Wo has a nice schema for how to generate counterexamples to transitivty of causation, assuming that something like the causation as influence theory is correct. Here’s an instance of his schema, designed to show that some of the things Lewis wants to say about events are in conflict.
bq. The Yankee Wars
As everyone feared, war broke out between Massachusetts and New York in July. The fighting was fierce, but largely one-sided. By early August, Massachusetts forces had sacked and pillaged a number of New York towns, most prominently Ithaca. As a result, classes were cancelled at Cornell that semester, as Goldwin Smith Hall was turned into a dormitory for Massachusetts troops.
Over those months the fighting was largely confined to the east coast. Out west, life went on as normal. In September California and Arizona sat down for their annual water sharing talks. Unfortunately, the talks went badly. So badly that California decided to go to war with Arizona, rather than having to engage in further negotiations. They decided to ally with Massachusetts, on the proviso that Massachusetts expand their war against New York to also be a war against Arizona. Massachusetts happily did this, and between them Massachusetts and California went on to smite their opponents into smitission.
Now for the philosophical problems. There is clearly a relation of influence between how the September water talks went and the war. Had the water talks gone differently, the war would have gone very differently indeed. (It would have been confined to the east coast, New York would have been able to resist for longer, etc.) And there’s a clear relation of influence between the war and classes at Cornell being cancelled. Had there not been a war at all, or had it favoured New York, classes would have largely gone ahead.
So Lewis seems committed to say that the water talks cause the war, and the war causes the cancellation of classes. But now we have backwards causation! For the water talks are in September, and the classes are cancelled in August. This is absurd.
I think the only way out of this for Lewis, as will be the case in many instances of Wo’s schema, is to deny that the war is an event in the sense relevant for causation. But to do that is to give up on a hope he has in “Events”, namely that the events that are the relata of a causal relation are the events that we ordinarily talk about. The war is a clear instance of an event in the common usage, but it just can’t be something that enters into causal relations, on pain of having absurd instances of backwards causation.
Of course, saying this means that we have to paraphrase away any other talk about the war’s putative causes or effects. I think this can be done, but it won’t be easy.