Coarse Addition and the St. Petersburg Paradox: A Heuristic Perspective (2507.12475v1)

Abstract: The St. Petersburg paradox presents a longstanding challenge in decision theory. It describes a game whose expected value is infinite, yet for which no rational finite stake can be determined. Traditional solutions introduce auxiliary assumptions, such as diminishing marginal utility, temporal discounting, or extended number systems. These methods often involve mathematical refinements that may not correspond to how people actually perceive or process numerical information. This paper explores an alternative approach based on a modified operation of addition defined over coarse partitions of the outcome space. In this model, exact numerical values are grouped into perceptual categories, and each value is replaced by a representative element of its group before being added. This method allows for a phenomenon where repeated additions eventually cease to affect the outcome, a behavior described as inertial stabilization. Although this is not intended as a definitive resolution of the paradox, the proposed framework offers a plausible way to represent how agents with limited cognitive precision might handle divergent reward structures. We demonstrate that the St. Petersburg series can become inert under this coarse addition for a suitably constructed partition. The approach may also have broader applications in behavioral modeling and the study of machine reasoning under perceptual limitations.