Axiomatic utility theories with the betweenness property

This paper focuses on the betweenness property of expected utility theory. It provides an axiomatization of the class of betweenness-conforming utility theories. Subclasses of betweenness-conforming preferences are axiomatized with ‘substitution’ axioms of intermediate generality. The latter axioms incorporate specifically the effects of replacing a certain outcome with a lottery that is indifferent to it. The present representation is applied to the second-price auction mechanism where it is shown that its demand-revelation property under expected utility is not robust with respect to the class of betweenness-conforming preferences.