Social Choice & Voting Paradoxes

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Abstractions about collective preference, public choice, median voters, strategic allocation, and impossibility or participation paradoxes in voting.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Arrow's Impossibility Theorem — Prove that no ranked-preference voting rule over three or more alternatives can jointly satisfy four minimal fairness axioms — certifying the 'fair in every respect' region of design space empty and reducing the debate to which axiom to knowingly sacrifice.
• Median Voter Theorem — Under majority rule with single-peaked preferences on one policy dimension, binary competition converges to the median voter's ideal point, because that position is the unique Condorcet winner — any platform away from it is beaten by one moving closer.
• Paradox of Voting (Downs Paradox) — Locate the puzzle that turnout far exceeds what instrumental rationality predicts by pinning the decisiveness term near zero in the pB − C calculus, so the entire observed turnout must be carried by non-instrumental terms outside it.
• Pirate game — A toy sequential-bargaining model showing how backward induction in a propose-vote-or-eliminate mechanism lets the most senior proposer capture nearly the whole prize, because each voter's price is their continuation payoff and downstream subgames impoverish enough players to buy a cheap minimum coalition.
• Public Choice — The research program applying economics' rational-self-interest assumptions to politics — modelling voters, politicians, and bureaucrats as utility-maximizers responding to institutional incentives, so government failures read as predicted equilibrium and reform runs through the rules, not the roster.