The Topological Problem with Voting

Video Description

We like to think that plurality voting is "fair", but it turns out that some unexpected paradoxes appear when you analyze it mathematically. In this video, we use topology and the Möbius strip to explain Chichilnisky's impossibility theorem, and we revisit the Möbius strip synthesizer. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds Thanks for the synths, Microkits! https://microkits.net/products/synth-a-sette 0:00 Introduction 2:21 The math of wanting things 4:20 Visualizing the constitution function 6:04 Möbius Piano v2 7:19 A strip can't retract onto its boundary 9:26 Does this mean anything? Möbius Voting: https://www.sciencedirect.com/science/article/abs/pii/0165176594900450 Arrow's Impossibility: https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/arrow.pdf Chichilnisky's Impossibility: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1367741 More Background on Chichilnisky: https://chichilnisky.com/wp-content/uploads/1982/11/The-Topological-Equivalence-of-the-Pareto-Condition-and-the-Existence-of-a-Dictator.pdf More Chichilnisky: https://www.jstor.org/stable/1880762