Hoover index¶

An inequality measure equal to the share of total income or another resource that would need redistribution to achieve equal per-capita shares.

Version: v2 · 2026-09-19 · History
Domain-specific #: 4910
Domain group: Social Sciences
Origin domain: Economics & Finance
Subdomain: Inequality Measurement → Economics & Finance

Core Idea¶

The Hoover index interprets distributional imbalance as the minimum total share transferred from above-average to below-average units to reach equality. Positive deviations above equal share exactly balance deficits below it, and half the sum of absolute deviations gives the required redistribution fraction. 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.

The load-bearing residual is not the broad topic of inequality measurement. It is An inequality measure equal to the share of total income or another resource that would need redistribution to achieve equal per-capita shares.

How would you explain it like I'm…

Cookies to Move

Imagine some kids have lots of cookies and some have only a few. You want everyone to have the same amount. The Hoover index tells you what part of all the cookies you'd have to move from the kids with extra to the kids with too few.

How Much to Move

The Hoover index measures how unequally something, like money, is shared. Picture every group getting exactly its fair share. Groups above their fair share have extra; groups below have a shortfall, and the extra exactly equals the shortfall. The Hoover index is the smallest fraction of the total you'd need to move from the 'too much' groups to the 'too little' groups to make it equal. It goes from 0, already equal, up toward 1.

Minimum Redistribution Share

The Hoover index measures inequality as the smallest share of a total resource, such as income, that would have to be redistributed so that every unit gets an equal per-person share. For each group, compare its share of the resource with its share of the population. Groups above their fair share have surpluses, and groups below have deficits, and these two always balance exactly. Adding up all the gaps, ignoring their signs, and dividing by two gives the fraction that has to move. For this to work, the resource shares and population shares must be measured over the same groups, and each set must add to one. The index then runs from 0 to 1.

The Hoover index quantifies inequality as the minimum fraction of a total resource that must be transferred from above-average to below-average units to achieve equal per-capita shares. With a partition into groups, let r_i be group i's share of the resource and p_i its share of the population; the index is H = ½ Σ |r_i − p_i|. The factor of one half appears because positive deviations above equal share exactly balance deficits below it, so half the total absolute deviation equals the amount that must move. The construction requires that resource and population shares use the same partition and each sum to one, which bounds the index between zero and one. Results depend on the chosen partition, so it should be declared. It is a specific redistribution-based measure, distinct from other inequality indices, and should be compared with them rather than conflated.

Scope of Application¶

Hoover index belongs to inequality measurement and is useful where the analyst can specify population units, nonnegative resource shares, equal-share benchmark, absolute deviations, normalization and aggregation level, then evaluate resource and population shares use the same partition and sum to one, producing an index between zero and one. The scope is broad within that domain but bounded by the need for resource and population shares use the same partition and sum to one, producing an index between zero and one. 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 resource and population shares use the same partition and sum to one, producing an index between zero and one 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 Hoover index 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 Hoover index. Hoover 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: population units, nonnegative resource shares, equal-share benchmark, absolute deviations, normalization and aggregation level. Reject examples whose alleged carrier belongs to a different problem.
Lock the constitutive rule. Express resource and population shares use the same partition and sum to one, producing an index between zero and one independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of inequality measurement because they reuse population units, nonnegative resource shares, equal-share benchmark, absolute deviations, normalization and aggregation level, Positive deviations above equal share exactly balance deficits below it, and half the sum of absolute deviations gives the required redistribution fraction., and type the carrier, state every parameter and convention in the definition, test that resource and population shares use the same partition and sum to one, producing an index between zero and one, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Hoover index Domain-specific

Parents (1) — outgoing typed relations

Hoover index is a kind of Fairness Prime

What makes it its own entry: An inequality measure equal to the share of total income or another resource that would need redistribution to achieve equal per-capita shares.

Hierarchy path (1) — routes to 1 parentless root

Hoover index → is a kind of Fairness → presupposes Impartiality → is a decomposition of Symmetry

Neighborhood in Abstraction Space¶

Hoover index sits in a moderately populated region (54^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Descriptive Statistics & Correlation Measures (40 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25