An important puzzle in the study of complex systems is the conditions under which the aggregation of information from interacting agents results in a stable or an unstable collective outcome. We present a general framework for thinking about the stability and instability of collective outcomes that focuses on the effects of mutual knowledge. We show that if a complex system of aggregated choice respects a mutual knowledge structure, then the prospects of a stable collective outcome are considerably improved. Our domain-independent results apply to collective choice ranging from perception, where an interpretation of sense data is made by a collection of perceptual modules, to social choice, where a group decision is made from a set of preferences held by individuals.
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