I talk about “utility” in neoclassical welfare economics often enough, but maybe I should say a few more words about one of the famous scholastic, doctrinal disputes in mathematically formalized neoclassical welfare economics, is it meant to be “ordinal” or “cardinal?”
I find the issue a little comical because, of course, once one defines “utility,” it becomes perfectly obvious whether the concept is ordinal and cardinal, and whether it makes sense, given the available data, to use ordinal or cardinal mathematical functions to describe it. Economists, inept ethical philosophers but passable mathematicians that they are, tend to do things backwards. They start with some mathematical expression or expressions involving “utility,” then try to piece together what they must be talking about. That’s how the definition of “utility,” something everyone should understand is a normative choice based on normative evaluation, if it’s meant to be normatively significant at least, became for many economists a positive, empirical question, something to be discovered based on the evidence. Hmm, what are we actually talking about? It’s an artifact of the risible academic positive approach to normative economics, in which economists don’t take ownership of the essentially normative concept of “utility” but treat it as a given, part of someone else’s ethical theory they found lying on the floor one day, which they need to investigate.
If one is talking about individual preference rank “utility,” the most common explicit definition in modern neoclassical welfare economics, a sort of “utility” that doesn’t correspond to anything that exists, per se, then one can obviously only use ordinal mathematical functions to discuss it. The concept itself is ordinal. In contrast, if one is talking about internal perceptions of satisfaction from preference fulfillment “utility,” the older, more traditional, but no longer really current definition, that’s a cardinal concept, but if one believes those perceptions are inaccessible except for observed choice, it can only be described empirically in ordinal terms. However, moving away from the empirical data one accepts as relating to that sort of “utility,” one can talk sensibly about different levels of amounts of “utility,” adding up “utility” across different people, total social “utility,” social welfare functions, etc. And, of course, in this nexus of the characteristics of mathematical functions versus those of underlying normative concepts enters all the complications of engineering model versus science, positive versus normative, unreal ethical half-theory versus ethical full theory addressing reality, etc., so distinctive of bad economics in the conservative style.
Indeed, there appears to have been a years long dispute within the closed, cloistered Villa of Academic Economics about whether certain mathematical propositions, usually Arrow’s this or that, involve / require / permit ordinal or cardinal “utility.” Some economists seem quite satisfied to use that as the reason they can happily explain to others how society should maximize “utility” despite not actually knowing what it is. Hey, they’re working on it. Have been for some time. Will be for quite some time yet. They’re scientists, dammit, not ethical philosophers! (Did I use that one already?) But then, they’re talking about a normative or ethical theory, with normative or ethical conclusions and implications, and implying we should pay attention, sometimes all but insisting.
Let’s cut the nonsense, shall we? If academic economists mean anyone to be interested in maximizing “utility,” it’s their responsibility to define exactly what it is, so people can evaluate the proposition. It’s not a math problem; it’s a philosophical, ethical decision. Decide a definition, then enforce it within the profession, or as I’ve suggested before, just stop using the term “utility” and refer instead to individual preference rankings or internal perceptions of satisfaction from preference fulfillment. Or I guess those are just the most common definitions, aren’t they? The ones consistent with neoclassical welfare economics. The “utility can mean anything” crowd has plenty more where those came from including, say, observable indications of human welfare, variously defined. Granted, those definitions are inconsistent with the internal logic of neoclassical welfare economics and all the rigamarole about Pareto optimality, “economic” efficiency, revealed preferences, and so on, but if one just does “general welfare analysis,” hey, the sky’s the limit. In the meantime, we apparently have no recourse but parallel normative discussions and evaluations based on the two types of “utility” consistent with the overall normative argument in neoclassical welfare economics, as I do in my blog and my short book. One should lead straightaway to an understanding of neoclassical welfare economics as an ethical half-theory, but comically often doesn’t. The other makes the theory into a very controversial, dodgy full ethical theory functioning as a half-theory in practice. Awkward.
Because if there’s one thing one has to understand about modern, mathematically formalized neoclassical welfare economics, it’s that it appears to have been purpose built to support bad economics in the conservative style, to create confusion and conflict, to obscure and mislead. Overcoming bad economics in the conservative style requires going beyond typical academic presentations of the subject, starting with scrupulous attention to the definition of “utility” and moving on to a proper philosophical evaluation of the ethical proposition society should “maximize” it.
