2025/03/04 by Chéze, Guillaume, Fieux, Etienne
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Multiagent Systems (cs.MA)
paper · doi:10.48550/arxiv.2503.02429
This article deals with ranking methods. We study the situation where a tournament between n players P1, P2, … Pn gives the ranking P1 \succ P2 \succ ⋯ \succ Pn, but, if the results of Pn are no longer taken into account (for example Pn is suspended for doping), then the ranking becomes Pn-1 \succ Pn-2 \succ ⋯ \succ P2 \succ P1. If such a situation arises, we call it an inversion paradox. In this article, we give a sufficient condition for the inversion paradox to occur. More precisely, we give an impossibility theorem. We prove that if a ranking method satisfies three reasonable properties (the ranking must be natural, reducible by Condorcet tournaments and satisfies the long tournament property) then we cannot avoid the inversion paradox, i.e., there are tournaments where the inversion paradox occurs. We then show that this paradox can occur when we use classical methods, e.g., Borda, Massey, Colley and Markov methods.