Voting Systems and the Condorcet Paradox | Infinite Series

by Super User, 2 months ago
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What is the best voting system? Voting seems relatively straightforward, yet four of the most widely used voting systems can produce four completely different winners. Get 10% off a custom domain and email address by going to

*Correction: The ballots at 1:20 were labeled incorrectly. At 1:20 the top ballot should read 1 Green, 2 Blue and 3 Purple and the bottom ballot should read 2 Green, 3 Blue and 1 Purple. Thank you to Hoarder who first noted this.

*Correction: What's stated is the converse of the Condorcet Criterion. Oops - Stating conditionals can be tricky! For more details, see:

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Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (

With access to a complete set of ranked ballots - which means we know every person’s opinions - it seems like a clear winner should emerge. But it doesn’t. The outcome of the election depends critically on what process you use to convert all those individual’s preferences into a group preference.

Further Resources:

Voting and Election Decision Methods

The Mathematics of Voting

The Mathematics of Voting, Power and Sharing

CGP Grey Voting Playlist

Comments answered by Kelsey:


Abi Gail

Lucas Hoffses