In this paper we address the general question of how social influence determines collective outcomes for large populations of individuals faced with binary decisions. First, we define conditions under which the behavior of individuals making binary decisions can be described in terms of what we call an influence-response function: a one-dimensional function of the (weighted) number of individuals choosing each of the alternatives. And second, we demonstrate that, under the assumptions of global and anonymous interactions, general knowledge of the influence-response functions is sufficient to compute equilibrium, and even non-equilibrium, properties of the collective dynamics. By enabling us to treat in a consistent manner classes of decisions that have previously been analyzed separately, our framework allows us to find similarities between apparently quite different kinds of decision situations, and conversely to identify important differences between decisions that would otherwise appear very similar.
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