Ganesh Ayalvadi, Hauert Sabine, Valla Emma
School of Mathematics, University of Bristol, Bristol, BS8 1UG UK.
School of Engineering Mathematics and Technology, University of Bristol, Bristol, UK.
Swarm Intell. 2025;19(3):173-214. doi: 10.1007/s11721-025-00248-z. Epub 2025 May 6.
Collective decision-making is an important problem in swarm robotics arising in many different contexts and applications. The Weighted Voter Model has been proposed to collectively solve the best-of- problem, and analysed in the thermodynamic limit. We present an exact finite-population analysis of the best-of-two model on complete as well as regular network topologies. We also present a novel analysis of this model when agent evaluations of options suffer from measurement error. Our analytical results allow us to predict the expected outcome of best-of-two decision-making on a swarm system without having to do extensive simulations or numerical computations. We show that the error probability of reaching consensus on a suboptimal solution is bounded away from 1 even if only a single agent is initialised with the better option, irrespective of the total number of agents. Moreover, the error probability tends to zero if the number of agents initialised with the best solution tends to infinity, however slowly compared to the total number of agents. Finally, we present bounds and approximations for the best-of- problem.
集体决策是群体机器人技术中一个重要的问题，出现在许多不同的背景和应用中。加权投票者模型已被提出用于集体解决最佳问题，并在热力学极限下进行了分析。我们对完全网络拓扑以及规则网络拓扑上的二选一模型进行了精确的有限种群分析。当智能体对选项的评估存在测量误差时，我们还对该模型进行了新颖的分析。我们的分析结果使我们能够预测群体系统中二选一决策的预期结果，而无需进行大量的模拟或数值计算。我们表明，即使只有一个智能体初始化为更好的选项，达成次优解决方案共识的错误概率也会远离1，而与智能体总数无关。此外，如果初始化为最佳解决方案的智能体数量趋于无穷大，错误概率趋于零，不过与智能体总数相比增长缓慢。最后，我们给出了最佳问题的界限和近似值。
