What happens when a group has to decide. Aggregating rankings into one social order, May's theorem settling the two-candidate case, and the Condorcet paradox that opens the three-candidate one. Then the methods and their measured failures: Condorcet rules and the three ways they break cycles, the Borda count, plurality and the spoiler effect, approval voting, and a worked 17-voter election where raising the winner on two ballots makes that winner lose. Arrow's impossibility with its four conditions and the escapes each one buys, independence of irrelevant alternatives, Gibbard-Satterthwaite on strategic voting, and the median voter theorem as the reward for restricting the domain. It closes with apportionment (quota, Hamilton, the Alabama paradox worked through, divisor methods and Balinski-Young) and fair division (divide and choose, proportionality against envy-freeness, Selfridge-Conway). Scoped against boolean, which derives Arrow's theorem by Fourier analysis, and gametheory, which states Gibbard-Satterthwaite in passing.
Free to start · adaptive placement finds your level · reviews timed so it stays learned.
Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Social Choice exactly where it's useful.