Democracy might be mathematically impossible – here’s why. Head to to start your free 30-day 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.
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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. Massive thanks to Curtis Gilberts, and to Radiolab -- listen to their great episode on voting systems here
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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.-
Geanakoplos, J. (2005). Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26(1), 211-215. -
References:
Arrow, K. J. (2012). Social choice and individual values (Vol. 12). Yale university press. -
Arrow, K. J. (1950). A Difficulty in the Concept of Social Welfare. Journal of Political Economy -
Black, D. (1948). On the rationale of group decision-making. Journal of political economy, 56(1), 23-34. -
Black, D. (1969). On Arrow’s impossibility theorem. The Journal of Law and Economics, 12(2), 227-248. -
Maskin, E., & Sen, A. (2014). The Arrow impossibility theorem. Columbia University Press. -
Gehrlein, W. V., & Valognes, F. (2001). Condorcet efficiency: A preference for indifference. Social Choice and Welfare -
Dardanoni, V. (2001). A pedagogical proof of Arrow’s Impossibility Theorem. Social Choice and Welfare, 18(1), 107-112. -
McCune, D., & Wilson, J. (2023). Ranked-choice voting and the spoiler effect. Public Choice, 196(1), 19-50. -
Santucci, J. (2021). Variants of ranked-choice voting from a strategic perspective. Politics and Governance, 9(2), 344-353. -
Kaminski, M. M. (2018). Spoiler effects in proportional representation systems: evidence from eight Polish parliamentary elections, 1991–2015. Public Choice, 176(3), 441-460. -
Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72(3), 831-847. -
Other references and election results -
Images & Video:
Minneapolis 2013 Debate Images:
4 Images from this article:
Arrow Nobel Prize Image from NYT Article:
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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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