Choice Paradoxes & Collective Decision-Making

Abstractions about how individual and collective choice breaks from rational-choice predictions — expected-utility violations like the Allais and Ellsberg paradoxes, voting-theory results like Arrow's impossibility and the median voter theorem, and coordination puzzles like the El Farol bar problem.

14 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.

• Allais Paradox — An engineered pair of lottery choices whose majority preference pattern (A over B, D over C) violates the independence axiom of expected-utility theory, isolating the certainty effect as the culprit.
• Ambiguity Aversion — The regularity that people prefer options with known probabilities over those with unknown ones even at equal expected value — a Savage-violating tilt toward the precise that the single-prior model can't represent, repaired by scoring acts against a set of priors.
• 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.
• Certainty Effect — Capture the way people overweight an outcome made fully certain relative to one merely probable of equal expected value, so the move from 0.99 to 1.0 commands a disproportionate premium the arithmetic does not justify.
• Decoy Effect — Add a third option that is worse than one existing choice on every dimension but not strictly worse than the other, and preferences shift toward the option that dominates the decoy — even though the decoy itself is never chosen.
• Default Effect — Shift the distribution of choices without changing any option by flipping which alternative is preselected as the no-action outcome, because a stack of retention mechanisms makes people disproportionately keep whatever the default is.
• El Farol Bar Problem — The congestion model in which each agent independently decides whether to attend a capacity-limited bar, enjoyable only if uncrowded — so any prediction rule shared by all self-destructs, and the system resolves only through heterogeneous inductive predictors rather than convergence.
• Ellsberg Paradox — Show that people prefer betting on a known-composition urn over an ambiguous one of equal expected value on both colors at once — a pattern no single subjective probability can rationalize — proving ambiguity is a separately priced dimension of uncertainty distinct from risk.
• Filter bubble — The algorithmic narrowing of a user's information exposure when a recommender optimizes for short-term engagement on revealed preference — a self-reinforcing feedback loop that no user chose and no user effort can dissolve, correctable only in the ranking pipeline.
• 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.
• Monty Hall problem — A worked three-door puzzle in which switching wins ⅔ of the time because the host's reveal was constrained by what he knew — drilling the move of updating on the protocol that produced an observation, not on its bare surface.
• 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.
• St. Petersburg Paradox — A gamble whose expected monetary value is infinite yet which real deciders will pay only a few coins to enter, exposing that a value function linear in money mishandles fat-tailed payoffs and must be replaced by a concave or bounded utility.