School of Mathematics, Southeast University, Nanjing, 210096, China.
Institute of Industrial and Systems Engineering, College of Information Science and Engineering, Northeastern University, Shenyang, 110891, China.
Phys Rev E. 2020 Jun;101(6-1):062419. doi: 10.1103/PhysRevE.101.062419.
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.
惩罚被认为是促进和维持合作的有效机制。在大多数现有模型中，惩罚总是与合作和背叛一起作为第三种策略出现，并且通常假设它是根据个体决策规则而不是集体决策规则来执行的。与以往的工作不同，我们采用了一种民主程序，即合作者独立且同时投票决定是否对背叛者施加惩罚，我们建立了合作者对背叛者的惩罚意愿（WTPD）与是否对背叛者施加惩罚之间的关系。结果表明，在一致同意的惩罚下，群体可以进化为完全合作。值得注意的是，与自主惩罚相比，一致同意的惩罚是否更有利于合作，关键取决于执行惩罚所需的最少票数以及合作者的 WTPD。我们的研究结果强调了集体决策在合作进化中的重要性，并可能为解释现代社会民主的普遍性提供一个数学框架。
