Geometric Dispersion Theory for Decisions Under Risk: Accurate Out-of-Sample Predictions and Four Distinct Behavioral Patterns

Abstract

We illustrate that the central failures of Expected Utility, Rank-Dependent Expected Utility, and Cumulative Prospect Theory models are caused by ignoring dispersions of prospects. Mean-variance considers dispersion but it violates first-order stochastic dominance, is symmetric, and cannot explain risk. Geometric Dispersion Theory (GDT) is based on new asymmetric dispersion measures that overcome the above limitations. To provide an intuitive perspective of GDT, suppose that the Decision-Maker arbitrates the risk solutions of three independent and competing agents. The first agent is extremely risk averse. The second agent is extremely risk prone, and the third agent is risk neutral. There is no solution that satisfies these three agents. The decision maker chooses the best compromise solution. GDT provides simple explanations for the most credible experimental data and accurately predicts out-of-sample behaviors. GDT can generalize Expected Utility, Rank-Dependent Expected Utility, Cumulative Prospect Theory, and Mean-Variance models.