Testing Axioms Against Human Reward Divisions in Cooperative Games
Bibliographic record
Abstract
Axiomatic approaches are an appealing method for designing fair algorithms, as they provide formal structure for reasoning about and rationalizing individual decisions. However, to make these algorithms useful in practice, their axioms must appropriately capture social norms. We explore this tension between fairness axioms and socially acceptable decisions in the context of cooperative game theory. We use two crowdsourced experiments to study people's impartial reward divisions in cooperative games, focusing on games that systematically vary the values of the single-player coalitions. Our results show that people select rewards that are remarkably consistent, but place much more emphasis on the single-player coalitions than the Shapley value does. Further, their reward divisions violate both the null player and additivity axioms, but support weaker axioms. We argue for a more general methodology of testing axioms against experimental data, retaining some of the conceptual simplicity of the axiomatic approach while still using people's opinions to drive the design of fair algorithms.
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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 | 0.068 | 0.352 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.014 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".