Resumen de A Theory of Choice over Time
Human beings are affected by a fundamental cognitive shortcoming: the perception of future events becomes increasingly �blurred� as the events are pushed further in time. Deciding between alternatives to be obtained in the distant future is intrinsically more complex than deciding between the same alternatives available earlier. For instance, an individual may find 1000 euros now distinctly preferable to 1500 euros in one year time, but may nevertheless hesitate when asked to decide between 1000 euros in five years or 1500 euros in six years. That is, the distance in time makes comparisons more difficult; it confounds what would be easy choices if made between the same alternatives available earlier.
In this paper we propose a novel approach to modeling time preferences which has this type of cognitive feature at its core. This approach allows us to explain some types of behaviour which are incompatible with the standard exponential discounting model (EDM), according to which an outcome x available at time t is evaluated as ätu (x), with ä a constant discount factor and the instantaneous utility of x. In the last decade evidence has accumulated which has contradicted the predictions of the EDM. In particular, it is clear that individuals often exhibit the so-called preference reversal phenomenon, whereby an initial preference between an earlier outcome and a later one is reversed once both outcomes are delayed by the same amount of time. Recently, an alternative model, which is consistent with this type of evidence, has enjoyed considerable prominence and success in the literature.
This is the model of hyperbolic discounting (HDM), in which the discount factor is a hyperbolic function of time. The central point of this approach is that the rate of time preference between alternatives is not constant but varies, and in particular decreases, with the passage of time. The simplest and most popular form of hyperbolic discounting occurs in a two-parameter model which may be termed the â . ä model. In this model, the rate of time preference between a present alternative and a future one is âä, whereas the rate of time preference between two future alternatives is ä. Though the HDM approach is extremely fruitful in resolving some of the issues raised by the experimantal evidence, we believe that a more fundamental assessment of the cognitive aspects of time preferences is needed. Our view is in line with an observation formulated by Rubinstein (1998) who shows experimentally that precisely the same type of decision situations that may create a difficulty for the EDM may also be problematic for the HDM. He argues that, in this sense, the change from a constant to hyperbolic functional form to discount future utility is not radical enough.
We view the evidence against the EDM as indicating that human agents use heuristic procedures to make choices over time which differ fundamentally from the stark maximisation of a complete preference ordering which is common to both EDM and HDM. In our theory we propose that behaviour can be rationalised by a combination of three factors: (a) impatience; (b) �vagueness� in the perception of future alternatives; and (c) a suitable heuristics to make a choice when vagueness is �high�. We provide a parsimonious representation of individual preferences in which a measure of an individual�s vagueness is added to the standard individual�s discount factor (which embodies the �pure time preference� component of utility) as a factor influencing individual choice. In this way we provide an explanation for the phenomenon of preference reversal whose interpretation seems to us more adherent to the psychological basis for it.
The model can also account for cyclical patterns of choice, which are obviously incompatible with the maximisation of a preference ordering. Moreover, our framework can explain a phenomenon of time inconsistency which we dub the �slippery slope�: an agent avoids an activity altogether for fear that engaging in it once will generate the temptation to indulge in it to an undesirable extent (e.g gambling, pregnacies, and so on). The slippery slope phenomenon hinges directly on a cyclical pattern of preference (as well as time-inconsistency).
Finally, we move from individual decisions to strategic behaviour. In particular, we study the implications of our theory to bargaining behaviour. In an alternating offer setting, we find support for equal division. Our theory is close in spirit to Rubinstein�s (2001) suggestion to extend his own similarity-based approach from risk to time preferences. He argues that, when evaluating alternatives, agents may perceive these alternatives to be �similar� in either the time or the outcome dimension. This notion of similarity is closely related to our notion of vagueness. The crucial difference is that in our model vagueness applies to alternatives (outcome-dates pairs), not only to each date or outcome dimension separately. In our opinion, vagueness (or similarity) in one dimension may not be defined independently of the other dimension. For example, 1 Milion today may be clearly distinct from 1.01 Milion today; but from today�s perspective the two amounts in in thirty years time may well be considered similar. This difference is important. Indeed, Rubinstein (1988) shows that his similarity approach generates a transitive preference relation on alternatives, and takes it as evidence that utility theory is hardly reconcilable with experimental data. On the contrary, as observed above, our theory, though utility based, can easiliy explain cyclical preferences.
