 Cases like these are discussed by Hall (2000) and Sartorio (2005, 2013), among others. This particular example comes from Pearl (2000). In these kinds of cases, there are five events (or facts, or what-have-you): f, p, l, r, and e, with the following features: if p happens, it will cause either l or r to happen, depending upon whether f happens. And if either l or r happens, it will cause e to happen. For instance, in our example, f is Filipa flipping the switch to the right, p is Phoebe turning on the power, l and r are the left and right bulbs turning on, respectively, and e is the room being illuminated. In this case, it can seem that there’s an important difference between Filipa and Phoebe. Whereas Filipa made a difference to how the room got illuminated (whether by the left bulb or the right one), she did not make a difference to whether the room got illuminated. Phoebe, in contrast, did make a difference to whether the room got illuminated. It seems natural to say that, while Phoebe’s turning on the power was a cause of the room being illuminated, Filipa’s flipping the switch was not.