David Leslie, David Wolpert
Paper #: 11-09-45
We introduce a general framework for formalizing and analyzing the problem faced by a Decision Maker (DM) working under information-theoretic constraints on their observational ability. The random utility model and the “hedonic utility” model of Netzer and Robson (NR) are special cases of this framework. We begin by applying information theory to our framework to derive general results concerning the expected regret of DM under observational limitations. We then turn our attention to the effects of observational limitations on choice behavior (rather than the regret values induced by that behavior), focusing on the special case of NR. First we provide a simple derivation of two assumptions made by NR, and then of the result of NR that a particular hedonic utility function satisfies certain optimality principles. We then extend NR to allow a countable rather than uncountable set of states of the world. In particular we show how to use dynamic programming to solve for the optimal preference order of DM in this extension. We also extend NR by considering the case where more than two options are presented to DM , showing that the results of NR change in such a case.