Why Democracy Is Mathematically Impossible

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

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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.

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A few great proofs of Arrow’s impossibility theorem:
Yu, N. N. (2012). A one-shot proof of Arrow's impossibility theorem. Economic Theory, 523-525.- https://ve42.co/Yu2012
Geanakoplos, J. (2005). Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26(1), 211-215. - 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 decision-making. Journal of political economy, 56(1), 23-34. - https://ve42.co/Black1948
Black, D. (1969). On Arrow's impossibility theorem. The Journal of Law and Economics, 12(2), 227-248. - 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), 107-112. - https://ve42.co/Dardanoni2001
McCune, D., & Wilson, J. (2023). Ranked-choice voting and the spoiler effect. Public Choice, 196(1), 19-50. - https://ve42.co/McCune2023
Santucci, J. (2021). Variants of ranked-choice voting from a strategic perspective. Politics and Governance, 9(2), 344-353. - 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), 441-460. - https://ve42.co/Kaminski2018
Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72(3), 831-847. - 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

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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
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https://www.youtube.com/watch?v=qf7ws2DF-zk