Some Problems Of Mathematical Formalism In Economics

Speaking of the confusion and intellectual sloppiness introduced into neoclassical welfare economics by rigorous mathematical formalism, can we just review the concept of “utility one more time? It’s an interesting case study.

Have you ever had someone tell you it just doesn’t really matter what exactly “utility” in economic theory means and, in particular, it can refer to either individual preference rankings or inaccessible internal perceptions of satisfaction from preference fulfillment? In one case, interpersonal utility comparisons are undefined; in the other case, they’re impossible. It amounts to the same thing as far as deriving theoretical conclusions, so just choose whatever interpretation calls out to you?

The supposed equivalence of the two conceptions of utility is only true in a formal, mathematical sense. Obviously, when trying to explain, discuss, assess, evaluate, support or reject the normative propositions involved, it makes a big difference. The now more usual “individual preference ranking” utility leads straightaway to an understanding of neoclassical welfare economics as an ethical half-theory. That sort of utility is not even defined in interpersonal conflict situations. One obviously can’t base a full system of ethics on a concept like that. The older “inaccessible internal perceptions of satisfaction from preference fulfillment” utility, in contrast, can be related to an extraordinarily weak, indeed entirely implausible, full ethical theory in the utilitarian vein. That theory can lead to an endorsement of practical amorality on the grounds one can never know the ethically correct answer, one only knows all other answers about how to ethically resolve interpersonal conflicts of preferences, needs, desires, are wrong. As an aside, I should mention if one is going to do that, one should at least be consistent and not carve out random exceptions for status quo property arrangements, markets, laws, or anything else. If one is treading this well worn path, everything relating to resolving interpersonal conflicts of preferences, needs, wants, desires, is just as ethically incorrect as anything else.

The notion it doesn’t matter which form of utility one is using when discussing normative propositions in neoclassical welfare economics, such as we should “maximize” total social “utility,” is the positive analysis of normative economics at its worst and most confusing. Expressing a normative or ethical theory without defining the concepts, specifying and explaining the normative inputs, ostensibly because one is simply checking the positive logic that leads to the conclusions, so whatever works is fine, is intellectually disingenuous. If one is presenting arguments ostensibly demonstrating this, that, or the other is “optimal” or “maximizes social welfare” and so on, one is going well beyond simply checking the internal logic of someone else’s random, unevaluated normative or ethical theory. One is presenting a normative or ethical theory of one’s own. That this sort of thing is so common demonstrates why economists have no business delving into the normative or ethical issues associated with evaluating economic systems or outcomes, even in the positive sense of checking the internal logic of ostensibly arbitrary, unevaluated normative arguments. Just for the record, one can be a positive economist without playing rhetorical games relating to bad, unexamined, unexplained, unevaluated ethical philosophy. It’s called doing science. One can direct one’s attention to objective, empirical phenomena rather than matters of subjective ethics. Just saying. One does have options.

Want more? Fine by me. Have you ever had someone suggest the only relevant issue when it comes to “utility” in neoclassical welfare economics is the mathematical difference between ordinal and cardinal utility functions? Again, that may be all that matters from a mathematical perspective, but not from a conceptual, philosophical, normative, ethical perspective. Preference rank utility seems obviously an ordinal concept requiring an ordinal function, but one could model the essentially cardinal notion of inaccessible internal perceptions of satisfaction from preference fulfillment with either ordinal or cardinal functions. If one wants to be get serious about neoclassical welfare economics, one will want to go beyond mathematical functions, often perceived as arbitrary modeling choices, and look at the underlying concepts themselves.

Its a never-ending source of wonder to me that neoclassical welfare economics, a theory extolled by its practitioners for its supposed rigor and clarity, is based on a concept it can’t be bothered to fully define, leading to perpetual conflict and confusion. Just choose one for goodness sake. What reason can there be to not do that, beyond the rhetorical one of playing funny word games? On the one hand, if we’re talking about individual preference ranking utility, stop with the “interpersonal utility comparisons are impossible.” They’re undefined, not “impossible.” Stop talking about aggregating “utility” across people. That doesn’t make sense. Stop introducing unrelated ethical propositions by weighting “utility” and then adding it up, that’s gibberish. If necessary, just introduce some exogenous ethical propositions. Indeed, as I’ve suggested before, just stop talking about “utility” altogether and start talking about “individual preference rankings.” All you’re doing with the superfluous term “utility” is introducing opportunities for equivocation on concepts and terms. On the other hand, if we’re talking about inaccessible inner perceptions of satisfaction from preference fulfillment utility, draw out the implications, help people evaluate it, discuss what it means for interpersonal conflict situations, etc. If that’s what you have in mind, don’t treat it like it’s someone else’s random concept you found lying on the floor when you arrived. It’s yours. Own it. Understand it. Discuss it.

We really need to introduce some rigor into the field of neoclassical economics, and I don’t mean the empty, superficial rigor of mathematic formalism, but real, substantive, philosophical, intellectual rigor dealing with concepts, definitions, normative propositions, ethics, etc. Bad economics creates confusion and conflict. We should fix bad economics.