Lottery (decision theory)¶
A discrete probability distribution over mutually exclusive outcomes or states, treated as an object of preference and choice under risk and often evaluated by probability-weighted utility in expected-utility theory.
Core Idea¶
A lottery in decision theory is a discrete probability distribution over possible outcomes. The lottery is the risky option as a whole, not the random mechanism, ticket, or outcome that eventually occurs. Expected-utility theory evaluates a lottery by assigning a utility to each outcome and taking the probability-weighted sum. Expected-utility theory evaluates a lottery by assigning a utility to each outcome and taking the probability-weighted sum.
Scope of Application¶
Use lottery for formal risky options whose outcome support and probability weights are explicit. Use lottery for formal risky options whose outcome support and probability weights are explicit.
- Expected utility. Computes probability-weighted utility.
- Choice under risk. Ranks alternative distributions.
- Game theory. Represents random outcomes and mixed consequences.
- Behavioral economics. Tests departures from expected-utility predictions.
- Policy analysis. Compares probabilistic consequences.
Clarity¶
Calling any uncertainty a lottery loses the formal object. Probabilities must be attached to mutually exclusive outcomes, and the whole distribution must be one option. The closest near miss sets the boundary: A probability distribution is closest: it becomes a decision lottery when its outcomes constitute one option whose preference can be compared with other options.
Manages Complexity¶
The representation separates beliefs about chance from values assigned to consequences. This allows two people to agree on probabilities yet rank the same lottery differently because their utilities differ. The central probability–utility tradeoff is this: Chance and value combine in expected utility but represent different judgments. A second normative axioms–descriptive behavior tension matters because Coherent preference models simplify analysis while people violate them systematically.
Abstract Reasoning¶
Use three linked moves: list the mutually exclusive outcomes; assign probabilities and verify they sum to one; treat the distribution as one option among alternatives. As a collapse test, the case exits when probabilities do not sum to one, outcomes are not the option's alternatives, or only the realized result remains. A fourth check is to if using expected utility, map outcomes to utilities separately.
Knowledge Transfer¶
Probability-weighted consequence representation transfers to medicine and engineering, but choice among risky options distinguishes a decision lottery from generic uncertainty. The nearest stopping boundary is explicit: A probability distribution is closest: it becomes a decision lottery when its outcomes constitute one option whose preference can be compared with other options. The inclusion test remains: An object is a decision-theoretic lottery when it specifies a discrete probability distribution over outcomes and is treated as a risky option available for comparison. The structure no longer applies when the case exits when probabilities do not sum to one, outcomes are not the option's alternatives, or only the realized result remains. No canonical parent prime is currently asserted; broader structural comparisons remain related-prime analogies until separately adjudicated in the DAG. Probabilities allocate unit mass over outcomes. Decision makers rank whole lotteries.
Relationships to Other Abstractions¶
Current abstraction Lottery (decision theory) Domain-specific
Parents (1) — more general patterns this builds on
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Lottery (decision theory) is a kind of Probability Distribution Domain-specific
Lottery (decision theory) is a strict kind of Probability Distribution: its frozen identity entails the parent's defining structure while adding domain-specific restrictions.
Hierarchy paths (5) — routes to 3 parentless roots
- Lottery (decision theory) → Probability Distribution → Random Variable → Function (Mapping)
- Lottery (decision theory) → Probability Distribution → Probability → Measure → Set and Membership
- Lottery (decision theory) → Probability Distribution → Probability → Measure → Aggregation → Micro Macro Linkage
- Lottery (decision theory) → Probability Distribution → Random Variable → Probability → Measure → Set and Membership
- Lottery (decision theory) → Probability Distribution → Random Variable → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Lottery (decision theory) sits in a moderately populated region (47th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Strategic Decision Biases & Mechanisms (29 abstractions)
Nearest neighbors
- Participation constraint (mechanism design) — 0.87
- Correlated equilibrium — 0.87
- Evaluation function — 0.86
- Evidential Decision Theory — 0.86
- Certainty Effect — 0.86
Computed from structural-signature embeddings · 2026-10-08