Relative Net Utility and the Saint Petersburg Paradox

TL;DR

This paper introduces the concept of relative net utility as a universal approach to resolving the Saint Petersburg Paradox by capturing broader decision impacts and aligning utility functions to avoid paradoxical outcomes.

Contribution

It proposes the use of relative net utility to explain behavioral economics and resolve the paradox, defining conditions for utility functions and a theorem of indifference.

Findings

Relative net utility explains both behavioral economics and the paradox.

Necessary conditions for utility functions to avoid the paradox are identified.

The role of net utility polarity in value rational decision-making is highlighted.

Abstract

The famous Saint Petersburg Paradox (St. Petersburg Paradox) shows that the theory of expected value does not capture the real-world economics of decision-making problems. Over the years, many economic theories were developed to resolve the paradox and explain gaps in the economic value theory in the evaluation of economic decisions, the subjective utility of the expected outcomes, and risk aversion as observed in the game of the St. Petersburg Paradox. In this paper, we use the concept of the relative net utility to resolve the St. Petersburg Paradox. Because the net utility concept is able to explain both behavioral economics and the St. Petersburg Paradox, it is deemed to be a universal approach to handling utility. This paper shows how the information content of the notion of net utility value allows us to capture a broader context of the impact of a decision's possible achievements. It discusses the necessary conditions that the utility function has to conform to avoid the paradox. Combining these necessary conditions allows us to define the theorem of indifference in the evaluation of economic decisions and to present the role of the relative net utility and net utility polarity in a value rational decision-making process.