Non-participant externalities reshape the evolution of altruistic punishment

TL;DR

This paper explores how non-participants, who can influence public goods positively or negatively, affect the evolution and sustainability of altruistic punishment in populations, challenging previous assumptions of their neutrality.

Contribution

It introduces the role of non-participants exerting externalities into evolutionary models of altruistic punishment, revealing their impact on the conditions for its dominance.

Findings

Positive externalities lower the threshold for altruistic punishment to dominate.

Negative externalities raise the threshold, hindering altruistic punishment.

Altruistic punishment can persist even when non-participation is discouraged under negative externalities.

Abstract

While voluntary participation is a key mechanism that enables altruistic punishment to emerge, its explanatory power typically rests on the common assumption that non-participants have no impact on the public good. Yet, given the decentralized nature of voluntary participation, opting out does not necessarily preclude individuals from influencing the public good. Here, we revisit the role of voluntary participation by allowing non-participants to exert either positive or negative impacts on the public good. Using evolutionary analysis in a well-mixed finite population, we find that positive externalities from non-participants lower the synergy threshold required for altruistic punishment to dominate. In contrast, negative externalities raise this threshold, making altruistic punishment harder to sustain. Notably, when non-participants have positive impacts, altruistic punishment thrives only if non-participation is incentivized, whereas under negative impacts, it can persist even when non-participation is discouraged. Our findings reveal that efforts to promote altruistic punishment must account for the active role of non-participants, whose influence can make or break collective outcomes.