This paper defends the claim that mere temporal proximity always and without exception strengthens certain moral duties, including the duty to save – call this view Robust Temporalism. Although almost all other moral philosophers dismiss Robust Temporalism out of hand, I argue that it is prima facie intuitively plausible, and that it is analogous to a view about special obligations that many philosophers already accept. I also defend Robust Temporalism against several common objections, and I highlight its relevance to a (...) number of practical policy debates, including longtermism. My conclusion is that Robust Temporalism is a moral live option, that deserves to be taken much more seriously in the future. (shrink)

According to Craig Callender [2022], the ‘received view’ across the social sciences is that, when it comes to time and preference, only exponential time discounting is rational. Callender argues that this view is false, even pernicious. Here I endorse what I take to be Callender’s main argument, but only in so far as the received view is understood in a particular way. I go on to propose a different way of understanding the received view that makes it (...) true. In short: When time discounting is suitably conceived, the exponential form of the discounting function is indeed uniquely rational. (shrink)

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is exponential discounting. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that (...) exponential time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as hyperbolic discounting. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs. (shrink)

Controversies about time discounting loom large in decisions about climate change. Prominently, a particularly controversial debate about time discounting in climate change decision-making has been conducted within climate economics, between the authors of Stern et al. and their critics :977–981, 2006; Weitzman in J Econ Lit XLV:703–724, 2007; Nordhaus in J Econ Lit XLV:686–702, 2007). The article examines the role of values in this debate. Firstly, it is shown that time discounting is a case (...) in which values are key because it is at heart an ethical problem. Secondly, it is argued that time discounting in climate economics is a case of economists making frequent and routine references to ethical values and indeed conduct ethical debates with each other. Thirdly, it is argued that there is evidence for deep and pervasive entanglement between facts and values in the prevalent methodologies for time discounting. Finally, it is argued that this means that economists have given up the ‘value-free ideal’ concerning time discounting, and discussed how the current methodology of time discounting in economics can be improved. (shrink)

The concept of time discounting introduces weights on future goods to make these less valu- able. Famously, both the specic functional form of time discounting and its normative sta- tus are contested. To address these problems, this paper provides a measurement-theoretic framework of representation for time discounting. The general representation theorem char- acterises time discounting factors as ratio-scale representations of dierences in temporally extended prospects. This framework of representation is used to reconsider (...) interpretations of time discounting factors such as time preferences, uncertainty and preference change. It also allows to compare these interpretations with regards to their normative appeal, the kinds of reductionism regarding time and preference they imply and the specic functional form of time discounting they suggest. Farther, multiple-self interpretations of decision-makers become available, such that a time discounting factor represents the degree of connectedness between temporal selves in a person. (shrink)

In economics, the concept of time discounting introduces weights on future goods to make these less valuable. Yet, both the conceptual motivation for time discounting and its specic functional form remain contested. To address these problems, this paper provides a measurement-theoretic framework of representation for time discounting. The representation theorem characterises time discounting factors by representations of time dierences. This general result can be interpreted with existing theories of time (...) class='Hi'>discounting to clarify their formal and conceptual assumptions. It also provides a conceptually neutral framework for comparing the descriptive and normative merits of those theories. (shrink)

I find much to like in Craig Callender's [2022] arguments for the rational permissibility of non-exponential time discounting when these arguments are viewed in a conditional form: viz., if one thinks that time discounting is rationally permissible, as the social scientist does, then one should think that non-exponential time discounting is too. However, time neutralists believe that time discounting is rationally impermissible, and thus they take zero time discounting to (...) be the normative standard. The time neutralist rejects time discounting because they think it is rationally impermissible to prefer to live a worse life in expectation because of arbitrariness. Callender’s attack on the time-neutralist position is the following: the time-neutralist’s non-arbitrariness intuition assumes the existence of nonexistent ‘pure’ time preferences. In response, I aim to clarify the time-neutralist position and show that the non-arbitrariness argument does not rely on the existence of pure time preferences. Instead, the debate between time neutralism and permissivism about time discounting boils down to a methodological question: can we ever criticize the content of preferences? If so, we should embrace time neutralism. (shrink)

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)

Drugs are much more expensive whilst they are subject to patent protection than once patents expire: patented drugs make up only 20% of NHS drugs prescriptions, but consume 80% of the total NHS drugs bill. This article argues that, given the relatively uncontroversial assumption that we should save the greater number in cases where all are equally deserving and we cannot save both groups, it is more difficult than is usually thought to justify why publicly funded healthcare systems should pay (...) for patented treatments. The claim to medical treatment of those who will be sick with a given condition once the patent runs out is just as strong as those who are sick with it now, but we will be able to treat more people with the same unit of resource in the future. Hence, when resource constraints entail that both cannot be funded, publicly funded healthcare systems ought to wait until patents expire before approving drugs for general use in the publicly funded system. (shrink)

The concept of behavioural mass provides one avenue for justifying (or making rational) the phenomenon of declining impatience, according to which decision makers put more value on delays that will occur in the near future than on those that will occur later.

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)

Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in which the past is exponentially discounted or forgotten. Often, models in this subclass have the property of becoming trapped with probability 1 in some degenerate state. While previous work has concentrated on such limit results, we concentrate here on a contrary effect, namely that the time to become trapped (...) may increase exponentially in 1/x as the discount rate, 1− x, approaches 1. As a result, the time to become trapped may easily exceed the lifetime of the simulation or of the physical data being modeled. In such a case, the quasi-stationary behavior is more germane. We apply our results to a model of social network formation based on ternary (three-person) interactions with uniform positive reinforcement. (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)

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)

In carrying out cost-benefit or cost-effective analysis, a discount rate should be applied to some kinds of future benefits and costs. It is controversial, though, whether future health is in this class. I argue that one of the standard arguments for discounting (from diminishing marginal returns) is inapplicable to the case of health, while another (favouring a pure rate of time preference) is unsound in any case. However, there are two other reasons that might support a positive discount (...) rate for future health: one relating to uncertainty, and the other relating to the instrumental benefits of improved health. While the latter considerations could be modelled via a discount rate, they could alternatively be modelled more explicitly, in other ways; I briefly discuss which modelling method is preferable. Finally, I argue against the common claims that failing to discount future health would lead to paradox, and/or to inconsistency with the way future cash flows are treated. (shrink)

This paper examines explore the issues of intergenerational equity raised by climate change. A number of different reasons have been suggested as to why current generations may legitimately favor devoting resources to contemporaries rather than to future generations. These - either individually or jointly - challenge the case for combating climate change. In this paper, I distinguish between three different kinds of reason for favoring contemporaries. I argue that none of these arguments is persuasive. My answer in each case appeals (...) to the concept of human rights. It maintains that a human rights-centered perspective to climate change enables us to address each of these reasons. (shrink)

Craig Callender [2022] provides a novel challenge to the non-arbitrariness principle. His challenge plays an important role in his argument for the rational permissibility of a non-exponential temporal discounting rate. But the challenge is also of wider interest: it raises significant questions about whether we ought to accept the non-arbitrariness principle as a constraint on rational preferences. In this paper, I present two reasons to resist Callender’s challenge. First, I present a reason to reject his claim that the non-arbitrariness (...) principle only targets pure time preferences. Second, I criticize the inference Callender draws from a modest claim to a much stronger claim. The modest claim is that it can be hard to reveal the contents of an agent’s preferences. The stronger claim is that this provides us with a reason to reject a certain kind of normative constraint on rational preferences. I argue that the modest claim doesn’t motivate the stronger claim. The upshot of my two arguments is good news for those sympathetic to the non-arbitrariness principle: Callender’s challenge can be overcome, at least as it currently stands. (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)

The best justification of time-discounting is roughly that it is rational to care less about your more distant future because there is less of you around to have it. I argue that the standard version of this argument, which treats both psychological continuity and psychological connectedness as reasons to care about your future, can only rationalize an irrational—because exploitable—form of future discounting.

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)

Temporal discounting is a technical operation in climate change economics. When discount rates are positive, economic evaluation treats future benefits as less important than equivalent present benefits. This chapter explains and critically evaluates four different reasons economists have given for tying discount rates to the interest rates we observe in real-world markets. I suggest that while philosophers have correctly criticized three of these reasons, their criticisms of the fourth miss the mark. This is because philosophers have not taken heed (...) of the distinct analytical framework in which the fourth reason arises. (shrink)

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)

The social discount rate – the rate at which future benefit flows from government investment are discounted to present value – has been a frequent subject of technical debate among professional economists. From a broader perspective, however, the selection of an appropriate rate enjoins consideration of questions that define the very contours of our public philosophy. It carries implicit assumptions about the nature of citizenship, the relation between public and private spheres, and, most singularly, the status of a political society (...) as it is located in time. A key determinant of intertemporal economic allocation, the social discount rate provides a unique registry of a polity's historical consciousness and perceptions of its intergenerational obligations. Yet the highly technical nature of the debate over the discount rate has proven inhospitable to scholars otherwise inclined to investigate its ethical dimensions. Some, notably A. K. Sen, have begun to address these philosophical issues, though much territory remains to be explored. (shrink)

Humans discount rewards as a function of the delay to their receipt. This tendency is referred to as delay discounting and has been extensively researched in the last decades. The magnitude effect and the trait effect are two phenomena which have been consistently observed for a variety of reward types. Here, we wanted to investigate if these effects also occur in the context of the novel but widespread reward types of Instagram followers and likes and if delay discounting (...) of these outcomes is related to self-control and Instagram screen time. In a within-subject online experiment, 214 Instagram users chose between smaller, immediate and larger, delayed amounts of hypothetical money, Instagram followers and likes. First, we found that the magnitude effect also applies to Instagram followers and likes. Second, delay discounting of all three reward types was correlated, providing further evidence for a trait influence of delay discounting. Third, no relationships were found between delay discounting and self-control as well as Instagram screen time, respectively. However, a user’s average like count was related to delay discounting of Instagram likes. (shrink)

This article concentrates on the critique by John Rawls and Derek Parfit of the use of a discount rate in economics. In a presentation of the basic economics underlying the use of a discount rate, the inherently problematic nature of people’s preferences with respect to time are highlighted. The second part discusses the role of the discount rate in economic optimal growth models. An outline of the economic theory of optimal growth is provided, pointing out how Rawls’s analysis of (...) justice between generations fits nicely into this economic discussion, thus explaining his interest in the discount rate. For Rawls the basic problem with the discount rate is that one variable is caught between two objectives: guaranteeing an efficient and at the same time a fair solution. Finally Derek Parfit’s analysis of the use of discount rates is examined. Parfit points out that a discount rate is often used as a crude rule of thumb which wrongly represents our reasons for discounting. The article concludes with a discussion of a study undertaken by a number of respected economists for the IPCC which exhibits all the mistakes that Parfit warns us against. (shrink)

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)

Climate change is projected to have very severe impacts on future generations. Given this, any adequate response to it has to consider the nature of our obligations to future generations. This paper seeks to do that and to relate this to the way that inter-generational justice is often framed by economic analyses of climate change. To do this the paper considers three kinds of considerations that, it has been argued, should guide the kinds of actions that one generation should take (...) if it is to treat both current and future people equitably. In particular it examines the case for what has been termed pure time discounting, growth discounting and opportunity cost discounting; and it assesses their implications for climate policy. It argues that none of these support the claims of those who think they give us reason to delay aggressive mitigation policies. It also finds, however, that the second kind of argument can, in certain circumstances, provide support for passing on some of the costs of mitigation to future generations. (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)

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)

Future-biased individuals systematically prefer pleasures to be in the future and pains to be in the past. Empirical research shows that negative future-bias is robust: people prefer more past pain to less future pain. Is positive future-bias robust or fragile? Do people only prefer pleasures to be located in the future, compared to the past, when those pleasures are of equal value, or do they continue to prefer that pleasures be located in the future even when past pleasures outweigh future (...) ones? Some arguments against the rationality of future-bias require positive future-bias to be robust, while others require it to be fragile. We empirically investigate and show that positive future-bias is robust. (shrink)

People differ in the extent to which they discount the values of future rewards. Behavioural economists measure these differences in terms of functions that describe rates of reduced valuation in the future – temporal discounting – as these vary with time. They measure differences in preference for risk – differing rates of probability discounting – in terms of similar functions that describe reduced valuation of rewards as the probability of their delivery falls. So-called ‘impulsive’ people, including people (...) disposed to addiction, tend to choose rewards in patterns that are described by unusually steeply sloped discount functions. The empirical literature is ambivalent as to whether this applies to pathological gamblers (PGs) who manifest most other behavioural patterns associated with addiction, with different, equally careful studies suggesting opposite conclusions (Petry & Casarella 1999; Holt, Green & Myerson 2003). This puzzle may arise from the fact that most previous experiments on discounting behaviour were not designed so as to allow effects of high temporal discounting to be distinguished from effects of low probability discounting. (Addiction has sometimes been associated with the latter because it seems to involve, at least in the starting addict, under appreciation of risk.) Our research project investigates both forms of discounting behaviour and their relationship to severity of risk of PG in a community sample of South African gamblers. (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)

We consider future cash flows that are contingent both on dates in time and on uncertain states. The decision maker (DM) values the cash flows according to its decision criterion: Here, the payoffs’ expectation with respect to a capacity measure. The subjective measure grasps the DM’s behaviour in front of the future, in the spirit of de Finetti’s (1930) and of Yaari’s (1987) Dual Theory in the case of risk. Decomposition of the criterion into two criteria that represent the (...) DM’s preferences on uncertain payoffs and time contingent payoffs are derived from Ghirardato’s (1997) results. Conditional Choquet integrals are defined by dynamic consistency (DC) requirements and conditional capacities are derived, under some conditions on information. In contrast with other models referring to DC, ours does not collapse into a linear one because it violates a weak version of consequentialism. (shrink)

Temporal discounting is the tendency to devalue temporally distant rewards. Past studies have examined the k-value, the indifference point, and the area under the curve as dependent measures on this task. The current study included these three measures and a fourth measure, called the interest rate total score. The interest rate total score was based on scoring only those items in which the delayed choice should be preferred given the expected return based on simple interest rates. In addition, associations (...) with several individual difference measures were examined including intelligence, executive functions (inhibition, working memory, and set-shifting), thinking dispositions (Need for Cognition and Consideration of Future Consequences) and engagement in substance use and gambling behavior. A staircase temporal discounting task was examined in a sample of 99 university students. Replicating previous studies, temporal discounting increased with longer delays to reward and decreased with higher reward magnitudes. A hyperbolic function accounted for variance in temporal discounting better than an exponential function. Reaction time at the indifference point was significantly longer than at the other choice points. The four dependent measures of temporal discounting were all significantly correlated and were also significantly associated with our individual difference measures. That is, the tendency to wait for a larger delayed reward on all of the temporal discounting measures was associated with higher intelligence, higher executive functions and more consideration of future consequences. Associations between our measures of temporal discounting and outcomes related to substance use and gambling behavior were modest in our university sample. (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 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)

In this paper, we present a time-varying and non-stationary but non-hyperbolic discount function that explains dynamic preference reversal. The new discount function emerges from an analysis of intertemporal consumption and savings choices with mortality risk and an altruistic factor. Our analysis shows that the process of updating survival information may also account for dynamic preference reversal.

People seem to have pure time preferences about trade-offs concerning their own pleasures and pains, and such preferences contribute to estimates of people's individual time discount rate. Do pure time preferences also matter to interpersonal welfare trade-offs, including those concerning the welfare of future generations? Most importantly, should the intergenerational time discount rate include a pure time preference? Descriptivists claim that the intergenerational discount rate should reflect actual people's revealed preferences, and thus it should include (...) a pure time preference. Prescriptivists claim that the intergenerational discount rate should be based on moral analysis, and thus they (often) claim that the rate of pure time preference should be zero. I argue that regardless of which view is correct, a focus on pure time preference is misplaced. First, the most plausible interpretation of descriptive preferences for intergenerational trade-offs is that people are socially biased and not time biased. Second, social bias is superior to time bias as a prescriptive reason to discount the welfare of future people. Third, recent advances in measuring social bias as a social discount rate make social bias a viable replacement for time bias in economic analyses of intergenerational welfare trade-offs. (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)

Intergenerational impartiality requires putting the welfare of future generations at par with that of our own. However, rational choice requires weighting all welfare values by the respective probabilities of realization. As the risk of non-survival of mankind is strictly positive for all time periods and as the probability of non-survival is cumulative, the probability weights operate like discount factors, though justified on a morally justifiable and completely different ground. Impartial intertemporal welfare maximization is acceptable, though the welfare of people (...) in the very far future has lower effects as the probabilities of their existence are also lower. However, the effective discount rate on future welfare values (distinct from monetary values) justified on this ground is likely to be less than 0.1 per annum. Such discounting does not compromise environmental protection and sustainability unduly. The finiteness of our universe implies that the sum of our expected welfare to infinity remains finite, solving the paradox of having to compare different infinite values in optimal growth/conservation theories. (shrink)

Delay discounting is a common phenomenon in daily life, which refers to the subjective value of a future reward decreasing as a function of time. Previous studies have identified several cortical regions involved in delay discounting, but the neural network constructed by the cortical regions of delay discounting is less clear. In this study, we employed resting-state functional magnetic resonance imaging (RS-fMRI) to measure the spontaneous neural activity in a large sample of healthy young adults and (...) used the Monetary Choice Questionnaire to directly measure participants’ level of delay discounting. To identify the neural network of delay discounting at rest, we used an individual difference approach to explore brain regions whose spontaneous activities were related to delay discounting across the whole brain. Then, these brain regions served as seeds to identify the neural network of delay discounting. We found that the fractional amplitude of low-frequency fluctuations (fALFF) of the left insula were positively correlated to delay discounting. More importantly, its connectivity to the anterior cingulate cortex was read out for participants’ behavioral performance in the task of delay discounting. In short, our study provides empirical evidence that insula-anterior cingulate cortex connectivity may serve as a part of the neural network for delay discounting. (shrink)

Breaking one's dieting rule or resolution to quit smoking, procrastination, convenient lies, even the failure of entire nations to follow through with plans to cut greenhouse gas emissions or keep a pandemic in check - these phenomena have been discussed by philosophers and behavioural scientists as examples of weakness of will and delay discounting. Despite the common subject matter both fields have to date rarely worked together for mutual benefit. For the empirical literature is hardly accessible to a reader (...) not familiar with econometric theory; and researchers in the behavioural sciences may find philosophical accounts invoking discounting models difficult to understand without inside knowledge of the debates and historical background. -/- Nora Heinzelmann targets this lacuna by making the ideas and findings from both disciplines intelligible to outsiders. This reveals that discounting - as philosophers have conceived of it - is neither necessary nor sufficient for weakness of will, even though there is substantial overlap. Heinzelmann develops a richer descriptive account of weakness of will that is based on the empirically founded assumption that weak-willed behaviour is determined by uncertainty about whether or when a good materialises. She also explains why weakness of the will understood in this way is irrational: the agent yields to a cognitive bias that leads them to underestimate the greater good they think they ought to and can obtain. Finally, she explores practical implications for individuals and policymakers. (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)

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)

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)