Choice under Limited Uncertainty

This paper considers the problem of an agent's choice under uncertainty in a new framework. The agent does not know the true probability distribution over the state space but is objectively informed that it belongs to a specified set of probabilities. Maintaining the hypothesis that this agent is a subjective expected utility maximizer, we address the question of how the objective information influences her subjective prior.Three plausible rules are proposed. The first, named state independence, states that the subjective probability should not depend on how the uncertain states are `labeled'. Location-consistency, the second property, assumes that `similar' objective sets of probabilities result in `similar' subjective priors. The third rule is an `update-consistency' rule. Suppose the agent selects some probability p. She is then told that the likelihood assigned by p to some event A is in fact correct; then this should not cause her to revise her choice of p.Another property, alternative to update-consistency, is also proposed. When an agent forms her subjective prior assigning subjective probabilities to events in some ordered sequence, this property requires that the resulting prior be independent of that order. This last property, named order independence, is shown to be equivalent to update-consistency.A class of sets of probabilities is found on which state independence, location-consistency and update consistency (order independence) uniquely determine a selection rule. Some intuition is given regarding why these properties work in this collection of problems.