A calibration theorem for risk-weighted expected utility theory

Abstract

This paper establishes a calibration theorem for risk-weighted expected utility theory (REU). REU extends expected utility theory (EU) by introducing a risk function, which allows a decision-maker to weigh potential outcomes according to their respective risks when determining the instrumental value of an action. REU is intuitively appealing as it seems to resolve some of the classical challenges to EU, such as the Allais paradox and Rabin’s calibration result. Using only widely accepted and minimally controversial assumptions, I calibrate REU using Allais preferences and show that accommodating Allais preferences commits REU to questionable behaviors. Thus, REU resolves the Allais paradox only at the cost of becoming susceptible to a Rabin-style challenge (being calibratable). Compared to existing calibration results against REU, my approach relies on less demanding and more realistic assumptions.