The Import of Condorcet

Marquis de Condorcet with voters' preferences in the 2022 special election

The August 16, 2022 special election for Alaska’s one and only seat in the U.S. House was notable for several reasons, including being the first time ranked-choice voting (RCV) was used to fill the seat. Students of voting methods have also noted that it exhibited what’s known as a Condorcet failure: it failed to elect a candidate — Nick Begich, in this case — who was preferred by a majority in every head-to-head contest against his opponents.

Let me elaborate on what exactly happened and what it means.

Under Alaska’s new voting system, the top four winners of a nonpartisan first round advance to a runoff, which uses RCV. In this case, one of the four, the independent (Democratic-leaning) Al Gross, dropped out before the election, leaving three candidates: Mary Peltola, a Democrat, Sarah Palin, a Trump-endorsed Republican, and Nick Begich, a more moderate Republican. Voters ranked their choices on their ballot, and the tallying went round-by-round, eliminating the last-place candidate at each until one candidate had a majority of votes in the final round.

In the first round, Peltola won about 40 percent of the vote to Palin’s 31 percent and Begich’s 28 percent. Begich was therefore eliminated. According to the preferences of those who had ranked him first, about 50 percent of his votes transferred to Palin, about 29 percent transferred to Peltola, and the rest were “exhausted” — that is, they didn’t participate in subsequent rounds because those voters specified no next preference.

In the second round, Peltola won with 51.5 percent of the vote vs. Palin’s 48.5 percent. At first glance, a success for RCV, which ensured that the winner had majority support in the final-round contest against her opponent. RCV deems a mere plurality of votes insufficient to declare a winner, in alignment with Alexander Hamilton’s recognition, all the way back in 1788, that it’s “unsafe to permit less than a majority to be conclusive”. It helps reduce the vulnerability of the electoral system to vote-splitting, which is an obstacle to accurate representation.

So what’s the problem? RCV outcomes are very sensitive to the order in which candidates are eliminated, in the round-by-round tallying process. If Palin had been eliminated instead of Begich in the first round, he would have defeated Peltola in the second, and won the seat. That’s because Begich was a Condorcet winner in this election. This means that, using voters’ preferences as specified on their ballots, if you simulate a pair-wise election between him and each of his opponents, one at a time, you find that he wins a majority in each case.

According to a mathematical analysis of the ballot data, about 88,000 voters ranked Begich higher than Peltola, against 79,000 who preferred Peltola over Begich. Matched up against Palin, Begich fares even better, with about 101,000 preferring him vs. 64,000 preferring her. Since he is majority-preferred against all of his opponents, he is a Condorcet winner — named for the Marquis de Condorcet (pronounced “con-dor-say”), who first wrote about the idea in the late 18th century.

A Condorcet winner does not exist in every election, due to the intransitivity of collective preferences. When one does exist, it indicates a candidate with broad approval among the electorate — a consensus-oriented candidate, in other words, someone who may not command a lot of first preferences but is at least acceptable to a wide range of voters.

Enough background. The question to turn to now is, does this mean Begich should have won the election?

First of all, “should have” is in a sense a very subjective term, which many people will evaluate according to their own partisan political views. But that is not what I’m talking about here — I want to consider the question from a “meta-political” perspective, in terms of what procedures will generally work best for American democracy. The choice of voting method is meant to apply across elections and not just be favored or disfavored ad hoc, on the basis of particular outcomes. And what benefits one party in one instance may also hurt that same party in others.

Naturally, many Democrats will celebrate RCV for Alaska because a Democrat won. And many Republicans will decry it for the same reason. But the real question is, what method will give the best chance for the best representation?

To be clear, there is no question of RCV “misfiring” here. It worked as designed; and while it did not fully solve the vote-splitting problem, it was still a great improvement over the plurality method. One can’t blame RCV for the fact that the election was between two Republicans and one Democrat. Potentially, one of the Republicans could have withdrawn, and depending on which one it was, could have secured the seat for her party.

Still, it is notable — and, I would say, a matter worthy of investigation — that a mostly Republican-leaning state will now be represented by a member of the opposite party. To what extent did the voting method create this circumstance, and how does it fit into our working theory of democracy?

RCV is known not to satisfy the Condorcet winner criterion, which says that when a Condorcet winner exists, they must be elected. Any voting method that guarantees this is called a Condorcet method — and RCV isn’t one.

Now, this is not necessarily a fatal flaw for RCV. Condorcet failures seem to be a relatively rare occurrence — usually, either there’s no Condorcet winner, or RCV elects them despite not being guaranteed to. We also know that no voting method satisfies all the desirable fairness criteria that experts have devised.

But the criterion does seem to have some value. How negatively should we judge RCV’s failure to satisfy it? Might we want to change to a method which does satisfy it?

In a recent essay, RCV advocate Steven Hill argues that a voting method should promote both a broad base of support and a strong core of support. A broad base implies wide approval or acceptance, which Condorcet methods promote. A strong core, on the other hand, implies strong enough leadership to have many supporters who will rank the candidate highest. This, Hill argues, Condorcet methods do not promote — while RCV promotes both values.

I agree that both types of support are useful indicators of how deserving a candidate is of winning their seat. A candidate — and also, parties — should be able to adjust to the electoral rules given to them, and to generate enough enthusiasm to get a lot of first rankings, if they wish to win. At the same time, ideally they should also have broad approval from the electorate they will represent.

The consensus-promoting tendency of Condorcet methods is especially desirable, I think, where, as in Alaska, we are asking one individual to represent an entire state or district. Where we are filling multiple seats for a representative assembly, proportional representation (PR) is best, and can be achieved with multi-member districts and the single transferable vote — a multi-winner type of ranked-choice voting. (Other forms of PR are also possible.)

But with just one representative, there can be no proportionality. Doesn’t that make it all the more important that such a person command broad support? Perhaps even more important than the strength of their core support?

I’d say yes. I am supportive of RCV, especially in its multi-winner version, but for single-seat elections I think it’s important to have a method that satisfies the Condorcet criterion. For now, I see single-winner RCV as a step in the right direction. In the longer term, we should improve on it by adding Condorcet compliance. By this I mean specifying a method that works similarly to, but not the same as, standard RCV — because it guarantees the election of a Condorcet winner when one exists, whereas the latter does not.

Of course, complexity for voters is one thing that must be considered when evaluating voting methods. The idea of pair-wise comparisons between all pairs of candidates sounds daunting. But there’s good news — all voters would need to do is rank their choices, just as in standard RCV. Identifying the Condorcet winner, if any, can be done while crunching the ballots.

Condorcet-IRV works according to the same rules as RCV, with one exception — if the candidate you would eliminate in a given round under the standard rules is a Condorcet winner, eliminate the second-to-last-place candidate instead.

This system would give voters many of the same features as RCV, with less sensitivity to the order in which candidates are eliminated, and less scope for tactical voting to subvert the will of the electorate. Thus it would make for more accurate representation.

The main point is, especially in these highly polarized times, I don’t think we can afford to dismiss a principle that promotes consensus-oriented candidates.

So, is there a deficiency in the new method Alaska is using to elect its one House representative? I would say yes. But the response should not be to jettison RCV; it should be, rather, to improve on it.

Author: Dan Eckam

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