Friedman–Savage utility function¶
A wealth-dependent expected-utility curve with alternating concave and convex regions intended to explain simultaneous insurance purchase and lottery play.
Core Idea¶
The curve is concave at lower wealth, convex across an intermediate range and concave again at higher wealth, so local risk attitudes change as outcomes cross wealth regions. Expected utility weights outcome utilities by probability; changes in curvature alter whether a mean-preserving spread is disliked or preferred and can make insurance and gambling rational for the same person. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Friedman–Savage utility function belongs to decision theory and is useful where the analyst can specify the typed decision theory carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the wealth variable and utility normalization, locations and signs of curvature, lotteries or insurance contracts, initial wealth, expected-utility calculation and behavioral prediction are explicit. The scope is broad within that domain but bounded by the need for the wealth variable and utility normalization, locations and signs of curvature, lotteries or insurance contracts, initial wealth, expected-utility calculation and behavioral prediction are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the wealth variable and utility normalization, locations and signs of curvature, lotteries or insurance contracts, initial wealth, expected-utility calculation and behavioral prediction are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Friedman–Savage utility function can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Friedman–Savage utility function. Friedman–Savage utility function compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed decision theory carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the wealth variable and utility normalization, locations and signs of curvature, lotteries or insurance contracts, initial wealth, expected-utility calculation and behavioral prediction are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of decision theory because they reuse the typed decision theory carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, Expected utility weights outcome utilities by probability; changes in curvature alter whether a mean-preserving spread is disliked or preferred and can make insurance and gambling rational for the same person., and type the carrier, state every parameter and convention in the definition, test that the wealth variable and utility normalization, locations and signs of curvature, lotteries or insurance contracts, initial wealth, expected-utility calculation and behavioral prediction are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Friedman–Savage utility function Domain-specific
Parents (1) — more general patterns this builds on
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Friedman–Savage utility function is a kind of Expected Utility Prime
The proposed strict upward parent is
prime:expected_utility.
Hierarchy paths (4) — routes to 3 parentless roots
- Friedman–Savage utility function → Expected Utility → Expected Value → Aggregation → Micro Macro Linkage
- Friedman–Savage utility function → Expected Utility → Preference
- Friedman–Savage utility function → Expected Utility → Expected Value → Probability → Measure → Set and Membership
- Friedman–Savage utility function → Expected Utility → Expected Value → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Friedman–Savage utility function sits in a moderately populated region (40th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Welfare, Production & Economic Choice (45 abstractions)
Nearest neighbors
- Multi-attribute utility — 0.90
- Willingness to pay — 0.90
- Polytomous choice — 0.89
- Expectancy-value theory — 0.89
- Expenditure function — 0.89
Computed from structural-signature embeddings · 2026-09-08