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Volume 5 • Issue 3 | November 2021

So how to make group decisions? Arrow's impossibility theorem 70 years after

Hung T. Nguyen, Olga Kosheleva, and Vladik Kreinovich

09/11/2021 125 0 0
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Group decisions Arrow’s impossibility theorem Utility

Abstract:

Purpose
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.

Design/methodology/approach
In this paper we analyze this problem from the viewpoint of decision theory, the basic theory underlying all our activities – including economic ones.

Findings
We show how from the first-principles decision theory, we can extract explicit recommendations for group decision making.

Originality/value
Most of the resulting recommendations have been proposed earlier. The main novelty of this paper is that it provides a unified coherent narrative that leads from the fundamental first principles to practical recommendations.

References:

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  3. Arrow, K.J. (1951), Social Choice and Individual Values, Wiley, New York, NY.
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  11. Nguyen, H.T., Kosheleva, O. and Kreinovich, V. (2009), “Decision making beyond Arrow's ‘impossibility theorem’, with the analysis of effects of collusion and mutual attraction”, International Journal of Intelligent Systems, Vol. 24 No. 1, pp. 27-47.
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