How do we pick a winner? The Condorcet paradox and our crazy primary season

Remember a couple of weeks ago when I said I’d do a deeper dive on some new-to-me concepts? Well, primary season here in the U.S. seems like a good time to look at the Condorcet Paradox.

Let’s start with a brief look at Simpson’s paradox, since Condorcet is a variant.

Simpson’s paradox is the ability to use statistics to argue either side. This video makes it easy, but if you don’t want to take the four minutes to watch it, it goes something like this:

Let’s say you’re testing two drugs for effectiveness over two days. On Day 1, Drug A helps 63 of 90 people (70%) and Drug B helps 8 of 10 people (80%). On Day 2, Drug A helps 4 of 10 people (40%) and Drug B helps 45 of 90 people (50%).

Drug B won on both days, so it’s the more effective drug, right? Well, wrong. If you add them up over the two days, Drug A helped 67% of people while Drug B helped 53% of people.

You can go a little deeper with this video, which seems to prove that I’m a rabbit, or something like that.

The Condorcet variant applies specifically to elections involving more than two people (or options). It says you can’t accurately pick a winner.

The video below goes into why, and shows how, in a field of five candidates, a single round of voting can yield five different winners, depending upon how you decide to count.

Let’s move this briefly into the realm of U.S. politics. Briefly, because I’m probably not going to get it right if I go on too long.

First off, if you haven’t been following what’s going on in the Alabama Democratic Party (and really, unless you’re a democrat in Alabama, why would you?), spend five minutes watching a little something my colleague Kyle Whitmire put together last October.

It’s a perfect overview of politics in the U.S. these days.

Remember Paul Ryan? He was speaker of the House of Representatives until 2018. That ended 13 months ago and I have to ask if you remember him, which is a good illustration of the American attention span. He didn’t initially endorse Donald Trump during the 2016 election season, so his approval rating took a nosedive and he changed his mind.

Changing one’s mind is the sort of thing that in 2004 Republicans said, essentially, disqualifies you from office.

So basically, if you’re stubborn, refuse to incorporate new evidence into your opinions and only hold people who root for the other team accountable, it’s all good. Noah was 900 years old when he built a giant boat by himself, the Earth is flat and our planet is the center of the universe, because if you never accept new information, you’re all good on the old stuff!


In the biblical story of the Garden of Eden, when Eve eats the fruit of the Tree of Knowledge, Adam and Eve realize they’re naked. It’s not that they weren’t naked before, they simply didn’t notice, or understand what that meant.

That’s what happens here. Nothing changes with our election, we just get a better understanding of what we’re looking at when we see numbers.

A little knowledge, on one hand, is a dangerous thing. Ignorance, on the other, is bliss. Maybe. I kind of like having the control of knowing more stuff.

Polls might be the biggest problem with our elections, especially in primary season, when there can be a dozen or more candidates. You can lead a field of 12 with less than 10% of the vote. You could pick up 12% of the vote and be at 50% over everyone else (11 candidates at 8% is 88%, leaving you with 12%, or 50% more of the vote than everyone else).

It’s nice to be leading, but who wants to brag about being the candidate that 88% of people aren’t interested in? [The snarky answer, of course, being someone running against a bunch of candidates that 92% of voters aren’t interested in.]

Polls also don’t mean much when we get down to two candidates (while technically we’re never down to only two candidates, our de facto two-party system marginalizes third-party candidates and, for the most part, they tend to show up as rounding errors, at least over the past couple of decades — Ross Perot certainly took votes away from George W. Bush in 1992 and Ralph Nader probably had something of an impact in some states in 2000).

Polls don’t matter much for three reasons:

(a) If you poll people nationally, you’re gauging popular vote, which is not an indicator of who wins the election, since we have a representative democracy that makes use of an electoral college system. Donald Trump received 2.9 million fewer votes than Hillary Clinton in 2016. He was the fifth president to receive a minority of the popular vote.

(b) We don’t have the capacity as individuals to process large sets of data all at once. The more meaningful poll — and let’s be honest, not all polls are generalizable — would be percentage of voters in Alaska voting for a candidate, plus the percentage of voters in Alabama voting for a candidate, and Arizona and Wyoming and Maine and Oregon and Texas and … you get the idea. The reason that’s more meaningful is the electoral college system. Unfortunately, with the exception of perhaps a handful of outliers, you can’t just give people fifty-plus sets of percentages and expect them to be able to extrapolate the pertinent information.

(c) The Condorcet paradox. When we poll for Candidate A vs. Candidate B vs. Candidate C, you run into the problem where people prefer candidate A to candidate B, candidate B to candidate C, and candidate C to candidate A. Who wins? As we saw in the video above, it all depends on how you decide to count.


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