Naive Uncertainty and the Principle of Indifference

Abstract

The principle of indifference states that events should be assigned equal probabilities if no reason can be given for regarding one event as more likely than another. This paper provides a normative argument for the principle of indifference based on a new formal model of decision under uncertainty, called naive uncertainty. The model consists of a set of preferences and their utility representation, from which the principle of indifference arises as utility maximizing. Faced with a finite collection of choice alternatives to which allocation weights are to be assigned, the decision maker under naive uncertainty essentially considers all possible probability distributions associated with the random payoffs, and chooses the allocation that minimizes the variability of outcome across all probabilities. The optimal allocation under naive uncertainty is shown to be the equal weighted allocation. Diverse examples of applications of the model of naive uncertainty and the principle of indifference are given, including naive diversification, evolutionary behavior, and policy making using expert panels.