To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best option among a set of alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programmed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it. Thanks to their mathematical tractability, simple models like the voter model and the local majority rule model have proven useful to describe the dynamics of such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbors in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, by the need to reduce the cognitive load. Our analysis is grounded on the introduction of a model that generalizes the two existing models (local majority rule and voter model), showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show the presence of another speed-accuracy trade-off regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy.

翻译：为了达成目标，个体群体必须能够在具有不同质量的备选方案中，就最佳选项做出快速且准确的集体决策。群居动物始终致力于此，植物和真菌也被认为同样如此。自主机器人集群也可被编程以实现最佳-n 决策，从而协作完成任务。最终，人类对此至关重要，且在很多情况下需要做得更好。由于其数学易处理性，诸如投票者模型和局部多数规则模型等简单模型已被证明有助于描述此类集体决策过程的动态。为了达成共识，个体通过与其社交网络中的邻居互动来改变自身观点。至少在动物和机器人中，质量更优的选项更频繁地被交换，因此传播速度比低质量选项更快，从而导致集体选择最佳选项。通过我们的工作，我们研究了个体在汇总他人意见时因减少认知负荷等需求而产生错误的影响。我们的分析基于引入一个推广了现有两种模型（局部多数规则和投票者模型）的模型，该模型展示了一种由个体认知努力调节的速度-准确性权衡。我们还研究了交互网络拓扑结构对集体动态的影响。为此，我们扩展了模型，并利用异质平均场方法，展示了另一种由网络连接性调节的速度-准确性权衡。一个有趣的结果是，网络连接性的降低对应于集体决策准确性的提高。