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Why the Condorcet criterion is less important than it seems

by Alec Slatky // Published August 10, 2010

One of the criticisms made against instant runoff voting is that it doesn’t always elect the Condorcet winner – the candidate who theoretically would defeat all others in a one-on-one race. I will discuss this criticism through the lens of the instant runoff voting election for mayor in Burlington, Vermont.

Burlington’s 2009 Mayoral Election

Burlington (VT) is a three-party city, where the Progressive Party has established itself as an equal to the Democrats and Republicans in prominence and political power. In the 2009 mayoral election, there were three main candidates: Bob Kiss, the Progressive Party incumbent; Andy Montroll, a Democrat; and Kurt Wright, a Republican. There also were two additional candidates, including a strong independent candidate named Dan Smith who earned 15% of first choices.

The election utilized instant runoff voting. Once the two weakest candidates were eliminated, Kiss had 2,981 votes, Montroll had 2,554, and Wright led with 3,294. Montroll was thus eliminated. In the final pairing, Kiss defeated Wright by a margin of 4,313-4,061, keeping the incumbent Progressive in office. Although some Montroll supporters decided not to rank either Kiss (to Montroll’s left) or Wright (to Montroll’s right), a strong majority supported Kiss over Wright, vaulting him into the final round lead.

Supporters of instant runoff voting see this as a strong example of IRV at work. The frontrunner Wright had the most first choices and presumably would have won with plurality voting, but he lost when paired against his strongest opponent. Critics of instant runoff voting (IRV) focus on perceived problems with the election, however, and one of them is based on the fact that Montroll would have defeated both Kiss and Wright in a head-to-head election, yet was eliminated before the final round. More of Wright’s supporters backed the more centrist Montroll over the progressive Kiss and more of Kiss’s supporters backed Montroll over Wright. As a result, 4,067 voters overall preferred Montroll to Kiss, as opposed to 3,477 the other way around, and Montroll would have defeated Wright 4,597-3,668 in a two-candidate matchup.

The Condorcet criterion

Those are the basics in layman’s terms. Voting theorists would say that the Burlington mayoral race demonstrated that IRV fails the Condorcet criterion. It is named after the late 18th century French political scientist Marquis de Condorcet, who noticed a paradox in the aggregation of preferences through voting: even though any individual’s preferences are clearly defined, the collective ranking can be cyclic. In other words, in a 3-candidate race, it is possible for a majority of voters to prefer A to B, B to C, and C to A, making it hard to decide which candidate should be elected. Thus, there is not always a Condorcet winner – a candidate who defeats all others in pairwise elections.

The Marquis de Condorcet also noticed that even when there is a Condorcet winner, many voting systems do not necessarily elect that candidate. The basic plurality vote is one example, as was the method crafted by Condorcet’s rival, Jean-Charles de Borda – the Borda count, where voters rank candidates, and each ranking is worth a certain number of points. Other voting systems that similarly can fail to elect a Condorcet winner are instant runoff voting, approval voting, and range voting, and they are all said to fail the Condorcet criterion, which requires a voting system to always elect a Condorcet winner if there is one.

Condorcet proposed a new voting system to solve this problem, which today can be seen as a number of variants known as Condorcet methods. They differ in how they resolve ties in the absence of a Condorcet winner, but they all fulfill the Condorcet criterion. Such methods are not used by any government today, but nevertheless the Condorcet criterion continues to be one of the benchmarks by which a voting system is judged.

Why always electing the Condorcet Winner seems to make sense – but doesn’t

Nobody would dispute that in a two-person election, if more people like candidate A than candidate B, candidate A should win. It seems to follow, then, that in a three-person election, if more people like candidate A than candidate B, and more people like candidate A than candidate C, candidate A should win. The logic is simple enough: if you beat everybody, then you win. If the New Orleans Saints win every single football game on their schedule, they’re considered the best team, and the same standard should apply to elections. Indeed, if elections were held like football playoffs, then a Condorcet candidate would always win.

The problem is that in football, each game is inherently a one-on-one contest – not the case with elections. Voters must consider a full range of candidates before casting their ballot, and candidates compete for votes with more than one opponent. If there is a Condorcet winner, it means that he or she is preferred to every other candidate – not necessarily liked more than other candidates and not necessarily ready to represent the constituents.

Let me explain. If candidate A beats both B and C, that candidate is preferred to both of them by a majority of voters. That doesn’t mean that he is liked more than them, or even at all – very conceivably, it could mean that he is simply disliked less. Condorcet winners are centrist by nature, regardless of the preferences of the electorate. In modern political terms, they are embodied by conservative Democrats, liberal Republicans, and centrist independents like Joe Lieberman.

Consider an election with three candidates: a strong liberal who commands between 40% to 50% of the vote, a moderate with about 10% to 15%, and a strong conservative between 40% and 50%. By being everyone’s second choice, the moderate will certainly be the Condorcet winner as long as neither of the two more extreme candidates earns a majority of the vote. If the electorate is moderate, then great – the Condorcet winner makes sense. But if the electorate mostly wants something to the left or right of the center, is it still the case that the moderate should always win? Wouldn’t the 80% to 90% of voters who lean clearly to one side prefer that their candidate have a nonzero chance of winning, as opposed to the impossibility of victory under Condorcet methods?

Agreeing that the Condorcet criterion is desirable is equivalent to saying that moderate candidates should always win. But despite the hand-wringing over increasing partisanship and polarization, there are cases where more off-center candidates are deserving of election, no matter how much one might hate their policies. Any election system that favors extremists would be considered unreasonable; the same rationale must be applied to moderates.

Note that moderates can win with instant runoff voting – for example, Joe Lieberman won a near-majority in 2006 in his re-election for U.S. Senator after losing the Democratic Party primary, and would have cruised under IRV. But having them always win would not reflect the fact that sometimes a city, state or country wants leaders who want to transform the center, to move voters their way, like a Franklin Roosevelt or a Ronald Reagan.

Just because a candidate is hated the least doesn’t mean he or she is liked the most. Put another way, quite often a Condorcet winner might actually never have a chance to be win a one-on-one race against other candidates because that Condorcet candidate lacks enough support to keep other candidates from running. So choosing the centrist candidate every time is just falling into the fallacy of the middle ground. It’s tempting to always compromise between two distinct positions, but the compromise might be worse than either of them. We shouldn’t always revert to the least common denominator when electing our representatives, and neither should our electoral system.

Turning to Burlington

Looking to Burlington, Democrat Andy Montroll had a clear chance to defeat a relatively unpopular incumbent mayor to his left. His party had not been elected mayor for three decades, but still ran well in many elections in the city. The mayor was vulnerable, but Montroll only secured 22% of first choices and only 29% when the field was reduced to three, basically failing to make the case for his candidacy to enough people. If Montroll had won due to Condorcet voting being in place, the resulting controversy in Burlington would likely have been far louder than the outcry against Kiss’s IRV victory. Having a candidate win after being in last place when the field was reduced to three would have taken a lot of explaining to voters. They might have accepted the results; more likely, they would have challenged them, particularly if they understood that Democrats would suddenly be the dominant party in mayor’s race even when failing to finish in the top two.

Conclusion

Though I framed failing the Condorcet criterion as a criticism of IRV, advocates of other voting systems have been faced with the same accusations. While the Condorcet winner usually deserves to get elected, there are cases to the contrary. Thus this particular voting system criterion is far less important in discussions of single-winner methods than one might assume.