Quorums enable optimal pooling of independent judgements

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.\n\nImpact StatementTheory typically assumes that majority voting is optimal; this is incorrect - majority voting is typically sub-optimal, and should be replaced by sub-majority or super-majority quorum voting. This helps explain the prevalence of quorum-sensing in even the simplest collective systems, such as bacterial communities.