SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 636-659, January 2020.
Recent contributions have studied how an influence system may affect the wisdom of crowd phenomenon. In the so-called naïve learning setting, a crowd of individuals holds opinions that are statistically independent estimates of an unknown parameter; the crowd is wise when the average opinion converges to the true parameter in the limit of infinitely many individuals. Unfortunately, even starting from wise initial opinions, a crowd subject to certain influence systems may lose its wisdom. It is of great interest to characterize when an influence system preserves the crowd wisdom effect. In this paper we introduce and characterize numerous wisdom preservation properties of the basic French--DeGroot influence system model. Instead of requiring complete convergence to consensus as in the previous naïve learning model by Golub and Jackson, we study finite-time executions of the French--DeGroot influence process and establish in this novel context the notion of prominent families (as a group of individuals with outsize influence). Surprisingly, finite-time wisdom preservation of the influence system is strictly distinct from its infinite-time version. We provide a comprehensive treatment of various finite-time wisdom preservation notions, counterexamples to meaningful conjectures, and a complete characterization of equal-neighbor influence systems.

中文翻译：

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有限时间影响系统和人群效应的智慧

SIAM控制与优化杂志，第58卷，第2期，第636-659页，2020年1月。
最近的研究研究了影响系统如何影响人群现象的智慧。在所谓的朴素学习环境中，一群人持有的观点是统计学上对未知参数的独立估计。当平均意见在无限多的个体的范围内收敛到真实参数时，人群是明智的。不幸的是，即使是从明智的初步观点开始，受某些影响系统约束的人群也可能会失去智慧。刻画一个影响系统保留人群智慧效应的时间非常有趣。在本文中，我们介绍并描述了基本的法国-德格鲁特影响系统模型的众多智慧保存特性。与其像Golub和Jackson之前的幼稚学习模型一样，不需要完全收敛到共识，我们研究了法国-德格鲁特影响力过程的有限时间执行力，并在这种新颖的背景下确立了杰出家族（作为具有巨大影响力的个人群体）的概念。出人意料的是，影响系统的有限时间智慧保存与无限时间版本完全不同。我们提供了对各种有限时间智慧保存概念的全面处理，对有意义的猜想的反例，以及对等邻影响系统的完整描述。