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At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about the remaining (2^2^n - n) adversaries that might crash certain combination of processes and not others? This paper presents a precise way to characterize such adversaries by introducing the notion of disagreement power: the biggest integer k for which the adversary can prevent processes from agreeing on k values. We show how to compute the disagreement power of an adversary and how this notion enables to derive n equivalence classes of adversaries.