Survey_KMM_2005

Abstract

This paper presents a model of decision making that can explicitly reflect the circumstance that the DM is (subjectively) uncertain about the priors relevant to his decision. The model allows for the relaxation of P2 under such a circumstance, so that behavior, given the uncertainty about ex ante evaluation, may display aversion (or love) for that uncertainty along the lines of the justification discussed above. Among other things, the model could be used to analyze behavior in instances where the DM’s information is explicitly consistent with multiple probabilities on the state space relevant to the decision at hand. One instance is a portfolio investment decision. An investor, in the best circumstances, with access to all publicly available data, will in general be left with a range of return distributions that are plausible. As a second example, think of a monetary policy maker setting policy on the basis of a parametric model that solves to yield a probability distribution on a set of macroeconomic variables of interest. However, the probability distribution on variables is conditional on the value of the parameters, which, in turn, is uncertain. That might cause the DM to be concerned enough to seek a policy whose performance is more robust to the uncertainty as to which probability applies. The basic structure of the model and assumptions are as follows. Our focus of interest is the DM’s preferences over acts on the state space S. This set of acts is assumed to include a special subset of acts that we call lotteries, i.e., acts measurable with respect to a partition of S over which probabilities are assumed to be objectively given (or unanimously agreed upon). We start by assuming preferences over these lotteries are expected utility preferences. From preferences over lotteries, the DM’s risk preferences are revealed, represented by vN–M index u. We then consider preferences over acts each of whose payoff is contingent on which prior (on S) is the “right” probability: we call these acts second order acts. For the moment, to fix ideas, think of these acts as “bets over the right prior.” Our second assumption states that preferences over second order acts are subjective expected utility (SEU) preferences.