Bob Murphy has a great post on interpersonal utility comparisons here. Bob thinks Tyler Cowen knows all this, but isn't sure if Dan Klein does. Gene Callahan thinks that Dan Klein knows all this and I'm inclined to agree with him. And I'll add that neoclassical, non-libertarian, non-Austrian economists know this too. Hence my post earlier pointing out Hal Varian's notation of the exact same point in a very popular graduate-level neoclassical microeconomics textbook. I certainly know all this. This stuff was settled out 140 years ago at the latest.
I still think Bob is wrong in criticizing Dan Klein, although this may be semantics. I read the question with a little "holding all else equal" at the end, which I think is pretty fair. Presumably we were holding all else equal in Klein's minimum wage question too (which liberals were relatively "unenlightened" on), otherwise we can imagine a lot of what-if stories too. The diminishing marginal utility of wealth is a strong foundation for building up economic science, holding preferences constant, and we should wonder about the economic insights of people who for whom that insight is not instinctual.
I also think that the inability to compare subjective utilities should not grind economics to a halt. We really use utility in two ways: when we think about marginal behavior, and when we think about welfare implications. As long as we are willing to assume a few reasonable properties of utility functions, marginal analysis is legitimate even if interpersonal comparisons are not. That's the role that utility plays for most positive questions.
It's tougher when we get into questions of welfare analysis, because that's where we actually are aggregating total utilities. But these are inherently normative questions anyway, so I don't think it should trouble us too much to add some more normative assumptions about interpersonal comparisons. Definitions of optimality are inherently normative. For example, why should we ethically abhor someone being made worse off? Perhaps it is ethically right that they are worse off - perhaps ethically it would be sub-optimal if certain people were not made worse off. There's also ethical questions of standing. As I've pointed out before in discussions of "temporal autarky", we regularly make the assumption that future generations have no standing in today's decisions. Animals often have no standing either - is that ethically right? People who do not have these social constructions we call "property rights" also don't have standing. This is an ethical assumption too and it has nothing to do with the positive science of human behavior. We also make assumptions about equality. Typically welfare analysis is just about welfare maximization - there's often no assumption that that welfare ought to be evenly distributed. There is no objective reason for this - it's a normative assumption.
When we do welfare analysis we make all these ethical assumptions already. So I don't personally see why we should balk at making assumptions about interpersonal utility comparisons. We seem to feel that making these declarations about optimality, standing, egalitarianism, etc. when we do welfare analysis is useful even though it's normative. I would simply say that imposing a rescaling of personal utilities to enable interpersonal comparisons is a quite legitimate assumption to make in welfare analysis. That's not positive science, but then welfare analysis never was. Welfare analysis is the application of certain economic insights to practical economic problems. And since the solution to those problems has ethical implications, we are certainly within our rights to make normative assumptions in approaching them ("within our rights"... there I go making normative assumptions again!).
That's why I may get a little exasperated when people act like intersubjective utility comparison is lost on me when actually it's not lost on me - I just think it's irrelevant to a lot of what we do in economics.
11 hours ago