A Eliciting Predictions for Discrete Decision Making

We consider a decision maker who can select one of a finite set of possible actions, each of which will result in one of a finite set of possible outcomes. If the decision maker has preferences over these outcomes, it will naturally prefer taking some actions to others, but may be uncertain of the result of each action. In this paper we describe how a decision maker can elicit expert predictions about the outcome of each action, allowing the decision maker to make an informed decision. We show that strictly proper decision making, where experts have an incentive to accurately reveal their beliefs about the outcome of each action, allows the decision maker to take a preferred action with probability arbitrarily close—but not equal—to one; with positive probability, the decision maker must take an action at random. Requiring a decision maker to sometimes act randomly is clearly undesirable, so we also describe an alternative where a single expert directly reveals a preferred decision instead of predicting each action’s outcome.