The wisdom of stalemates: consensus and clustering as filtering mechanisms for improving collective accuracy

Collective rule-breaking

Rules form an important part of our everyday lives. Here we explore the role of social influence in rule-breaking. In particular, we identify some of the cognitive mechanisms underlying rule-breaking and propose approaches for how they can be scaled up to the level of groups or crowds to better understand the emergence of collective rule-breaking. Social contagion plays an important role in such processes and different dynamics such as linear or rapid nonlinear spreading can have important consequences for interventions in rule-breaking. A closer integration of cognitive psychology, microsociology and mathematical modelling will be key to a deeper understanding of collective rule-breaking to turn this field of research into a predictive science.

Quantifying the impact of network structure on speed and accuracy in collective decision-making

Found in varied contexts from neurons to ants to fish, binary decision-making is one of the simplest forms of collective computation. In this process, information collected by individuals about an uncertain environment is accumulated to guide behavior at the aggregate scale. We study binary decision-making dynamics in networks responding to inputs with small signal-to-noise ratios, looking for quantitative measures of collectivity that control performance in this task. We find that decision accuracy is directly correlated with the speed of collective dynamics, which is in turn controlled by three factors: the leading eigenvalue of the network adjacency matrix, the corresponding eigenvector's participation ratio, and distance from the corresponding symmetry-breaking bifurcation. A novel approximation of the maximal attainable timescale near such a bifurcation allows us to predict how decision-making performance scales in large networks based solely on their spectral properties. Specifically, we explore the effects of localization caused by the hierarchical assortative structure of a "rich club" topology. This gives insight into the trade-offs involved in the higher-order structure found in living networks performing collective computations.

The wisdom of stalemates: consensus and clustering as filtering mechanisms for improving collective accuracy

Groups of organisms, from bacteria to fish schools to human societies, depend on their ability to make accurate decisions in an uncertain world. Most models of collective decision-making assume that groups reach a consensus during a decision-making bout, often through simple majority rule. In many natural and sociological systems, however, groups may fail to reach consensus, resulting in stalemates. Here, we build on opinion dynamics and collective wisdom models to examine how stalemates may affect the wisdom of crowds. For simple environments, where individuals have access to independent sources of information, we find that stalemates improve collective accuracy by selectively filtering out incorrect decisions (an effect we call stalemate filtering). In complex environments, where individuals have access to both shared and independent information, this effect is even more pronounced, restoring the wisdom of crowds in regions of parameter space where large groups perform poorly when making decisions using majority rule. We identify network properties that tune the system between consensus and accuracy, providing mechanisms by which animals, or evolution, could dynamically adjust the collective decision-making process in response to the reward structure of the possible outcomes. Overall, these results highlight the adaptive potential of stalemate filtering for improving the decision-making abilities of group-living animals.