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