Why Democracy Is Mathematically Impossible

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. ▀▀▀ 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 ▀▀▀ 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: ▀▀▀ 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