Decision Under Risk & Ambiguity

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Abstractions about prospect theory, probability weighting, ambiguity aversion, paradoxical choices, minimax reasoning, and evaluation of uncertain outcomes.

13 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.
• 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.
• Cumulative Prospect Theory — A descriptive model that values gains and losses from a reference point and applies rank-dependent decision weights to cumulative probabilities before aggregating a risky prospect.
• 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.
• 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.
• Minimax Theorem — A theorem family giving hypotheses under which opposed max–min and min–max values coincide, thereby certifying a saddle value.
• Possibility Effect — People systematically overweight very small probabilities in risky choice, because crossing from impossible to barely-possible is a categorical shift in how an outcome is represented — the steep small-p branch of prospect theory's inverse-S weighting function.
• Probability Distribution — The complete specification of how probability mass or density is spread over a random variable's possible values — a measure that, once compressed to a named parametric family, encodes shape, moments, tails, and a generative claim about the process producing the data.
• Probability Weighting Function — Transform objective or stated probabilities into subjective decision weights, typically overweighting small probabilities, underweighting middle and high probabilities, and treating the zero and certainty boundaries nonlinearly.
• Random Variable — Translate an uncertain event into a measurable function X: Ω → ℝ on a probability space, so that a number attaches to each outcome and the whole apparatus of expectation, distribution, and convergence becomes computable before any value is observed.
• 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.
• Upside Potential Ratio — Compare an investment's expected above-target return with its downside deviation below the same minimum acceptable return by dividing first upper partial moment by the square root of second lower partial moment.