Atkinson index¶
An inequality measure equal to the proportional mean income society could forgo while retaining the same equally distributed equivalent welfare at a chosen inequality-aversion parameter.
Core Idea¶
The value depends on the normative aversion parameter and income-domain conventions, especially zeros and negatives; comparisons across different parameters do not share one welfare judgment. Individual incomes enter an isoelastic social-welfare function, whose equally distributed equivalent is compared with arithmetic mean income to express the welfare loss attributable to inequality. 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¶
Atkinson index belongs to welfare economics and is useful where the analyst can specify the typed welfare economics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the population and income concept, weights and mean, inequality-aversion parameter epsilon, admissible income domain, equally distributed equivalent formula including epsilon one and limiting cases, normalization, decomposability and interpretation as welfare-equivalent loss are explicit. The scope is broad within that domain but bounded by the need for the population and income concept, weights and mean, inequality-aversion parameter epsilon, admissible income domain, equally distributed equivalent formula including epsilon one and limiting cases, normalization, decomposability and interpretation as welfare-equivalent loss are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the population and income concept, weights and mean, inequality-aversion parameter epsilon, admissible income domain, equally distributed equivalent formula including epsilon one and limiting cases, normalization, decomposability and interpretation as welfare-equivalent loss 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.
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 Atkinson index. Atkinson index 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 welfare economics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the population and income concept, weights and mean, inequality-aversion parameter epsilon, admissible income domain, equally distributed equivalent formula including epsilon one and limiting cases, normalization, decomposability and interpretation as welfare-equivalent loss are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of welfare economics because they reuse the typed welfare economics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Individual incomes enter an isoelastic social-welfare function, whose equally distributed equivalent is compared with arithmetic mean income to express the welfare loss attributable to inequality., and type the carrier, state every parameter and convention in the definition, test that the population and income concept, weights and mean, inequality-aversion parameter epsilon, admissible income domain, equally distributed equivalent formula including epsilon one and limiting cases, normalization, decomposability and interpretation as welfare-equivalent loss are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Atkinson index Domain-specific
Parents (1) — more general patterns this builds on
-
Atkinson index is a kind of Measurement Prime
The proposed strict upward parent is
prime:measurement.
Hierarchy path (1) — routes to 1 parentless root
- Atkinson index → Measurement
Neighborhood in Abstraction Space¶
Atkinson index sits in a moderately populated region (44th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Welfare, Production & Economic Choice (45 abstractions)
Nearest neighbors
- Compensation principle — 0.93
- Willingness to pay — 0.90
- Privileged group — 0.89
- Monotone preferences — 0.89
- Demerit good — 0.88
Computed from structural-signature embeddings · 2026-09-08