2Majority-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.
Impact 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.
3Effective decision-making is essential in all areas of human society and, more generally, for all organisms. A fundamental question in this context is when a group of decision-makers is superior to individual decision-makers and vice-versa [1][2][3][4][5][6]. Both in human and animal collective decision making, the Condorcet Jury Theorem is one of the key principles guiding our thinking about this question [7][8][9][10][11][12][13][14]. In a nutshell, for pairwise decision problems (e.g. disease-, lie-or predator detection), Condorcet's Jury Theorem states that a group of decision-makers employing the majority rule is superior to individual decision-makers in contexts where individuals are relatively accurate (i.e. accuracy > 50%); conversely, individual decision-makers are superior to majority voting groups in contexts where individuals are relatively inaccurate (i.e. accuracy < 50%). Consequently, across a diverse range of fields ranging from organismal behaviour and human psychology to political sciences, two heuristics are commonly employed [7-12]: (i) groups of decision-makers outperform individuals only in contexts where individuals are relatively accurate and (ii) the majority rule is a powerful mechanism to reap the benefits of collective decision making. We here show that both statements are not true, and in doing so explain the ubiquity of quorum decision rules in the collective behaviour of humans and other organisms [15][16][17][18][19][20][21].Over the past few decades, substantial research effort has focussed on two key explicit assumptions underlying Condorcet's Jury Theorem, independence (i.e. judgments/votes by different members of th...