Homo economicus to model human behavior is ethically doubtful and mathematically inconsistent

Abstract

In many models in economics or business a dominantly self-interested homo economicus is assumed. Unfortunately (or fortunately), humans are in general not homines economici as e.g. the ultimatum game shows. This leads to the fact that all these models are at least doubtful. Moreover, economists started to set a quantitative value for the feeling of social justice, altruism, or envy and the like to execute utilitarian calculation. Besides being ethically doubtful, it delivers an explanation in hindsight with little predicting power. We use examples from game theory to show its arbitrariness. It is even possible that a stable Nash equilibrium can be calculated while it does not exist at all, due to the wide differences in human values. Finally, we show that assigned numbers for envy or altruism and the like do not build a field (in a mathematical sense). As there is no homomorphism to real numbers or a subset of it, any calculation is generally invalid or arbitrary. There is no (easy) way to fix the problem. One has to go back to ethical concepts like the categorical imperative or use at most semi quantitative approaches like considering knaves and knights. Mathematically one can only speculate whether e.g. surreal numbers can make ethics calculable.