So how to make group decisions? Arrow's Impossibility Theorem 70 years after

Authors

Hung T. Nguyen, New Mexico State UniversityFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-1-2021

Comments

Technical Report: UTEP-CS-21-65

Published in Asian Journal of Economics and Banking (AJEB), 2021, DOI 10.1108/AJEB-07-2021-0080

Abstract

In 1951, Kenneth Arrow proved that it is not possible to have a group decision making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result -- well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains -- so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision -- this is known, e.g., for different voting schemes. In this paper, we analyze this problem from the viewpoint of decision theory, the basic theory underlying all our activities -- including economic ones -- and describe the corresponding recommendations. Most of the resulting recommendations have been proposed earlier. The main objective of this paper is to provide a unified coherent narrative that leads from the fundamental first principles to practical recommendations.