It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated independently but rather comparatively: The time difference, or interval, between the options sometimes counts more and sometimes counts less if it is taken as a whole than if it is divided into shorter subintervals (superadditivity and subadditivity, respectively), and whether the interval counts more or less depends on the money difference, or compensation, involved (inseparability). We develop a model that replaces alternative-based discounting with attribute-based tradeoffs. In our model, people make intertemporal choices by weighing how much more they will receive or pay if they wait longer against how much longer the wait will be, or, conversely, how much less they will receive or pay if they do not wait longer against how much shorter the wait will be. This model, called the tradeoff model, accommodates, in a psychologically plausible way, all anomalies that the discounting approach can and cannot address.Keywords: intertemporal choice, delay discounting, alternative-based choice, tradeoffs, attribute-based choice Intertemporal choices involve tradeoffs between costs and benefits that occur at different points in time (Loewenstein & Elster, 1992;Loewenstein, Read, & Baumeister, 2003). These include choices such as taking a job now or getting an education and having a chance at a better job later, and spending money now or saving it and having more to spend later. Most intensively investigated, however, are much more elementary choices between smaller-sooner and larger-later amounts of money, such as receiving $100 now or $150 in 3 months. It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values to the options, and then comparing these discounted values. For this choice, they would compare the value of $100 now with the discounted value of $150 in 3 months. We argue that this does not accurately describe the psychology of intertemporal tradeoffs.Discounting models belong to the broad class of alternativebased choice models, in which the options are independently assigned an overall value, these values are compared, and the option with the highest value is chosen. Alternative-based choice models can be contrasted with attribute-based ones (Payne, Bettman, & Johnson, 1988), in which the options are directly compared along their attributes, and the option favored by these comparisons is chosen.1 Alternative-based discounting models can accommodate much of what we know about intertemporal choice, but there remains evidence, reviewed and strengthened in this article, that can only be addressed by an attribute-based choice model. In this article, we develop such a model, called the tradeoff mod...

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ccording to most models of intertemporal choice, an agent's discount rate is a function of how far the outcomes are removed from the present, and nothing else. This view has been challenged by recent studies, which show that discount rates tend to be higher the closer the outcomes are to one another (subadditive discounting) and that this can give rise to intransitive intertemporal choice. We develop and test a generalized model of intertemporal choice, the Discounting By Intervals (DBI) model, according to which the discount rate is a function of both how far outcomes are removed from the present and how far the outcomes are removed from one another. The model addresses past challenges to other models, most of which it includes as special cases, as well as the new challenges presented in this paper: Our studies show that when the interval between outcomes is very short, discount rate tends to increase with interval length (superadditive discounting). In the discussion we place our model and evidence in a broader theoretical context.

Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes and delays are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes.

People prefer to receive good outcomes immediately rather than wait, and they must be compensated for waiting. But what influences their decision about how much compensation is required for a given wait? To give a partial answer to this question, we develop the DRIFT model, a heuristic description of how framing influences intertemporal choice. We describe 4 experiments showing the implications of this model. In the experiments, we vary how the difference between a smaller sooner outcome and a larger later outcome is framed-either as total interest earned, as an interest rate, or as total amount earned (the conventional frame in studies of intertemporal choice)-and whether the larger later outcome is described as resulting from the investment of the smaller sooner one. These alternate frames have several effects. First, the investment language increases patience. Second, the explicit provision of the (otherwise implicit) experimental interest rate sharply reduces the magnitude effect. Correspondingly, we find that interest frames increase patience when the rewards are small, but they decrease patience when they are large. Third, the interest-rate frame induces somewhat greater discounting for longer time periods and, thus, reverses the common finding of "hyperbolic" discounting. Thus, many of the "stylized facts" implied by studies involving choices between a smaller sooner and a larger later amount are eliminated or reverse under alternate outcome frames.Keywords: intertemporal choice, delay discounting, framing, choice modelling Any interesting choice involves tradeoffs. For intertemporal choices, the tradeoffs involve time and amount-smaller sooner rewards compared with against larger later rewards. For some, the perfect real world example may be the decision of whether to endure lower (or no) wages during college so as to permit greater earnings later.The dominant method for investigating intertemporal choices in the lab has been to elicit choices between smaller-sooner and larger-later amounts of money (see, e.g., Ainslie & Haendel, 1983;Hardisty & Weber, 2009;Kirby, 1997;Read, 2001;Sayman & Öncüler, 2009;Weber et al., 2007;Zauberman, Kim, Malkoc, & Bettmann, 2009). Most of this research has focused on how discount rates are influenced by differences in the magnitude or timing of those outcomes (e.g., Benzion, Rapoport, & Yagil, 1989;Keren & Roelofsma, 1995;Kirby & Herrnstein, 1995;Scholten & Read, 2006;Thaler, 1981). A second research stream has focused on how these choices correlate with other individual differences, such as smoking behavior (Baker, Johnson, & Bickel, 2003;Chabris, Laibson, Morris, Schuldt, & Taubinsky, 2008) or demographic characteristics (Frederick, 2005). A third focus is on the influence of ephemeral states, such as whether participants have been aroused by viewing women in bikinis ( Van den Bergh, Dewitte, & Warlop, 2008) or by the sight or scent of freshly baked cookies (Li, 2008).The present article falls into a fourth stream of research that examines whether, and how, discounting ...

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It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated independently but rather comparatively: The time difference, or interval, between the options sometimes counts more and sometimes counts less if it is taken as a whole than if it is divided into shorter subintervals (superadditivity and subadditivity, respectively), and whether the interval counts more or less depends on the money difference, or compensation, involved (inseparability). We develop a model that replaces alternative-based discounting with attribute-based tradeoffs. In our model, people make intertemporal choices by weighing how much more they will receive or pay if they wait longer against how much longer the wait will be, or, conversely, how much less they will receive or pay if they do not wait longer against how much shorter the wait will be. This model, called the tradeoff model, accommodates, in a psychologically plausible way, all anomalies that the discounting approach can and cannot address.Keywords: intertemporal choice, delay discounting, alternative-based choice, tradeoffs, attribute-based choice Intertemporal choices involve tradeoffs between costs and benefits that occur at different points in time (Loewenstein & Elster, 1992;Loewenstein, Read, & Baumeister, 2003). These include choices such as taking a job now or getting an education and having a chance at a better job later, and spending money now or saving it and having more to spend later. Most intensively investigated, however, are much more elementary choices between smaller-sooner and larger-later amounts of money, such as receiving $100 now or $150 in 3 months. It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values to the options, and then comparing these discounted values. For this choice, they would compare the value of $100 now with the discounted value of $150 in 3 months. We argue that this does not accurately describe the psychology of intertemporal tradeoffs.Discounting models belong to the broad class of alternativebased choice models, in which the options are independently assigned an overall value, these values are compared, and the option with the highest value is chosen. Alternative-based choice models can be contrasted with attribute-based ones (Payne, Bettman, & Johnson, 1988), in which the options are directly compared along their attributes, and the option favored by these comparisons is chosen.1 Alternative-based discounting models can accommodate much of what we know about intertemporal choice, but there remains evidence, reviewed and strengthened in this article, that can only be addressed by an attribute-based choice model. In this article, we develop such a model, called the tradeoff mod...

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We extend the recently proposed tradeoff model of intertemporal choice (Scholten & Read, 2010) from choices between pairs of single outcomes to pairwise choices involving two-outcome sequences. The core of our proposal is that choices between sequences are made by weighing accumulated outcomes against outcome-adjusted delays. Thus extended, the tradeoff model offers a unified account of recently discovered anomalies in pairwise choices involving two-outcome sequences, including (a) the hidden-zero effect, in which explicit reference to the zero outcomes of the options increases patience, (b) the front-end amount effect, in which the addition of a front-end amount to both options decreases patience, and (c) the mere token effect, in which the addition of an early outcome to both options increases patience. Not only does the extended tradeoff model accommodate these anomalies, it also correctly predicts (d) violations of independence, (e) a reversal of the front-end amount effect, (f) the effect of relocating the front-end amount to the back end of both options, and (g) a dependence of the “mere” token effect on the magnitude of the token. In quantitative analyses, the extended tradeoff model offers an accurate account of the data.