A Resource-Rational, Process-Level Account of the St. Petersburg Paradox

Abstract

The St. Petersburg paradox is a centuries-old philosophical puzzle concerning a lottery with infinite expected payoff for which people are only willing to pay a small amount to play. Despite many attempts and several proposals, no generally accepted resolution is yet at hand. In this work, we present the first resource-rational, process-level explanation of this paradox, demonstrating that it can be accounted for by a variant of normative expected utility valuation which acknowledges cognitive limitations. Specifically, we show that Nobandegani et al.'s (2018) metacognitively rational model, sample-based expected utility (SbEU), can account for major experimental findings on this paradox. Crucially, our resolution is consistent with two empirically well-supported assumptions: (a) People use only a few samples in probabilistic judgments and decision-making, and (b) people tend to overestimate the probability of extreme events in their judgment. Our work seeks to understand the St. Petersburg gamble as a particularly risky gamble whose process-level explanation is consistent with a broader process-level model of human decision-making under risk.