The Problem of Extreme Cases

John Stuart Mill famously wrote, about pushing principles to the extreme, that “unless the reasons are good for an extreme case, they are not good for any case” (On Liberty). This is not obvious, for extremes often produce antinomic or non-generalizable results.

One may perhaps affirm that stealing $25 from Elon Musk without anybody knowing (I suspect that Musk rounds up his accounting figures to the nearest thousand) and giving it to a very poor family for a meal at McDonald’s would increase the latter’s utility more than it would decrease the former’s. But in less extreme cases, it becomes obvious (or so I argue with many if not most economists) that any concept of “aggregate utility” is meaningless because interpersonal comparisons of utility are scientifically impossible. As Anthony de Jasay kept repeating, it’s “my say-so against your say-so.” (See also my review of Lionel Robbins’s 1935 An Essay on the Nature and Significance of Economics.) Some principles or “laws”—such as the impossibility of interpersonal comparison of utility—may be considered absolutes, but they are only “relatively absolute absolutes” (to use James Buchanan’s expression) and may break down in extreme cases.

A Cretan’s statement that “all Cretans are liars” is antinomic: either it is true, which implies it is false; or else it is false, which implies it may be true. But, as Anthony de Jasay observes with his usual common-sense, down-to-earth approach, when we say in ordinary discourse that all Cretans lie, we are not literally meaning it; we metaphorically mean that most of them lie. This helps de Jasay build his argument for the possibility of private production of “public goods” in anarchy by ruling out extreme cases. If, concerning a given public good, all potential customers believe that none of them will free-ride (refuse to contribute or subscribe to the public good), then all of them will free-ride. In reality, some potential free riders will bet that some will free-ride and others not, and will cautiously decide to subscribe in case their own contributions could be decisive for the production of a public good they intensely want. (See de Jasay’s Social Contract, Free Ride, which I reviewed in Regulation.)

It may be a general phenomenon that, in our universe, extremes are puzzling or antinomic, at least for our limited minds. Mathematical infinity is an extreme that is difficult, if not impossible, to manipulate. But “tending toward infinity” is a useful concept. It is essential for calculating the present value of a perpetuity (or its special cases of a perpetual bond or a consol) as the recurrent coupon divided by the discount rate.

Thinking about a nearly omnipotent God may provide solutions to every problem, but an infinitely powerful God produces the “omnipotence paradox”: Can God create a rock so heavy that he cannot lift it? Aquinas answered that God is only omnipotent in “possible things,” in “whatever does not imply a contradiction.”—Summa Theologica, Part 1, Question 25, Article 3. So even God, it seems, cannot go to the extreme of canceling logical contradictions. Needless to say that a human government cannot be omnipotent, but it can cause much damage by moving in that direction.

The problem remains to find where the extremes are and to identify the extreme cases that cannot be used to test a theory. In some instances at least, identification is possible—for example, when a variable goes from 0% to 100%, as for the proportion of the Cretans who lie or the voluntary subscribers to a “public good.”

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