How Voting Systems Can Be Flawed A Condorcet Paradox Explained

Added: 2026-05-06

[00:00:00]Bohr doing worse in the first round actually leads to him winning the election.

[00:00:06]Let's say we have three candidates, Einstein, Curie, and Bohr. [music] Now, Einstein and Bohr have very conflicting views, while Curie is ideologically in the center. [music] So, let's say Einstein gets 25% of the vote, Curie gets 30, and Bohr gets 45.

[00:00:24]No one got a majority, so it goes to the second round with Einstein being eliminated. And because people who voted for Einstein put down Curie as their second choice, well, Curie ultimately [music] gets elected.

[00:00:37]But now imagine that Bohr has a terrible campaign speech or proposes a very unpopular policy, so bad that some of his voters actually switch over to Einstein's [music] side.

[00:00:49]Well, now it's Curie that gets eliminated.

[00:00:52]And because she's more moderate, half of her voters select Einstein and the other half select Bohr in the second round.

[00:00:59]And this leads to Bohr winning.

[00:01:02]So, Bohr doing worse in the first round actually leads to him winning the election.

[00:01:09]Clearly, this isn't something that we want in a voting system.

[00:01:13]This is what the French mathematician Condorcet also thought. Condorcet was one of the first people applying logic and mathematics to rigorously study voting systems, making him one of the founders of a branch of mathematics known as social choice theory.

[00:01:29]He was working during the time of the French Revolution, so fairly determining the will of the people was having a cultural moment right then.

[00:01:39]In 1784, Condorcet's contemporary at the French Royal Society of Science, Jean-Charles de Borda, proposed a voting method