It is an intriguing use of a geometric mean, but I don’t think it is right because I think there is no right way to do it given just the information you have specified. (The geometric mean may be better as a heuristic than the naive approach—I’d have to look at it in a range of cases—but I don’t think it is right.)
The section on Ratio Incorporation goes into more detail on this. The basic issue is that we could arrive at a given ratio either by raising or lowering the measure of each of the related quantities and the way you get to a given ratio matters for how it should be included in expected values. In order to know how to find the expected ratio, at least in the sense you want for consequentialist theorizing, you need to look at the details behind the ratios.
It is an intriguing use of a geometric mean, but I don’t think it is right because I think there is no right way to do it given just the information you have specified. (The geometric mean may be better as a heuristic than the naive approach—I’d have to look at it in a range of cases—but I don’t think it is right.)
The section on Ratio Incorporation goes into more detail on this. The basic issue is that we could arrive at a given ratio either by raising or lowering the measure of each of the related quantities and the way you get to a given ratio matters for how it should be included in expected values. In order to know how to find the expected ratio, at least in the sense you want for consequentialist theorizing, you need to look at the details behind the ratios.