Impacts of preferences on the emergence of cooperation.

Behavior decision making, where individuals can efficiently express their preferences for all options, has a great impact on cooperation. Hereby, we institute a minimal model in well-mixed populations where whether and how to sanction defectors are decided by cooperators via different decision-making mechanisms. The results illustrate that whether cooperation can outbreak depends on the cooperators' preferences for sanction and complying with the electoral outcome. We highlight the role of individuals' preferences in the emergence of cooperation and show that there exists an intermediate degree of the cooperators' preference for sanction at which the cooperators' preference for complying with the electoral outcome has a negligible impact on cooperation. We point out whether conformity facilitates the emergence of cooperation depends on the cooperators' preference for sanction. We find, compared with individual decision making, whether collective decision making is more conducive to promoting cooperation crucially depends on cooperators' preferences as well as the consensus required for employing sanction.

Evolution of cooperation under punishment.

Punishment has been considered as an effective mechanism for promoting and sustaining cooperation. In most existing models, punishment always comes as a third strategy alongside cooperation and defection, and it is commonly assumed to be executed based on individual decision rules rather than collective decision rules. Differently from previous works, we employ a democratic procedure by which cooperators cast votes independently and simultaneously for whether to impose punishment on defectors, and we establish a relationship between the cooperators' willingness to punish defectors (WTPD) and whether the punishment is inflicted on defectors. The results illustrate that the population can evolve to full cooperation under consensual punishment. It is noteworthy that, compared with autonomous punishment, whether consensual punishment is more in favor of cooperation crucially depends on the minimum number of votes required for punishment execution as well as the cooperators' WTPD. Our findings highlight the importance of collective decision making in the evolution of cooperation and may provide a mathematical framework for explaining the prevalence of democracy in modern societies.

Promote or hinder? The role of punishment in the emergence of cooperation.

Investigation of anti-social punishment has shaken the positive role of punishment in the evolution of cooperation. However, punishment is ubiquitous in nature, and the centralized, apposed to decentralized, punishment is more favored by certain modern societies in particular. To explore the underlying principle of such phenomenon, we study the evolution of cooperation in the context of pro- and anti-social punishments subject to two distinct patterns: costly centralized and decentralized punishments. The results suggest that the pattern of punishment has a great effect on the role of punishment in the evolution of cooperation. In the absence of anti-social punishment, the costly centralized punishment is more effective in promoting the emergence of cooperation. Anti-social punishment can subvert the positive role of punishment when anti- and pro-social punishments are in the same pattern. However, driven by centralized pro-social punishment, cooperation can be more advantageous than defection even in the presence of decentralized anti-social punishment.