Outside ideal settings, conventions are shaped by heterogeneous competing processes that can challenge the emergence of norms. In order to acknowledge this complexity, this paper develops a generalized account of conventions and identifies three trade-offs involved in their diffusion: (I) the trade-off between the imperatives of social, sequential, and contextual consistency that individuals balance when choosing between conventions; (II) the competition between local (bottom-up) and global (top-down) coordination, depending on whether individuals coordinate their behavior via interactions throughout a social network or external factors transcending the network; and (III) the balance between decision optimality (e.g., collective satisfaction) and decision costs when collectives with conflicting preferences choose a convention. A broadly applicable statistical physics framework for exploring these trade-offs is developed and applied to a sign convention in physics. The method can infer the structure of the underlying coordination game, the networks of social interactions involved, and the processes through which conflicts are resolved. This shows that the purpose of conventions may exceed coordination, and that individual preferences towards conventions are concurrently shaped by cultural factors and multiple social networks. Finally, this work emphasizes the role of leadership in the resolution of conflicts.

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