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The M-Set analysis of causation: objections and responses

This type of counterexample was brought to my attention (independently) by Cian Dorr and Adam Morton. Here is Dorr's version. A, B and C are generals going to a top-security bunker. The door will open if (and only if) any two of them touch the pad (one after the other) with their hands. A touches it (event a), and then B does (event b); C doesn't have to do anything since the door has opened (event e) . But, if either A or B hadn't touched the pad, C would have (event c). Now here's the problem. Intuitively, a is a cause of e (as is b); by condition [B] of the M-set analysis (1997, p. 274), this is so only if there are no M-sets for e, M and N, such that M contains a and N differs only in that it contains one or more nonactual events in place of a. But there are such M-sets: e.g. M {a, b} and N= {c, b}. The problem is avoided if we revise the analysis to the following: