How complicated are betweenness preferences?

Zvi Safra, Uzi Segal*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper we suggest a complexity-based taxonomy of some families of preferences over lotteries. We define the complexity of a given family 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 differ on only n outcomes at most. We first show that the complexities of the expected utility family, the weighted utility family and the betweenness family are all of order 3. We then show that the complexity of singletons is always equal to 3. Finally, we provide examples of families of preferences with arbitrary orders of complexities. The paper also provides a better understanding of the large body of experimental results in the theory of decision making under risk.

Original languageEnglish
Pages (from-to)371-381
Number of pages11
JournalJournal of Mathematical Economics
Issue number4
StatePublished - 1995


  • Complexity
  • Experiments
  • Non-expected utility


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