HOW COMPLICATED ARE BETWEENNESS PREFERENCES

In this paper we suggest a complexity-based taxonomy of some families of preferences over lotteries. We define the complexity of a given fam ily to be of order n if the question whether or not a given preference belongs to this family can be determined by comparing lotteries who d iffer on only n outcomes at most. We first show that the complexities of the expected utility family, the weighted utility family and the be tweenness family are all of order 3. We then show that the complexity of singletons is always equal to 3. Finally, we provide examples of fa milies of preferences with arbitrary orders of complexities. The paper also provides a better understanding of the large body of experimenta l results in the theory of decision making under risk.