Group Size, Coordination, and the Effectiveness of Punishment in the Voluntary Contributions Mechanism: An Experimental Investigation
Bibliographic record
Abstract
We examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the marginal per capita return (MPCR), i.e. the return to each participant from each dollar that is contributed, is held constant. Moreover, the efficiency gains from the punishment mechanism are significantly higher in the 40-participant than in the four-participant treatment. This is true despite the coordination problems inherent in an institution relying on decentralized individual punishment decisions in the context of a larger group. It reflects increased per capita expenditures on punishment that offset the greater coordination difficulties in the larger group. However, if the marginal group return (MGR), i.e. the return to the entire group of participants, stays constant, resulting in an MPCR that shrinks with group size, no such offset occurs and punishment loses much but not all of its effectiveness at encouraging voluntary contributions to a public good. Efficiency is not significantly different from the small-group treatment.
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How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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) | 0.000 | 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 teacher head, 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".