Index Number Theory Using Differences Rather Than Ratios
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A bstract Traditional index number theory decomposes a value ratio into the product of a price index times a quantity index. The price (quantity) index is interpreted as an aggregate price (quantity) ratio. The present paper takes an alternative approach to index number theory, started by Bennet and Montgomery in the 1920s, which decomposes a value difference into the sum of a price difference plus a quantity difference. Axiomatic and economic approaches to this alternative branch of index theory are considered in the present paper. The analysis presented has some relevance to accounting theory in which revenue, cost, or profit changes need to be decomposed into price quantity components or where standard or budgeted performance is compared with actual performance (variance analysis). The methodology presented in the paper is also relevant for consumer surplus analysis.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it