Applied Mathematics

Learn Social Choice

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.

What you'll learn

18 lessons in Social Choice

The aggregation problemMajority rule and May's theoremThe Condorcet paradoxCondorcet methodsThe Borda countPlurality and the spoiler effectApproval votingInstant-runoff and non-monotonicityArrow's impossibility theoremIndependence of irrelevant alternativesStrategyproofnessThe median voter theoremApportionment and quotaApportionment paradoxesDivisor methodsDivide and chooseEnvy-freenessStable matching and Gale-Shapley
How Erudia teaches

Built to be understood — and remembered.

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.

Related Applied Mathematics subjects