In order that maximizing some kind of an expectation be acceptable as a descriptive theory of risky decision making it is necessary that a gamble made up of a probability mixture of two others lie between them in the perference order. It should not be the most preferred nor the least preferred of the three. The two experiments reported here test that condition and find it is significantly violated. According to Portfolio theory and expected risk theory the mixture may be most preferred but not least preferred. This condition is found to obtain. © 1976.
Coombs, C. H., & Huang, L. C. (1976). Tests of the betweenness property of expected utility. Journal of Mathematical Psychology, 13(3), 323–337. https://doi.org/10.1016/0022-2496(76)90024-9