On a Statistical Approach to Choice under Uncertainty

This article is concerned with criteria of choice under uncertainty which are based on long sequences of independent experiments. To state a rule of comparison for such sequences, we first specify it for sequences of certain numbers (say, of certain incomes). Eventually, the problem is reduced to a connection between preferences on sequences of certain numbers and those on probability distributions. We take into consideration a notion of statistically stable criteria for which choice based on a single random experiment does not disagree with that based on a "sufficiently long" sequence of independent replicas of the same experiment. The main aim of the article is to establish conditions under which a statistically stable criterion exists and to give its explicit representation.