Why Condorcet Consistency is Essential

TL;DR

This paper argues that Condorcet consistency is essential in voting systems, showing that it aligns with majority rule in two-candidate races and highlighting its importance through theoretical reasoning and simulation results.

Contribution

It provides a three-step argument demonstrating why Condorcet consistency should be considered essential in single-winner elections, linking it to majority rule and strategic voting considerations.

Findings

Condorcet consistency dismisses conflicting electoral criteria.

Majority rule in two-candidate races implies Condorcet consistency.

Simulation studies show MR outperforms alternatives in selecting centrist candidates.

Abstract

In a single winner election with several candidates and ranked choice or rating scale ballots, a Condorcet winner is one who wins all their two way races by majority rule or MR. A voting system has Condorcet consistency or CC if it names any Condorcet winner the winner. Many voting systems lack CC, but a three step line of reasoning is used here to show why it is necessary. In step 1 we show that we can dismiss all the electoral criteria which conflict with CC. In step 2 we point out that CC follows almost automatically if we can agree that MR is the only acceptable system for elections with two candidates. In step 3 we make that argument for MR. This argument itself has three parts. First, in races with two candidates, the only well known alternatives to MR can sometimes name as winner a candidate who is preferred over their opponent by only one voter, with all others preferring the opponent. That is unacceptable. Second, those same systems are also extremely susceptible to strategic insincere voting. Third, in simulation studies using spatial models with two candidates, the best known alternative to MR picks the best or most centrist candidate significantly less often than MR does.