Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure (...) outcomes. The paper proposes an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann :199–205, 1963, p. 201). (shrink)

Recent evidence on intertemporal choice suggests that decision-makers may exhibit both increasing and decreasing impatience simultaneously, called inverse-S discounting. This paper introduces trichotomic discounted utility to model inverse-S discounting. Under trichotomic discounted utility the decision-maker distinguishes between short-term delays, medium-term delays, and long-term delays. Exponential discounting holds within each category, but not necessarily across each category. We provide preference foundations for trichotomic discounted utility in the timed outcomes framework and in the consumption streams framework. (...) The key axiom is a weakening of the time consistency axiom that allows for both increasing and decreasing impatience. We also consider a weak, local version of time consistency, and show that this plausible condition is satisfied only by discount functions with exponential “pieces”. (shrink)

Classical utilitarianism is very demanding and entails some counter-intuitive implications in moral dilemmas such as the trolley problem in deontological ethics and the repugnant conclusion in population ethics. This article presents how one specific modification of utilitarianism can avoid these counter-intuitive implications. In this modified utilitarian theory, called ‘discounted’ or ‘mild’ utilitarianism, people have a right to discount the utilities of others, under the condition that people whose utility is discounted cannot validly complain against such discounting. A (...) complaint made by a utility discounted person is not valid if either the existence of the discounting people in that option is in a specific sense necessary or the existence of the discounted person is in a sense not necessary. According to mild utilitarianism, we should choose the option that maximizes the total validly discounted or complaint-free discounted utility, i e. the sum of everyone’s utility minus the complaint-free discounts. As there are two conditions that make a complaint invalid, this right to discount can be translated into two versions: the right to bodily autonomy and the right to procreation autonomy. The former right relates to the mere means principle in deontological ethics, the latter right is useful in avoiding the repugnant conclusion problem in population ethics. The possibility of democratically imposing an upper bound on the permissible amount of discounting is discussed. (shrink)

Utility discounting in intertemporal economic modelling has been viewed as problematic, both for descriptive and normative reasons. However, positive utility discount rates can be defended normatively; in particular, it is rational for future utility to be discounted to take into account model-independent outcomes when decision-making under risk. The resultant values will tend to be smaller than descriptive rates under most probability assignments. This also allows us to address some objections that intertemporal considerations will be overdemanding. A (...) principle for utility discount rates is suggested which is rooted in probability discounting. Utility discounting is defended against objections from Parfit (1984) and Broome (2005); Broome (2012). A sample utility discount rate is estimated. [Open access]. (shrink)

We consider a situation where an individual is facing an uncertain situation, but may costly alter his knowledge of the uncertainties. We study in this context how risk aversion may modify the individual search behavior. We consider a one-armed bandit problem (where one arm is safe and the other is risky) and study how the agent risk aversion can change the sequence of arms selected. The main result is that when the utility function is more concave, the agent has (...) more chances to select the safe arm. We also discuss how search is affected by risk aversion. (shrink)

This paper is about time preferences, the phenomenon that the very same things are usually considered the less valuable the farther in the future they are obtained. The utilities of those things are discounted at a certain rate. The paper presents a novel normative argument for exponential discount rates, whatever their empirical adequacy. It proposes to take indexical utility seriously, i.e. utilities referring to indexical propositions (that speak of ‘I’, ‘now’, etc.) as opposed to non-indexical propositions. Economic focus (...) is only on the latter, while the former are neglected. The potential ignorance of when is now generates a difference between indexical and non-indexical utility that can be exploited for a novel argument in favour of exponential discount rates. (shrink)

We consider a situation where an individual is facing an uncertain situation, but may costly alter his knowledge of the uncertainties. We study in this context how risk aversion may modify the individual search behavior. We consider a one-armed bandit problem (where one arm is safe and the other is risky) and study how the agent risk aversion can change the sequence of arms selected. The main result is that when the utility function is more concave, the agent has (...) more chances to select the safe arm. We also discuss how search is affected by risk aversion. (shrink)

This paper formulates and axiomatizes utility models for denumerable time streams that make no commitment in regard to discounting future outcomes. The models address decision under certainty and decision under risk. Independence assumptions in both contexts lead to additive or multiplicative utilities over time periods that allow unambiguous comparisons of the relative importance of different periods. The models accommodate all patterns of future valuation. This discount-neutral feature is attained by restricting preference comparisons to outcome streams or probability distributions on (...) outcome streams that differ in at most a finite number of periods. (shrink)

We present a new axiomatization of the classical discounted expected utility model, which is primarily used as a decision model for consumption streams under risk. This new axiomatization characterizes discounted expected utility as a model that satisfies natural extensions of standard axioms as in the one-period case and two additional axioms. The first axiom is a weak form of time separability. It only requires that the choice between certain constant consumption streams and lotteries should be made (...) by just taking into account the time periods where the consumption is different. The second axiom, the time–probability equivalence, requires that risk and time preferences basically work in the same way. Moreover, we prove that preferences satisfying the natural extensions of the standard axioms as well as the first axiom can be represented in a simple form relying on three functions linked to the risk or time preferences in simple situations. Finally, we illustrate that several examples that are not fully time separable satisfy all our axioms except for the time–probability equivalence. (shrink)

The desirable gambles framework offers the most comprehensive foundations for the theory of lower pre- visions, which in turn affords the most general ac- count of imprecise probabilities. Nevertheless, for all its generality, the theory of lower previsions rests on the notion of linear utility. This commitment to linearity is clearest in the coherence axioms for sets of desirable gambles. This paper considers two routes to relaxing this commitment. The first preserves the additive structure of the desirable gambles framework (...) and the machinery for coherent inference but detaches the interpretation of desirability from the multiplicative scale invariance axiom. The second strays from the additive combination axiom to accommodate repeated gambles that return rewards by a non-stationary processes that is not necessarily additive. Unlike the first approach, which is a conservative amendment to the desirable gambles framework, the second is a rad- ical departure. Yet, common to both is a method for describing rewards called discounted utility. (shrink)

Exponential discounted utility theory provides the normative standard for future discounting as it is employed throughout the social sciences. Tracing the justification for this standard through economics, philosophy and psychology, I’ll make what I believe is the best case one can for it, showing how a non-arbitrariness assumption and a dominance argument together imply that discounting ought to be exponential. Ultimately, however, I don’t find the case compelling, as I believe it is deeply flawed. Non-exponential temporal discounting is (...) often rational–indeed, the paragon of rationality. If this is correct, it’s an important point when considering policy interventions. Instead of trying to “fix” non-exponetial discounting because it is irrational and associated with negative life outcomes, we might instead focus attention on why the conditions obtain that make such discounting rational. (shrink)

When assessing the cost effectiveness of health care programmes, health economists typically presume that distant events should be given less weight than present events. This article examines the moral reasonableness of arguments advanced for positive discounting in cost-effectiveness analysis both from an intergenerational and an intrapersonal perspective and assesses if arguments are equally applicable to health and monetary outcomes. The article concludes that behavioral effects related to time preferences give little or no reason for why society at large should favour (...) the present over the future when making intergenerational choices regarding health. The strongest argument for discounting stems from the combined argument of diminishing marginal utility in the presence of growth. However, this hinges on the assumption of actual growth in the relevant good. Moreover, current modern democracy may be insufficiently sensitive to the concerns of future generations. The second part of the article categorises preference failures (which justify paternalistic responses) into two distinct groups, myopic and acratic. The existence of these types of preference failures makes elicited time preferences of little normative relevance when making decisions regarding the social discount rate, even in an intrapersonal context. As with intergenerational discounting, the combined arguments of growth and diminishing marginal utility offer the strongest arguments for discounting in the intrapersonal context. However, there is no prima facie reason to assume that this argument should apply equally to health and monetary values. To be sure, selecting an approach towards discounting health is a complex matter. However, the life-or-death implications of any approach require that the discussion not be downplayed to merely a technical matter for economists to settle. (shrink)

This paper challenges the conventional wisdom dominating the social sciences and philosophy regarding temporal discounting, the practice of discounting the value of future utility when making decisions. Although there are sharp disagreements about temporal discounting, a kind of standard model has arisen, one that begins with a normative standard about how we should make intertemporal comparisons of utility. This standard demands that in so far as one is rational one discounts utilities at future times with an exponential discount (...) function. Tracing the justification for this standard through economics, philosophy and psychology, I’ll make what I believe is the best case one can for it, showing how a non-arbitrariness assumption and a dominance argument together imply that discounting ought to be exponential. Ultimately, however, I don’t find the case compelling. Non-exponential temporal discounting is often rational. If this is correct, Instead of trying to ‘fix’ non-exponential discounting because it is irrational and associated with negative life outcomes, we might instead focus attention on why the conditions obtain that make such discounting rational. (shrink)

For decisions whose consequences accrue over time, there are several possible techniques to compute total utility. One is to discount utilities of future consequences at some appropriate rate. The second is to discount per-period certainty equivalents. And the third is to compute net present values (NPVs) of various possible streams and to then apply the utility function to these net present values. We find that the best approach is to first compute NPVs of various possible income streams and (...) then take the utility of such NPVs. We show the drawbacks of other alternative models of evaluating income streams. The article discusses the advantages of the power and logarithmic forms in the modeling of time preference. These are the only forms for which utility of income and utility of consumption are strategically equivalent. Further, these forms permit the flexibility in the choice of a time period (e.g., monthly or quarterly) without modifying the utility function, thus simplifying analysis. (shrink)

While broadly in agreement with the conclusion that the exponentially discounted utility model (EDU) is not a universally valid rationality standard, I want to defend some intertemporal rationality criteria related to EDU, which Craig Callender might not share. My commentary explores the tension between these intuitions and Callender's arguments. In the first place, I show that many of the concerns that he raises are in fact compatible with intertemporal consistency (and sometimes even with EDU). Secondly, I rebut those (...) arguments that directly challenge consistency. I conclude that while we disagree on the rationality of consistency, we can nevertheless agree on its non-universality and its limited justification of policy interventions. (shrink)

How should one discount utility across time? The conventional wisdom in social science is that one should use an exponential discount function. Such a function is a representation of the axioms that provide a well-defined utility function plus a condition known as stationarity. Yet stationarity doesnt really have much intuitive normative pull on its own. Here I try to cast it in a normative glow by deriving stationarity from two explicitly normative premises, both suggested by the philosophical thesis (...) of temporal neutralism. Putting the argument in this form helps us better understand exponential discounting and challenges to it. (shrink)

This article is a critical survey of the debate over the value of the social discount rate, with a particular focus on climate change. The ma- jority of the material surveyed is from the economics rather than from the philosophy literature, but the emphasis of the survey itself is on founda- tions in ethical and other normative theory rather than highly technical details. I begin by locating the standard approach to discounting within the overall landscape of ethical theory, and explaining (...) the assumptions and simplifications that are needed in order to arrive at the model that is standard in the discounting literature. The article then covers the general theory of the Ramsey equation and its relationship to observed interest rates, arguments for and against a positive rate of pure time preference, the consumption elasticity of utility, and the effect of various sorts of uncertainty on the discount rate. Finally, it turns specifically to the ap- plication of this debate to the case of climate change, focussing on the recent controversy over the low discount rate used in the Stern Review of the Economics of Climate Change. (shrink)

Discounted utility theory and its generalizations use discount functions for weighting utilities of outcomes received in different time periods. We propose a new simple test of convexity–concavity of discount function. This test can be used with any utility function and any preferences over risky lotteries. The data from a controlled laboratory experiment show that about one third of experimental subjects reveal a concave discount function and another one third of subjects reveal a convex discount function.

This paper studies the interaction between savagean uncertainty and time preferences. We introduce a variation of the discounted subjective expected utility model, where time preferences are state dependent. Before uncertainty is resolved, the individual is unsure about the discount factor that will be used, even when evaluating certain payoffs. The model can account for the present bias and diminishing impatience, even if the future is discounted geometrically. The present bias disappears when the immediate payoff becomes uncertain. Although (...) preferences are not stationary, choices may be time consistent. (shrink)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

I argue that the use of a social discount rate to assess the consequences of climate policy is unhelpful and misleading. I consider two lines of justification for discounting: (i) ethical arguments for a "pure rate of time preference" and (ii) economic arguments that take time as a proxy for economic growth and the diminishing marginal utility of consumption. In both cases I conclude that, given the long time horizons, distinctive uncertainties, and particular costs and benefits at stake in (...) the climate context, discount rates are at best a poor proxy for the normative considerations they are meant to represent. (shrink)

Orthodox decision theory is fanatical in the way it treats small probabilities of enormous value, if unbounded utility functions are allowed. Some have suggested a fix, Nicolausian discounting, according to which outcomes with small enough probabilities should be ignored when making decisions. However, there are lotteries involving only small-probability outcomes, none of which should intuitively be ignored. So the Nicolausian discounter needs a procedure for distinguishing the problematic cases of small-probability outcomes from the unproblematic ones. In this paper, I (...) present a dilemma for Nicolausian discounting: the view must be coupled either with a procedure that delivers fanatical verdicts of its own, as bad as those of orthodox decision theory, or with one that entails intransitive cyclic preferences. (shrink)

Ramsey famously pronounced that discounting “future enjoyments” would be ethically indefensible. Suppes enunciated an equity criterion implying that all individuals’ welfare should be treated equally. By contrast, Arrow accepted, perhaps rather reluctantly, the logical force of Koopmans’ argument that no satisfactory preference ordering on a sufficiently unrestricted domain of infinite utility streams satisfies equal treatment. In this paper, we first derive an equitable utilitarian objective based on a version of the Vickrey–Harsanyi original position, extended to allow a variable and (...) uncertain population with no finite bound. Following the work of Chichilnisky and others on sustainability, slightly weakening the conditions of Koopmans and co-authors allows intergenerational equity to be satisfied. In fact, assuming that the expected total number of individuals who ever live is finite, and that each individual’s utility is bounded both above and below, there is a coherent equitable objective based on expected total utility. Moreover, it implies the “extinction discounting rule” advocated by, inter alia, the Stern Review on climate change. (shrink)

Discounting is a manifestation of behavioral impulsivity, which is closely related to self-regulation processes. The decision-making process for intertemporal choices is governed by the inhibition of impulses, which can influence both risk and time-related attitudes. This paper utilizes self-reported measures of risk, impatience, and impulsivity attitudes to examine their impact on the implicit discount rate used when weighing the current purchase cost against future energy savings of appliances. It analyzes and tests the interplay between these attitudes using specific functional forms (...) and causal models. The results highlight the role of risk, impatience and impulsivity on the discount rate and the biases that arise from omitting impulsive attitudes. In addition, other factors such as environmental and social preferences, attitudes, and financial constraints contribute to the implicit discount rate. (shrink)

One’s generosity to others declines as a function of social distance, which is known as social discounting. We examined cultural similarities and differences in social discounting and the mediating roles of the two aspects of interdependence (self-expression and distinctiveness of the self) as well as the two aspects of independence (harmony-seeking and rejection avoidance). Using the same procedure that previous researchers used to test North Americans, Study 1 showed that compared to North Americans, Japanese discount more steeply a partner’s outcomes (...) compared to their own future outcomes, whereas the decrease in the subjective value of the partner’s outcomes accelerates less as a function of social distance. To examine the cultural similarities and differences in social discounting in more detail, Study 2 tested Japanese and Germans and found that the hyperbolic with exponent model fitted the participants’ discounting behaviors better than the other models, except for the loss condition in Germans where the utility of the q-exponential model was indicated. Moreover, although the social discounting rate was higher in Japanese than in Germans, the cultural difference was limited to the gain frame. However, the decline in a person’s generosity accelerated less as a function of social distance in Japanese than in Germans. Furthermore, the cultural difference in the social discounting in gains was mediated by the level of harmony-seeking, which was higher in Germans than in Japanese. Implications for individuals’ generosity against the backdrop of cultural characteristics are discussed. (shrink)

The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell. We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable (...) utility games, moreover, the model implements the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-consistent values in the nontransferable utility setting. (shrink)

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 (...) class='Hi'>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. (shrink)

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 accepted, perhaps reluctantly, what he called Koopmans’ :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. (shrink)

We consider fixed and asking price strategies in the context of selling an asset with Bernoullian updating of the seller’s subjective probability of sale at a given price. The determination of optimal fixed, asking and endogenous reservation prices is discussed under risk-neutrality and expected utility maximisation. With risk-neutrality, the optimal asking price exceeds the optimal fixed price when the expected gain is a strictly concave function. The seller’s choice between the fixed and the asking price strategies depends on several (...) factors: the expected cost of haggling, price competition and the seller’s attitude towards risk. (shrink)

The social discount rate typically consists of two components: differences in the marginal utility of consumption across time, and the pure time preference rate as applied to cardinal utility. Within this framework, intragenerational and intergenerational time preference rates must be the same, if we are to avoid strongly counterintuitive results. Both rates, however, can be plausibly equal at zero rather than at a positive level; pure time preference should not necessarily be applied to cardinal utility, even when (...) we apply it to goods. The other component of the discount rate, the marginal utility of consumption, is appropriate only for very small changes in individual wealth; this assumption does not match most of the intergenerational scenarios in question. I conclude that economics does not provide a prima facie case for a positive rate of intergenerational discount for most policy issues. (shrink)

The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.

This study proposes a model of non-unitary time discounting and examines its welfare implications. A key feature of our model lies in the disparity of time discounting between multiple distinct goods, which induces an individual’s preference reversals even though she normally discounts her future utilities for each good. After characterizing the time-consistent decision-making by such an individual, we compare welfare achieved in the market economy and welfare in the planner’s allocation from the perspective of all selves across time. Under certain (...) situations, the selves in early periods strictly prefer the social planner’s allocation, whereas the selves in future periods strictly prefer the market equilibrium. Therefore, the welfare implications of our model are quite different from those in the canonical discounting model and in models of other time-inconsistent preferences. (shrink)

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a (...) selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper. (shrink)

The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up (with high probability) poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.

One of the reasons for adopting hyperbolic discounting is to explain preference reversals. Another is that this value structure suggests an elegant theory of the will. I examine the capacity of the theory to solve Newcomb's problem. In addition, I compare Ainslie's account with other procedural theories of choice that seem at least equally capable of accommodating reversals of preference.

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...) prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (shrink)

This paper investigates two assumptions of the exponential discounted utility theory (EDU) to which Callender draws our attention: namely that we can cleanly distinguish pure from impure temporal preferences, and that past discounting can be ignored. Drawing on recent empirical work in this area, we argue that in so far as one might have thought that past-directed preferences are more pure than future ones, then there is evidence that people’s pure preferences (in so far as we can make (...) sense of that notion) show more interpersonal variation than has previously been thought. (shrink)

Intertemporal choice is the study of how people make choices about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time. Most choices require decision-makers to trade off costs and benefits at different points in time. These decisions may be about savings, work effort, education, nutrition, (...) exercise, health care and so forth. Since early in the twentieth century, economists have analyzed intertemporal decisions using the discounted utility model, which assumes that people evaluate the pleasures and pains resulting from a decision in much the same way that financial markets evaluate losses and gains, exponentially 'discounting' the value of outcomes according to how delayed they are in time. Discounted utility has been used to describe how people actually make intertemporal choices and it has been used as a tool for public policy. Policy decisions about how much to spend on research and development, health and education all depend on the discount rate used to analyze the decision. (shrink)

Recent influential accounts of temporal representation—the use of mental representations with explicit temporal contents, such as before and after relations and durations—sharply distinguish representation from mere sensitivity. A common, important picture of inter-temporal rationality is that it consists in maximizing total expected discounted utility across time. By analyzing reinforcement learning algorithms, this article shows that, given such notions of temporal representation and inter-temporal rationality, it would be possible for an agent to achieve inter-temporal rationality without temporal representation. It (...) then explores potential upshots of this result for theorizing about rationality and representation. (shrink)

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero probability. Chapters (...) 3–6 discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future. (shrink)

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also (...) from “residual” consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)

Several areas of welfare economics seek to evaluate states of affairs as a function of interpersonally comparable individual utilities. The aim is to map each state of affairs onto a vector of individual utilities, and then to produce an ordering of these vectors that can be represented by a mathematical function assigning a real number to each. When this approach is used in intertemporal contexts, a central theoretical question concerns the evaluative weight to be applied to utility coming at (...) different times. This question concerns the rate of pure time preference, which is one key determinant of the social discount rate. This article argues that the standard philosophical account of pure time preference is mistaken, because it ascribes to economists a methodological commitment they need not, and often do not, accept. This in turn undercuts the most common philosophical objection to pure time preference, which traces at least to Rawls’s A Theory of Justice. The article then evaluates three further objections to pure time preference, concluding that it might still be defensible under certain circumstances. The article closes by articulating a final argument that is suggested by the “Social, Economic and Ethical Concepts and Methods” chapter of the most recent Intergovernmental Panel on Climate Change report. If this further argument is sound, it would constitute a decisive objection to pure time preference as it currently figures in much intertemporal welfare economics. (shrink)

Canonical utility theory may have adopted its selfishness postulate because it lacked theoretical rationales for two major kinds of incentive: empathic utility and self-signaling. Empathy – using vicarious experiences to occasion your emotions – gives these experiences market value as a means of avoiding the staleness of self-generated emotion. Self-signaling is inevitable in anyone trying to overcome a perceived character flaw. Hyperbolic discounting of future reward supplies incentive mechanisms for both empathic utility and self-signaling. Neither can be (...) effectively suppressed for an experimental game. (shrink)

The use of aggregated quality of life estimatesin the formation of public policy and practiceguidelines raises concerns about the moralrelevance of variability in values inpreferences for health care. This variabilitymay reflect unique and deeply held beliefs thatmay be lost when averaged with the preferencesof other individuals. Feminist moral theorieswhich argue for attention to context andparticularity underline the importance ofascertaining the extent to which differences inpreferences for health states revealinformation which is morally relevant toclinicians and policymakers. To facilitatethese considerations, we present (...) an empiricalstudy of preferences for the timing andoccurrence of health states associated withhormone replacement therapy (HRT). Sixteenwomen between the ages of 45 and 55 wereenrolled in this pilot study. Theirpreferences regarding five health statesassociated with HRT (menopausal symptoms, sideeffects of HRT, breast cancer, myocardialinfarction, and osteoporosis) were assessed inquantitative terms known as utilities. Twostandard methods, the visual analog scale (VAS) and the standard gamble (SG), were used toassess utility and time preference (calculatedas a discount rate). The wide variability ofresponses underlines the importance oftailoring health care to individual women'spreferences. Policy guidelines whichincorporate utility analysis must recognize thenormative limitations of aggregatedpreferences, and the moral relevance ofindividual conceptions of health. (shrink)

Health policymakers employ utility measures to inform resource allocation decisions. They often rely on a conceptual tool called the quality-adjusted life year that discounts the value of years lived in a state of disability relative to years lived in full health. A representative sample of the general public is asked to place values on hypothetical health states as part of a standard gamble or time trade-off task. Policymakers use the resulting values to calculate the number of QALYs gained through (...) particular interventions. Utilitarian reasoning mandates that policymakers maximize QALYs gained per unit cost.Although many scholars have explored the problems of distributive justice that arise from this system... (shrink)

We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.

Should we remain neutral between our interests and those of future generations? Or are we ethically permitted or even required to depart from neutrality and engage in some measure of intergenerational discounting? This Article addresses the problem of intergenerational discounting by drawing on two different intellectual traditions: the social welfare function (“SWF”) tradition in welfare economics, and scholarship on “prioritarianism” in moral philosophy. Unlike utilitarians, prioritarians are sensitive to the distribution of well-being. They give greater weight to well-being changes affecting (...) worse-off individuals. Prioritarianism can be captured, formally, through an SWF which sums a concave transformation of individual utility, rather than simply summing unweighted utilities in utilitarian fashion. The Article considers the appropriate structure of a prioritarian SWF in intergenerational cases. The simplest case involves a fixed and finite intertemporal population. In that case, I argue, policymakers can and should maintain full neutrality between present and future generations. No discount factor should be attached to the utility of future individuals. Neutrality becomes trickier when we depart from this simple case, meaning: (1) “non-identity” problems, where current choices change the identity of future individuals; (2) population-size variation, where current choices affect not merely the identity of future individuals, but the size of the world’s future population (this case raises the specter of what Derek Parfit terms “the repugnant conclusion,” i.e., that dramatic reductions in the average level of individual well-being might be compensated for by increases in population size); or (3) an infinite population. The Article grapples with the difficult question of outfitting a prioritarian SWF to handle non-identity problems, population-size variation, and infinite populations. It tentatively suggests that a measure of neutrality can be maintained even in these cases. (shrink)

A theory of right action is implicit in Hume's delineation of the virtues. It gives qualified priority to 'rules of justice' as Hume's remarks on 'that species of utility which attends this virtue' require. It is a useful actual-rule, not an ideal possible-rule, purely utilitarian theory that discounts rules of justice in 'extraordinary cases', has a problem when rules conflict and invites the question 'Why not hark directly to the supreme law of utility in every case?'. It does (...) not reflect contractarian considerations of mutuality of interests evident in Hume's texts, which while sometimes relevant to what is reasonable, are in his view never also relevant to what is moral.(publisher). (shrink)