How Voting Is Like a Klein Bottle
A new topological model connects a centuries-old voting paradox to a surface with no distinct inside or outside.
Quick read
Quanta explains how Condorcet’s voting paradox and Arrow’s impossibility theorem reveal limits to combining individual preferences into a collective decision. A new mathematical model represents the paradox as a Klein bottle, offering a geometric way to explore why reasonable voting rules can conflict.
- See how three consistent rankings can produce a cycle of pairwise winners.
- Learn why Arrow’s requirements cannot all be satisfied by one voting method.
- Explore a topological model built from the possible rankings of three candidates.
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