In a distributed system where scalability is an issue, the problem of enforcing mutual exclusion often arises in a {\em soft} form: the infrequent failure of the mutual exclusion predicate is tolerated, without compromising the consistent operation of the overall system. For instance this occurs when the operation subject to mutual exclusion requires massive use of a shared resource. We introduce a scalable {\em soft mutual exclusion} algorithm, based on token passing: one distinguished feature of our algorithm is that instead of introducing an overlay topology we adopt a random walk approach. The consistency of our proposal is evaluated by simulation, and we examplify its use in the coordination of large data transfers in a backbone based network.