A new solution to the St Petersburg paradox and estimates under uncertainty

Purpose–The purpose of this paper is to argue that Bernoulli's “utility function solution to the St Petersburg paradox” was wrong and to find a new method to solve the paradox. Design/methodology/approach–This goal is attained through two ways: using Bernoulli's and Kramer's utility function to construct new paradoxes; and designing and implementing a new St Petersburg game which does not carry the effect of diminishing marginal utility. Findings–In this paper, the author finds that Bernoulli's “utility function solution to the St Petersburg paradox” was wrong, and also finds a new model to solve the paradox, which is also a brand-new model of estimates under uncertainty. Research limitations/implications–Bernoulli put forward the diminishing marginal utility of currency and thus accordingly provided the utility function solution to solve the paradox. This paper indicates that the Bernoulli's utility function solution does not work. Thus, further research needs to be taken in several aspects: is the diminishing marginal utility of currency tenable? Does the marginal utility of currency decrease monotonically? Are concave utility functions represented by negative index functions which are widely used in theoretical study reasonable? Practical implications–The paper proposes a brand-new possible research idea and direction for economic theoretical researches based on uncertainty. Originality/value–This paper proved the untenability of the utility function solution to solve the St Petersburg paradox for the first time and proposed the pioneering “risk adjustment model” of estimates under uncertainty.