What Do Goedel's Theorem and Arrow's Theorem Have in Common: A Possible Answer to Arrow's Question

Authors

Miroslav Svitek, Czech Technical University in PragueFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-1-2023

Comments

Technical Report: UTEP-CS-23-16

Abstract

Kenneth Arrow, the renowned author of the Impossibility Theorem that explains the difficulty of group decision making, noticed that there is some commonsense similarity between his result and Goedel's theorem about incompleteness of axiomatic systems. Arrow asked if it is possible to describe this similarity in more precise terms. In this paper, we make the first step towards this description. We show that in both cases, the impossibility result disappears if we take into account probabilities. Namely, we take into account that we can consider probabilistic situations, that we can make probabilistic conclusions, and that we can make probabilistic decisions (when we select different alternatives with different probabilities).