Condorcet Minimax

Hello. This week, I wanted to talk about what I consider to be the fairest possible voting system.* Check out StuFLaW and the prologue of Natalia first. But now, let me explain the system known as Condorcet Minimax.

Notes on Other Voting Systems

There are also some other common voting systems that exist. However, I believe each of them have glitches. I'll go through them.

A random piece of clipart I found on the Interwebs.

First Past the Post ("normal" voting): encourages strategic voting, pushes towards a two-party system, disenfranchises candidates that everyone likes but no one loves, spoiler effect

Instant-Runoff Voting (ranked-choice voting): disenfranchises candidates that everyone likes but no one loves, increasing a candidate's vote total can cause them to lose

Borda Count: candidates preferred by a majority can lose, encourages strategic voting, reverse spoiler effect

Approval Voting: encourages strategic voting, often mimics First Past the Post when voters vote strategically

Score Voting: encourages strategic voting, often mimics First Past the Post when voters vote strategically

I won't go into depth about these issues, but of the above, I would probably pick ranked-choice. It largely doesn't encourage strategic voting** and is also relatively simple to explain, an advantage Condorcet Minimax does not have, which would make it difficult to advocate for.

Condorcet

To explain Condorcet Minimax, first I have to explain Condorcet. Here's the way Condorcet, also called Head-to-Head works. Everyone ranks the candidates, just like in several other systems, such as instant-runoff. For example, a rational ballot might look like this:

1. Elizabeth Warren

2. Kamala Harris

3. Joe Biden

This ballot indicates that this person's first choice is Elizabeth Warren, their second choice is Kamala Harris, and their third choice is Joe Biden. (Let's say that the rest of the field always loses to each of these three candidates, making them irrelevant.)

Now, with this data, you can look at the head-to-head matchups between each pair of candidates. Under the Condorcet system, the winning candidate is the one that beats everyone else in a head-to-head matchup. Let's say 65% of voters prefer Warren to Harris, 55% prefer Warren to Biden, and 75% prefer Harris to Biden. In this case, Warren has beaten everyone else in a head-to-head matchup, and she is declared the winner.

However, you might have noticed a problem. What if instead of 55% preferring Warren to Biden, 45% do? Then more voters prefer Biden than Warren. Wait, but more voters prefer Harris than Biden. And more voters prefer Warren than Harris. In this case, there is no winner. This is kind of a problem. You could have Condorcet fall back on another system, like ranked-choice or Borda. But that comes with the flaws of those other systems as well. Enter Condorcet Minimax.

Marquis de Condorcet, the inventor of the Condorcet system and, most importantly, a somewhat relevant image I can include in this post.

Condorcet Minimax

To explain how Condorcet Minimax works, let's look back at our example:

Warren beats Harris 65%-35%

Biden beats Warren 55%-45%

Harris beats Biden 75%-25%

Here's how you determine the winner. For each candidate, determine their worst matchup, and look at what percent of the votes they received. Whoever has the highest (or the maximum minimum) wins. So in this case, Harris's worst matchup is against Warren, where Harris got 35%. Biden's worst matchup is against Harris. He got 25%. Finally, Warren's worst matchup is against Biden, where she received 45% of the vote. So Warren wins again, since she had the maximum minimum.

But wait, plot twist. Let's say that Bernie Sanders got 48% of the vote against each of these three candidates, and beat everyone else. Or maybe he even lost to Marianne Williamson by a 48% margin as well; it doesn't matter. (She has met him in that field.) So actually, Sanders would win. What?***

A graphic of Marianne Williamson, from this article: https://thebulwark.com/the-intergalactic-presidency-of-marianne-williamson/

An Ethics Question

It's kind of an ethics question at this point, I think. There are a couple explanations for the vote total – maybe Sanders is well-liked by 48% of the population, his diehard supporters, his Bernie bros. Or maybe the population finds Sanders to be an acceptable choice in general, which is why he never gets gutted. Does he deserve to be elected?

I would say yes. The point of a Condorcet system is to find someone who no candidate is better than. In this system, no candidate is much better. I mean, in real life (not elections), is there that much of a difference between 48% of the population liking you and 51%? Anyway, that's the main "flaw" in Condorcet Minimax that I've seen. There's no spoiler effect, and it doesn't encourage you to strategically vote (I think).

Incentives

Another consideration is, what incentives would a Condorcet Minimax system create? Candidates would try to shore up their weakest matchups, making it so they would either shift their views to attract some voters of the other side, helping to create bipartisanship, trust, etc. though this could also be considered pandering. Alternatively, candidates might run attack ads on that candidate. Summarizing, I think this could be useful in terms of incentives to make candidates more likable all around, though it might encourage some dishonesty in campaigning.

Thanks for reading what I wrote. Remember Condorcet Minimax the next time you talk about voting methods with someone else.****

–beautifulthorns

Next: Addenda

*You may have heard about Arrow's Impossibility Theorem, which states that "no voting system is fair." This is a misrepresentation of what it states; it actually states that every voting system can screw up at times.

**Strategic voting is when you vote in a way that's different than your true preferences because you think voting that way could have a negative, or at least not maximally positive, impact. For example, if you supported Jill Stein in the 2016 election, you might not vote for her under First Past the Post, instead opting for Hillary Clinton, because voting for Jill Stein is essentially "throwing away your vote" since she has basically no chance to win.

***For fun, imagine I wrote one of these two paragraphs instead, and see if your opinions change. They shouldn't, if you're logical, but just let your emotions guide your opinions:

"But wait, plot twist. Let's say that Pete Buttigieg got 48% of the vote against each of these three candidates, and beat everyone else. Or maybe he even lost to Marianne Williamson by a 48% margin as well; it doesn't matter. (She has met him in that field.) So actually, Buttigieg would win. What?"

"But wait, plot twist. Let's say that Donald Trump got 48% of the vote against each of these three candidates, and beat everyone else. Or maybe he even lost to Marianne Williamson by a 48% margin as well; it doesn't matter. (She has met him in that field.) So actually, Trump would win. What?"

****Right after I wrote this sentence, I got worried that this wasn't a thing normal people had discussions about, and there might not be a next time. Oh well, I can talk to you about it if you want, using the chat feature. Or the comments.