The asymmetry between spite and altruism

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.