Accommodating Stake Effects under Prospect Theory

We investigate how to accommodate qualitative changes in risk preferences over outcomes and probabilities under prospect theory. We find a double two-fold pattern of risk preferences for gains, one over probabilities and one over outcomes. While such patterns over probabilities are an integral part of prospect theory, a solution on how to incorporate two-fold patterns over outcomes has only recently been proposed by Scholten and Read (2014) [Prospect theory and the 'forgotten' fourfold pattern of risk preferences. JRU 48(1)]. We use this insight to address violations of probability-outcome separability under prospect theory as stakes increase [Fehr-Duda, Bruhin, Epper, and Schubert (2010). Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size. JRU 40(2)]. We replicate the violations using traditional functional forms such as power or exponential utility. Using logarithmic utility instead makes the violations disappear, showing the importance of accommodating changing risk preferences across the outcome dimension.