Democracy might be mathematically impossible – here’s why. Head to https://brilliant.org/veritasium to start your free 30day trial and get 20% off an annual premium subscription.

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically. https://snatoms.com/

▀▀▀
Massive thanks to Prof. Eric Maskin for helping with the script. Thanks to Chris Dong for inspiring this video. Massive thanks to Latif Nasser for being part of this video. Massive thanks to Curtis Gilberts, and to Radiolab listen to their great episode on voting systems here https://radiolab.org/podcast/tweakvote

▀▀▀

A few great proofs of Arrow’s impossibility theorem:
Yu, N. N. (2012). A oneshot proof of Arrow's impossibility theorem. Economic Theory, 523525. https://ve42.co/Yu2012
Geanakoplos, J. (2005). Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26(1), 211215. https://ve42.co/Geanakoplos2005

References:
Arrow, K. J. (2012). Social choice and individual values (Vol. 12). Yale university press. https://ve42.co/Arrow2012
Arrow, K. J. (1950). A Difficulty in the Concept of Social Welfare. Journal of Political Economy https://ve42.co/Arrow1950
Black, D. (1948). On the rationale of group decisionmaking. Journal of political economy, 56(1), 2334. https://ve42.co/Black1948
Black, D. (1969). On Arrow's impossibility theorem. The Journal of Law and Economics, 12(2), 227248. https://ve42.co/Arrow1969
Maskin, E., & Sen, A. (2014). The Arrow impossibility theorem. Columbia University Press. https://ve42.co/Maskin2014
Gehrlein, W. V., & Valognes, F. (2001). Condorcet efficiency: A preference for indifference. Social Choice and Welfare https://ve42.co/Gehrlein2001
Dardanoni, V. (2001). A pedagogical proof of Arrow's Impossibility Theorem. Social Choice and Welfare, 18(1), 107112. https://ve42.co/Dardanoni2001
McCune, D., & Wilson, J. (2023). Rankedchoice voting and the spoiler effect. Public Choice, 196(1), 1950. https://ve42.co/McCune2023
Santucci, J. (2021). Variants of rankedchoice voting from a strategic perspective. Politics and Governance, 9(2), 344353. https://ve42.co/Santucci2021
Kaminski, M. M. (2018). Spoiler effects in proportional representation systems: evidence from eight Polish parliamentary elections, 1991–2015. Public Choice, 176(3), 441460. https://ve42.co/Kaminski2018
Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72(3), 831847. https://ve42.co/Brams1978

Other references and election results https://ve42.co/IODRefs

Images & Video:
Minneapolis 2013 Debate Images: https://ve42.co/Minn2013Debate
4 Images from this article: https://ve42.co/MinnDebateMPR
Arrow Nobel Prize Image from NYT Article: https://ve42.co/ArrowNYT

▀▀▀
Special thanks to our Patreon supporters:
Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Bruce, Burt Humburg, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, I. H., Jack Cuprill, John H. Austin, Jr., Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, TTST, Tj Steyn, Ubiquity Ventures, gpoly, john kiehl, meg noah, wolfee

▀▀▀
Directed by Petr Lebedev and Derek Muller
Written by Petr Lebedev and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Jakub Misiek and Ivy Tello
Filmed by Derek Muller
Additional Research by Gabriel Bean
Produced by Petr Lebedev, Derek Muller, Gabriel Bean, Rob Beasley Spence, Emily Lazard, Luke Lewis
Thumbnail contributions by Jakub Misiek, Ren Hurley, Peter Sheppard
Additional video/photos supplied by Getty Images
Music from Epidemic Sound

#democracy #voting #mathematics