In optimal stopping problems, decision makers are assumed to search randomly to learn the utility... more In optimal stopping problems, decision makers are assumed to search randomly to learn the utility of alternatives; in contrast, in one-shot multi-attribute utility optimization, decision makers are assumed to have perfect knowledge of utilities. We point out that these two contexts represent the boundaries of a continuum, of which the middle remains uncharted: How should people search intelligently when they possess imperfect information about the alternatives? We assume that decision makers first estimate the utility of each available alternative and then search the alternatives in order of their estimated utility until expected benefits are outweighed by search costs. We considered three well-known models for estimating utility: (i) a linear multi-attribute model, (ii) equal weighting of attributes, and (iii) a single-attribute heuristic. We used 12 real-world decision problems, ranging from consumer choice to industrial experimentation, to measure the performance of the three models. The full model (i) performed best on average but its simplifications (ii and iii) also had regions of superior performance. We explain the results by analyzing the impact of the models' utility order and estimation error.
ABSTRACT Prospect theory is the most popular theory for predicting decisions under risk. This pap... more ABSTRACT Prospect theory is the most popular theory for predicting decisions under risk. This paper investigates its predictive power for decisions under ambiguity, using its specification through the source method. We find that it outperforms its most popular alternatives, including subjective expected utility, Choquet expected utility, and three multiple priors theories: maxmin expected utility, maxmax expected utility, and a-maxmin expected utility.
ABSTRACT Behavioral conditions such as compound invariance for risky choice and constant decreasi... more ABSTRACT Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one nonzero outcome. We indicate implications for richer domains with multiple outcomes, and with both risk and time involved.
Preference foundations give necessary and sufficient conditions for a decision model, stated dire... more Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine generalizations of de Finetti's and Savage's finitely additive setups to unbounded utility.
In optimal stopping problems, decision makers are assumed to search randomly to learn the utility... more In optimal stopping problems, decision makers are assumed to search randomly to learn the utility of alternatives; in contrast, in one-shot multi-attribute utility optimization, decision makers are assumed to have perfect knowledge of utilities. We point out that these two contexts represent the boundaries of a continuum, of which the middle remains uncharted: How should people search intelligently when they possess imperfect information about the alternatives? We assume that decision makers first estimate the utility of each available alternative and then search the alternatives in order of their estimated utility until expected benefits are outweighed by search costs. We considered three well-known models for estimating utility: (i) a linear multi-attribute model, (ii) equal weighting of attributes, and (iii) a single-attribute heuristic. We used 12 real-world decision problems, ranging from consumer choice to industrial experimentation, to measure the performance of the three models. The full model (i) performed best on average but its simplifications (ii and iii) also had regions of superior performance. We explain the results by analyzing the impact of the models' utility order and estimation error.
ABSTRACT Prospect theory is the most popular theory for predicting decisions under risk. This pap... more ABSTRACT Prospect theory is the most popular theory for predicting decisions under risk. This paper investigates its predictive power for decisions under ambiguity, using its specification through the source method. We find that it outperforms its most popular alternatives, including subjective expected utility, Choquet expected utility, and three multiple priors theories: maxmin expected utility, maxmax expected utility, and a-maxmin expected utility.
ABSTRACT Behavioral conditions such as compound invariance for risky choice and constant decreasi... more ABSTRACT Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one nonzero outcome. We indicate implications for richer domains with multiple outcomes, and with both risk and time involved.
Preference foundations give necessary and sufficient conditions for a decision model, stated dire... more Preference foundations give necessary and sufficient conditions for a decision model, stated directly in terms of the empirical primitive: the preference relation. For the most popular descriptive model for decision making under risk and uncertainty today, prospect theory, preference foundations have as yet been provided only for prospects taking finitely many values. In applications, however, prospects often are complex and involve infinitely many values, as in normal and lognormal distributions. This paper provides a preference foundation of prospect theory for such complex prospects. We allow for unbounded utility and only require finite additivity of the underlying probability distributions, leaving the restriction to countably additive distributions optional. As corollaries, we generalize previously obtained preference foundations for special cases of prospect theory (rank-dependent utility and Choquet expected utility) that all required countable additivity. We now obtain genuine generalizations of de Finetti's and Savage's finitely additive setups to unbounded utility.
Uploads
Papers by Amit Kothiyal