An axiomatic characterization of the Slater rule

Abstract

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An axiomatic re-characterization of the Kemeny rule

“…Our results also differ from Can and Storcken (2013) by proposing two new conditions, i.e., being strongly tie-breaking and strongly gradual, which also enables a comparison with the characterization of the Slater rule Can et al (2021). This paper shows that the Kemeny rule is the only rule that is unbiased, monotone, weighed tournamental, strongly tie-breaking, strongly gradual.…”

“…In what follows, we first show how these two preference rules, i.e., the Borda and the Kemeny preference rules relate to one another axiomatically. Thereafter, we show how our results relate to those of Can et al (2021) regarding the Slater preference rule. We conclude the paper by showing the logical independence of the characterizing conditions laid out in Sect.…”

“…The final condition ensures that in case of an even number of agents, if all outcomes decisively put an alternative over another, a single elementary change reversing these two alternatives in the profile, cannot reverse the ordering of these alternative in all outcomes. This is a slight variation of the graduality condition introduced in Can et al (2021) for characterizing the Slater rule. Formally:…”

“…This paper shows that the Kemeny rule is the only rule that is unbiased, monotone, weighed tournamental, strongly tie-breaking, strongly gradual. Can et al (2021) shows that Slater rule is the only rule that is unbiased, monotone, tournamental, tie-breaking and gradual. Therefore, we also strengthened their result by imposing being strongly gradual.…”

“…Being (update) monotone requires that if an update occurs in one of the agent's preferences towards one of the outcomes, then this update should change the result in such a way that the new outcomes still contain this preference, and possibly more but no more than what was present before the update. 4 In Can et al (2021), being tournamental is defined as "outcomes should only depend on the tournament results on pairs of alternatives in the profiles". We use a weaker version of this condition, i.e., being weighed tournamental, which requires that outcomes depend also on the pairwise margins of these tournaments.…”