Outside ideal settings, conventions are shaped by competing processes that can challenge the emergence of norms. This paper identifies three trade-offs challenging the diffusion of conventions: (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 and global 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. We develop a broadly applicable statistical physics framework for measuring each of these trade-offs, which we then apply to a sign convention in physics. Our method can recover the structure of the underlying coordination game, the networks of social interactions involved, and the processes through which conflicts are resolved in collaborations. We find that the purpose of conventions may exceed coordination, and that individual preferences towards conventions are concurrently shaped by cultural factors and multiple social networks. Additionally, we reveal the role of leadership in the resolution of conflicts. Finally, this work provides a generalization of Lewis' account of conventions.