Bibliographic record
Abstract
Empirical evidence suggests that altruistic social behavior (helping others at a cost to oneself) is more common than spiteful behavior (harming others at a cost to oneself) in nature. Here, we provide a general mathematical explanation for this asymmetry based on fundamental constraints on the composition of social groups. Since both behaviors are costly to the actor, they require additional mechanisms to avoid being eliminated by natural selection, such as assortative interactions. When interactions tend to occur between similar individuals (positive assortment), altruism can evolve, whereas spite requires negative assortment. We use a linear game in groups of fixed size n to derive an index of assortativity, and we analyze evolution in both infinite and finite populations. We show that positive assortment faces no fundamental limits - complete segregation into homogeneous groups is always mathematically possible. In contrast, negative assortment is constrained, especially in larger groups and unbalanced populations. This asymmetry creates more opportunities for altruism to evolve than spite. Our results explain the empirical rarity of spiteful behavior without assuming any specific population structure or group formation mechanism, suggesting that the scarcity of spite may reflect fundamental mathematical constraints inherent to assortment patterns.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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".