Determining this, even with the information available today, seems like folly; like a never ending circle of statistical manipulations and justifications to support preconceived notions.
Action on just about any social issue of note can be argued one way or another to be satisfying this guideline.
It would be worse for central planning, because in addition to the problem you mention, central planning has the problem of getting the necessary information to the central planner, which in the general case is impossible: the information goes up as the exponential of the population size, but the bandwidth of information channels to the central planner only goes up linearly with the population size.
Does that mean you can't actually know what the greatest good is? We can probably get very close to knowing it, and the little details shouldn't matter. But most of our "social issues" are squabbles over these details, and the good never gets done, or becomes reduced.