Alternation Bias and Reduction in St. Petersburg Gambles: An Experimental Investigation

Abstract:     
The Reduction of compound lotteries is an implicit assumption both in the statement of the St. Petersburg Paradox as well as in its resolution by Expected Utility (EU). Yet despite the pivotal role of this assumption, to date there has been no empirical substantiation of its validity. Here we report three real-money experiments in which the standard compound-lottery form of the (truncated) St. Petersburg Gamble is explicitly juxtaposed with its reduced form. In the first experiment, we elicit Subjects' Certainty Equivalents for each form of the gamble. In the second experiment, Subjects choose between reduced and compound forms within a multiple price list format, where a different sure payment (in 1 Euro increments), is added either to the reduced or the compound form. With this instrument, we can test for both 'weak-form' and 'strong-form' violations of Reduction. The third experiment checks for robustness against range and increment manipulation. In the first experiment we find that the Certainty Equivalent of the compound form is stochastically dominated by, and statistically significantly smaller than, the objectively equivalent reduced form. This bias toward the reduced form is borne out in the second (and third) experiments, where 48% (88%) display strong-form violation of Reduction. These rejections of Reduction are consistent with the predictions of alternation bias, which may be understood as a subjective distortion of conditional probability. Together these experiments offer evidence that the Reduction assumption may have limited descriptive validity in St. Petersburg gambles -- and consequently in EU and other theoretical resolutions of the St. Petersburg Paradox predicated on Reduction.

Number of Pages in PDF File: 33

Keywords: St. Petersburg Paradox, reduction of compound lotteries axiom, alternation bias, law of small numbers, test for indifference, dominance precept, stront-form violation of reduction

JEL Classification: D81, C91

working papers series