On guarantees, vetoes and random dictators

Bogomolnaia, A. , Holzman, R. and Moulin, H. (2023) On guarantees, vetoes and random dictators. Theoretical Economics, 18(1), pp. 97-127. (doi: 10.3982/TE4832)

Abstract

A mechanism guarantees a certain welfare level to its agents, if each of them can secure that level against unanimously adversarial others. How high can such a guarantee be, and what type of mechanism achieves it? In the n-person probabilistic voting/bargaining model with p deterministic outcomes a guarantee takes the form of a probability distribution over the ranks from 1 to p. If n ≥ p, the uniform lottery is shown to be the only maximal (unimprovable) guarantee. If n < p, combining (variants of) the familiar random dictator and voting by veto mechanisms yields a large family of maximal guarantees: it is exhaustive if n = 2 and almost so if p ≤ 2n. Voting rules à la Condorcet or Borda, even in probabilistic form, are ruled out by our worst case viewpoint.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Moulin, Professor Herve and Bogomolnaia, Professor Anna
• Authors: Bogomolnaia, A., Holzman, R., and Moulin, H.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Theoretical Economics
• Publisher: Wiley
• ISSN: 1933-6837
• ISSN (Online): 1555-7561
• Published Online: 21 January 2023
• Copyright Holders: Copyright © 2023 The Authors.
• First Published: First published in Theoretical Economics 18(1):97-127
• Publisher Policy: Reproduced under a Creative Commons license