Betting on odds on Favorites as an Optimal Choice in Cumulative Prospect Theory

It is well known that the parametric version of Cumulative Prospect theory (CPT) proposed by Kahneman and Tversky (1979) and Tversky and Kahneman (1992) (KT) can explain gambling at actuarially unfair odds on long shots due to the over weighting of small probabilities. However betting on odds favorites appears problematic. We demonstrate using a parametric model of Cumulative Prospect Theory that nests that of Kahneman and Tversky that if agents are risk averse enough over gains and risk-seeking enough over losses then they will gamble on odds on chances at actuarially unfair odds even when there is no probability distortion. This previously unappreciated fact is interesting since many experimental results suggest that some respondents are very risk averse over gains.