The Economics and Mathematics of Aggregation: Formal Models of Efficient Group Behavior
Bibliographic record
Abstract
The goal of this article is to provide a general characterization of group behavior in a market environment. A crucial feature of our approach is that we do not restrict the form of individual preferences or the nature of individual consumptions; we allow for public as well as private consumption, for intragroup production, and for any type of consumption externalities across group members. Our only assumption is that the group always reaches Pareto efficient decisions. We analyze two main issues. One is testability: what restrictions (if any) on the aggregate demand function characterize the efficient behavior of the group? The second question relates to identifiability; we investigate the conditions under which it is possible to recover the underlying structure — namely, individual preferences, the decision process and the resulting intragroup transfers — from the group’s aggregate behavior. Our approach applies to large (markets) or small (households) groups, with both private and public consumptions, with and without restrictions on trade, with monetary or real endowments. In particular, our approach generalizes the classical analysis of the aggregate demand of a market economy, as pioneered by Gerard Debreu, Ralph Manted and Hugo Sonnenchein; we devote a section of our work to this specific but important case. We show that in all these contexts, aggregation of individual behaviors involves a common mathematical structure, whereby the aggregate demand of the group, considered as a vector field, can be decomposed into a sum of gradients. The proper way to understand this structure, and ultimately to find necessary and sufficient condition for such a decomposition to be possible, is to use tools which were developed about 100 years ago, mainly by the French mathematician Elie Cartan, and which are known now-a-days as exterior differential calculus (EDC). The last section of this article is devoted to an exposition of EDC and contains the proofs of the results in the preceding ones.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".