Axiomatizations of a simple Condorcet voting method for Final Four and Final Five elections

TL;DR

This paper axiomatizes a simple Condorcet voting method for Final Four elections, extends it to Final Five elections, and provides normative principles and characterizations for these methods.

Contribution

It introduces a new axiomatic characterization of a simple Condorcet method for Final Four elections and proposes a straightforward extension to Final Five elections.

Findings

Unique axiomatic characterization of the Final Four method

A simpler extension to Final Five elections based on head-to-head wins and losses

Clarification of principles supporting Condorcet-based voting in small elections

Abstract

Proponents of Condorcet voting face the question of what to do in the rare case when no Condorcet winner exists. Recent work provides compelling arguments for the rule that should be applied in three-candidate elections, but already with four candidates, many rules appear reasonable. In this paper, we consider a recent proposal of a simple Condorcet voting method for Final Four political elections. Our question is what normative principles could support this simple form of Condorcet voting. When there is no Condorcet winner, one natural principle is to pick the candidate who is closest to being a Condorcet winner. Yet there are multiple plausible ways to define closeness, leading to different results. Here we take the following approach: identify a relatively uncontroversial sufficient condition for one candidate to be closer than another to being a Condorcet winner; then use other principles to help settle who wins in cases when that condition alone does not. We prove that our principles uniquely characterize the simple Condorcet voting method for Final Four elections. This analysis also points to a new way of extending the method to elections with five or more candidates that is simpler than an extension previously considered. The new proposal is to elect the candidate with the most head-to-head wins, and if multiple candidates tie for the most wins, then elect the one who has the smallest head-to-head loss. We provide additional principles sufficient to characterize this simple method for Final Five elections.