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The asymmetry between spite and altruism.
Shun Kurokawa1, Sabin Lessard2
1Graduate School of Information Science and Technology, The University of Osaka, 1-5 Yamadaoka, Suita, 565-0871, Osaka, Japan.
Theoretical Population Biology
|November 20, 2025
Summary
Altruistic behavior is more common than spiteful behavior due to mathematical constraints on social groups. Positive assortment favors altruism, while negative assortment, needed for spite, is mathematically limited, especially in larger groups.
Area of Science:
- Evolutionary biology
- Game theory
- Mathematical modeling
Background:
- Empirical data show altruism is more frequent than spite in nature.
- Both altruistic and spiteful behaviors are costly to the actor and require evolutionary support mechanisms like assortative interactions.
Purpose of the Study:
- To provide a general mathematical explanation for the observed asymmetry between altruism and spite.
- To investigate the role of social group composition and assortment patterns in the evolution of these behaviors.
Main Methods:
- Utilized a linear game model with fixed group size (n).
- Derived an index of assortativity to quantify interaction patterns.
- Analyzed evolutionary dynamics in both infinite and finite populations.
Main Results:
- Positive assortment, favoring altruism, has no fundamental mathematical limits, allowing for complete group segregation.
- Negative assortment, required for spite, faces significant constraints, particularly in larger or unbalanced populations.
- The mathematical feasibility of positive assortment creates more evolutionary opportunities for altruism than for spite.
Conclusions:
- The rarity of spiteful behavior can be explained by fundamental mathematical constraints on negative assortment patterns.
- Assortment patterns, rather than specific population structures, are key to understanding the prevalence of altruism over spite.
- This study offers a general framework for the evolution of social behaviors based on group composition and interaction biases.
Keywords:
Group-structured populationHamilton’s ruleIndex of assortativityNegative relatednessSocial behaviorMore Related Videos
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