Flagging Prospect Theory

Abstract

The basic tenets of prospect theory, a bedrock principle of behavioral economics, can be illustrated by what Daniel Kahneman has called prospect theory’s "flag": an asymmetrical sigmoid curve whose inflection point occurs at the origin (thus reflecting human beings' adaptation level relative to their starting economic position), whose slope to the left of the origin is discernibly steeper than its slope to the right (thus reflecting loss aversion), and whose upper and lower asymptotes reflect diminishing sensitivity to losses as well as gains.

This paper describes a surprisingly simple and supple method for parametrically modeling prospect theory with closed-form expressions and elementary functions. It accomplishes this task by transforming the cumulative distribution function of the log-logistic distribution. In plainer language, this paper "draws" the flag of prospect theory with the simplest available mathematical functions and the minimum amount of algebraic manipulation needed to generate that flag. The resulting formula can expressed with exactly two parameters. That formula can be readily modified to fit empirical data garnered in support of nearly any hypothesis informed by prospect theory.