The Squared Coefficient of Variation as an Inequality Index: A Social Evaluation Characterization
Bibliographic record
Abstract
The squared coefficient of variation (C2) is a well-known index of relative inequality. However, the existing economic theory of inequality does not contain a characterization of this index in terms of the properties of the underlying social evaluation function. It is well-known that if the Atkinson-Kolm-Sen (AKS) index of relative inequality derived from a social evaluation relation defined on a space of distributions is C2, it is necessary that the relation satisfies a ¡®transfer neutrality¡¯ condition. This paper obtains a complete characterization of the index by proving the converse. It is shown that, in the presence of other standard assumptions on the social evaluation relation, transfer neutrality implies a particular social evaluation function and that the corresponding AKS relative inequality index coincides with C2. This inequality index and the corresponding social evaluation function is then applied in a relatively unexplored area of empirical research. It is shown that in India inequality (as measured by C2) in the distribution of a variable that indicates the width of accessibility of bank credit increased in the ten or so years following the introduction of economic reforms in the early 1990s. At the same time there was an increase in the average value of this indicator. The question, therefore, arises as to the direction of change of over-all social welfare from this particular attribute. The social evaluation underlying C2 implies that, on balance, there was a decline in the welfare of the country in this respect.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".