Department of Computer Science, University of Sheffield, Sheffield, United Kingdom.
Centre for Adaptive Rationality, Max Planck Institute for Human Development, Berlin, Germany.
Elife. 2019 Feb 13;8:e40368. doi: 10.7554/eLife.40368.
Collective decision-making is ubiquitous, and majority-voting and the Condorcet Jury Theorem pervade thinking about collective decision-making. Thus, it is typically assumed that majority-voting is the best possible decision mechanism, and that scenarios exist where individually-weak decision-makers should not pool information. Condorcet and its applications implicitly assume that only one kind of error can be made, yet signal detection theory shows two kinds of errors exist, 'false positives' and 'false negatives'. We apply signal detection theory to collective decision-making to show that majority voting is frequently sub-optimal, and can be optimally replaced by quorum decision-making. While quorums have been proposed to resolve within-group conflicts, or manage speed-accuracy trade-offs, our analysis applies to groups with aligned interests undertaking single-shot decisions. Our results help explain the ubiquity of quorum decision-making in nature, relate the use of sub- and super-majority quorums to decision ecology, and may inform the design of artificial decision-making systems.
This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).
集体决策无处不在，多数表决和孔多塞陪审团定理充斥着对集体决策的思考。因此，人们通常认为多数表决是最好的决策机制，并且存在个体决策能力较弱的情况下不应汇集信息的情况。孔多塞及其应用隐含地假设只能犯一种错误，但信号检测理论表明存在两种错误，“假阳性”和“假阴性”。我们将信号检测理论应用于集体决策，以表明多数表决通常是次优的，并且可以通过法定人数决策来最优地替代。虽然法定人数被提议用于解决群体内部冲突或管理速度准确性权衡，但我们的分析适用于具有一致利益的群体进行单次决策。我们的结果有助于解释法定人数决策在自然界中的普遍存在，将使用亚多数和多数法定人数与决策生态学联系起来，并可能为人工决策系统的设计提供信息。
本文经过编辑过程，作者决定如何回应同行评审中提出的问题。审稿人的评估是所有问题都已得到解决（见评审意见）。
