Abstract
Expected utility theory (EUT) is currently the standard framework which formally defines rational decision-making under risky conditions. EUT uses a theoretical device called von Neumann–Morgenstern utility function, where concepts of function and random variable are employed in their pre-set-theoretic senses. Any von Neumann–Morgenstern utility function thus derived is claimed to transform a non-degenerate random variable into its certainty equivalent. However, there can be no certainty equivalent for a non-degenerate random variable by the set-theoretic definition of a random variable, whilst the continuity axiom of EUT implies the existence of such a certainty equivalent. This paper also demonstrates that rational behaviour under utility theory is incompatible with scarcity of resources, making behaviour consistent with EUT irrational and justifying persistent external inconsistencies of EUT. A brief description of a new paradigm which can resolve the problems of the standard paradigm is presented. These include resolutions of such anomalies as instant endowment effect, asymmetric valuation of gains and losses, intransitivity of preferences, profit puzzle as well as the St. Petersburg paradox.
Highlights
It is generally accepted that science is provisional by nature
This paper aims to re-examine expected utility theory (EUT) by first setting out the claims of EUT and the problems that they generate, and later by identifying the generic cause of these problems and indicating how they can be resolved
This article notes that contrary to the definition of a random variable, a von Neumann–Morgenstern (vN-M) utility function is claimed to transform a non-degenerate random variable into its certainty equivalent, and brings to light the internal contradictions that this implies for EUT
Summary
Improve or reject it, it must be open to impartial and rigorous re-examination It is this openness to challenge which distinguishes science from dogma and mythology. Any rejection of the extant views as a result of such a re-examination is a bitter pill to swallow for unsuspecting holders of those views, and their understandable surprise and resistance to a change of views, a resistance which must be overcome for science to progress. In this context, this paper aims to re-examine expected utility theory (EUT) by first setting out the claims of EUT and the problems that they generate, and later by identifying the generic cause of these problems and indicating how they can be resolved. This article peruses the issues that EUT raises, with the care and respect that they deserve, i.e., rigorously and thoroughly from the perspectives of the disciplines of mathematics/statistics and economics/finance, the length of it
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