Calibration Results for Betweenness Functionals

A reasonable level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. This was demonstrated by Rabin for expected utility theory. Later, Safra and Segal extended this result by showing that similar arguments apply to almost all non-expected utility theories, provided they are Gateaux differentiable. In this paper we drop the differentiability assumption and by restricting attention to betweenness theories we show that much weaker conditions are sufficient for the derivation of similar calibration results.