Abstract
We present a theoretical account of the origin of the shapes of utility, probability weighting, and temporal discounting functions. In an experimental test of the theory, we systematically change the shape of revealed utility, weighting, and discounting functions by manipulating the distribution of monies, probabilities, and delays in the choices used to elicit them. The data demonstrate that there is no stable mapping between attribute values and their subjective equivalents. Expected and discounted utility theories, and also their descendants such as prospect theory and hyperbolic discounting theory, simply assert stable mappings to describe choice data and offer no account of the instability we find. We explain where the shape of the mapping comes from and, in describing the mechanism by which people choose, explain why the shape depends on the distribution of gains, losses, risks, and delays in the environment.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1853 .This paper was accepted by Yuval Rottenstreich, judgment and decision making.
Highlights
Central to our economic behavior are the attributes money, probability, and time
We present a theoretical account of the origin of the shapes of utility, probability weighting, and temporal discounting functions
The bias parameter allows for an overall bias toward safe or risky choices independently of the amounts and probabilities in the gambles. (Though we do find bias differences in some experiments, fixing bias across conditions produces almost identical revealed utility, weighting, and discounting functions and the same pattern of statistical significance in for every experiment in this paper, except in two places we note below.) The cond subscripts indicate that the utility function u can differ between conditions, as can the and bias parameters
Summary
Central to our economic behavior are the attributes money, probability, and time. Our representations of these attributes are thought to determine our economic behavior. Theories of decision under risk and delay generally assume that we transform money, probability, and delay into subjective equivalents, and integrate information across these equivalents These transformations are typically modeled using utility (or value), weighting, and discounting functions. We show that by manipulating the distribution of monies, probabilities, and delays in the question set used to elicit utility, weighting, and discounting functions, we can systematically change their shape; that is, we show that if you ask different questions, the revealed subjective values of given monies, probabilities, and delays can be adjusted, to some extent, at the experimenter’s will. Our theoretical account of the choice process does not involve utility, weighting, and discounting functions, but does explain both the success of the traditional approach and accounts for the systematic variation of these functions across question sets
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