Mean, Median or Mode? A Striking Conclusion from Lottery Experiments

16 Pages Posted: 1 Apr 2010

Date Written: March 30, 2010


This paper deals with estimating data from experiments determining lottery certainty equivalents. The paper presents the parametric and nonparametric results of the least squares (mean), quantile (including median) and mode estimations. The examined data are found to be positively skewed for low probabilities and negatively skewed for high probabilities. This observation leads to the striking conclusion that lottery valuations are only nonlinearly related to probability when means are considered. Such nonlinearity is not confirmed by the mode estimator in which case the most likely lottery valuations are close to their expected values. This means that the most likely behavior of a group is fully rational. This conclusion is a significant departure from one of the fundamental results concerning lottery experiments presented so far.

Keywords: Lottery experiments, Certainty Equivalents, Least Squares, Quantile, Median, and Mode Estimators, Relative Utility Function, Prospect Theory

JEL Classification: C01, C13, C14, C21, C51, C81, C91, D03, D81, D87

Suggested Citation

Kontek, Krzysztof, Mean, Median or Mode? A Striking Conclusion from Lottery Experiments (March 30, 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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