Proposing a Normative Basis for the S-Shaped Value Function

Abstract

The S-shaped value function is pervasive in its occurrence in preference tasks and prospect theory is based on the view that all preference tasks are comprehensively captured by an S-shaped value function which is concave in gains and convex for losses. In this work, we propose a normative basis for the ubiquitous S-shaped value function of Kahneman and Tversky’s prospect theory (1979, 1992). We argue that it is best accommodated within the paradigmatic context of evolutionary theory. Proceeding from this paradigm, we show that the S-shaped value or utility function must necessarily result from rational actions by the decision agent. The value function, ν(x) for changes in wealth is normally concave above the reference point i.e., ν ′′(x) 0 and often convex below it i.e., ν ′′(x)> 0, for x< 0 (Kahneman & Tversky, 1979). These bounds imply that the value function is S-shaped. Kahneman and Tversky have summarized the properties of the S-Shaped value function as being: (a) generally concave for gains and convex for losses; (b) steeper for losses than for gains, and (c) defined on deviations from the reference point. Although the pervasive occurrence of the S-shaped value function has been confirmed in the field (Collins, Musser, & Mason, 1991; Fishburn & Kochenberger, 1979; Galanter & Pliner, 1974), there is as yet no satisfactory normative explanation