Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility

20 Pages Posted: 30 May 2010

Date Written: May 28, 2010


This paper discusses two approaches for the analysis of multi-outcome lotteries. The first uses Cumulative Prospect Theory. The second is the Relative Utility Function, which strongly resembles the utility function hypothesized by Markowitz (1952). It is shown that the relative utility model follows Expected Utility Theory with a transformed outcome domain. An illustrative example demonstrates that not only it is a simpler model, but it also provides more sound predictions regarding certainty equivalents of multi-outcome lotteries. The paper discusses estimation procedures for both models. It is noted that Cumulative Prospect Theory has been derived using two-outcome lotteries only, and it is hard to find any evidence in the literature of its parameters ever having been estimated by using lotteries with more than two outcomes. Least squares (mean) and quantile (including median) regression estimations are presented for the relative utility model. It turns out that the estimations for two- and three-outcome lotteries are essentially the same. This confirms the correctness of the model and vindicates the homogeneity of responses given by subjects. An additional advantage of the relative utility model is that it allows multi-outcome lotteries, together with the estimation results, to be presented on a single graph. This is not possible using Cumulative Prospect Theory.

Keywords: Multi-Prize Lotteries, Lottery/Prospect Valuation, Markowitz Hypothesis, Prospect/Cumulative Prospect Theory, Aspiration/Relative Utility Function

JEL Classification: C13, C21, C51, C91, D03, D81, D87

Suggested Citation

Kontek, Krzysztof, Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility (May 28, 2010). Available at SSRN: or

Krzysztof Kontek (Contact Author)

Warsaw School of Economics (SGH) ( email )

aleja Niepodleglosci 162
PL-Warsaw, 02-554

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