To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best among 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! Despite their simplicity, mathematical tractability made models like the voter model (VM) and the local majority rule model (MR) useful to describe in simple terms such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbours 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, to reduce the cognitive load. Our analysis in grounded on the introduction of a model that generalises the two existing VM and MR models, 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 that another speed-accuracy trade-off is 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，个体群体必须能够快速且准确地在不同质量的备选方案中做出最佳集体决策。群居动物始终致力于此，植物和真菌也被认为具有类似能力。自主机器人集群可通过编程实现最佳-n决策，以协作完成各项任务。最终，人类对此有至关重要的需求，但许多时候本应表现更佳！尽管投票模型（VM）和局部多数规则模型（MR）结构简单，但其数学可处理性使其能够简洁描述此类集体决策过程。为达成共识，个体通过与社交网络中的邻居互动来改变观点。至少在动物与机器人群体中，更优质量的选项往往被更频繁交换，从而比低质量选项传播更快，最终促成最优选项的集体选择。本研究探讨了个体在汇总他人意见时出现错误的影响——例如因降低认知负荷所导致的失误。我们的分析基于一个统一现有VM与MR两种模型的新框架，揭示了由个体认知努力调节的速度-精度权衡。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，并采用异质平均场方法证明网络连接性同样调节着另一种速度-精度权衡。一个有趣的发现是：网络连接性降低反而会提升集体决策的准确性。