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Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi 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 https://www.hover.com/InfiniteSeries *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: https://www.reddit.com/r/math/comments/6hh9sb/voting_systems_and_the_condorcet_paradox_infinite/diyft53/ Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Pantographs and the https://www.youtube.com/watch?v=KYaCtHPCARc Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) 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 http://www.ams.org/samplings/feature-column/fcarc-voting-decision The Mathematics of Voting https://www.math.ku.edu/~jmartin/courses/math105-F11/Lectures/chapter1-part1.pdf The Mathematics of Voting, Power and Sharing http://web.math.princeton.edu/math_alive/6/Notes1.pdf CGP Grey Voting Playlist https://www.youtube.com/playlist?list=PLej2SlXPEd37YwwEY7mm0WyZ8cfB1TxXa Comments answered by Kelsey: FossilFighters101 https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z12fi1jgnle5wre0k22puzfojxnbzjirk04 Abi Gail https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z13kin5rcqatih1i004cjdfwsofhi1hopgo Lucas Hoffses https://www.youtube.com/watch?v=XOzhF3QoTCA&lc=z13nilewrtbmfp24t04cgdlziqafvzbahkk0k