# Utility and Interpersonal Comparisons of Utility

This article describes cardinal and ordinal utility as I understand them and then argues that analysis under cardinal utility is more productive. I also argue for the plausibility of interpersonal comparisons of utility.

Ordinal and Cardinal Utility

When the preference of A to B is understood in as ordinal we may simply suppose that an individual will consume A rather than B, nothing further. When preferences are understood as cardinal we may say something further, which is that we can speak of the magnitude of the preference. In addition to the fact of the preference of A to B, we may further state the degree of the preference.

On a more abstract level, the idea of cardinal utility is that preference is something other than a simple revelation from observation of consumption. It is the idea that preference itself is a measurable substance, the unit of which is the util.

1. Pro of the ordinal view: Under a particular analytical framework it becomes a straightforward result.
2. Cons of the ordinal view:
1. The idea of a marginal good becomes incompatible with the mathematical notion of a derivative, making mathematical forecasting extremely imprecise or totally untenable.
2. Incompatible with genuine indifference

Pros of the cardinal view:

1. Allows for genuine indifference
2. Makes interpersonal comparisons of utility plausible
3. Lends itself to precise forecasting and modeling
4. I think it lends itself more to the idea of goal-imputed value, as described later

In Defense of Utils

The idea of utils is a bit tricky because it is a subjective unit, variably and contextually constituted, but I think we can conceive of them in a substantive way. Specifically, I would measure a util as the marginal productivity of consumption, where consumption produces by means of bringing an individual closer to realization of some goal or basket of goals.

Under this framework, suppose we know an individual has only the objective of arriving at work as quickly as possible. We can then say that his choice to purchase a car rather than a bike is a choice made under cardinal preference, and simultaneously revealing an ordinal preference. This approach allows us to more effectively engage in counterfactual thinking. Suppose a regulation is passed the next day such that cars may only travel at 10 mph. Through Rothbardian demonstrated preference we have no a priori grounds to suppose this individual would prefer the bike to the slow car, we can only recognize such preference a posteriori.

A critical thinker might suppose that the goal is sometimes directly consumable, in which case the util is simply the measurement of the degree of relative preference for goods A and B in terms of C. I think this is almost exactly right, except that if it were possible to consume C directly then there would be no preference for A or B. Even still, it’s fair to essentially explain the value of A as being due to the ability of A to produce C.

Interpersonal Comparisons of Utility (ICU)

Considering the goals-oriented approach, it is possible to conduct interpersonal comparisons of utility if a particular individual understands the goals set of another individual. Individual A may be able to establish that some good, G, is more useful to individual B.

What Others Have Said

Most economists are on the side of cardinal utility, although they understand it differently than I have described above. Here is a quote from Armen Alchian:

Can we assign a set of numbers (measures) to the various entities and predict that the entity with the largest assigned number (measure) will be chosen? If so, we could christen this measure “utility” and then assert that choices are made so as to maximize utility. It is an easy step to the statement that “you are maximizing your utility”, which says no more than that your choice is predictable according to the size of some assigned numbers… Unfortunately, the term “utility” has by now acquired so many connotations, that it is difficult to realize that for present purposes utility has no more meaning than this.

Bob Murphy represents a cool middle-ground, and I’m not sure how many economists are on his side. He is cool with VNM utility functions, but he interprets these functions as a stand-in for ultimately ordinal-ranked preference. Using a Milton Friedman vocabulary, it’s as if a VNM utility function were ordinal even though it’s not.

On the other hand, most economists are against the possibility of interpersonal comparisons of utility. David Henderson has said “One of the things we are most sure of in economics is that you can’t compare utility, marginal or otherwise, across individuals.” Of course, I must finish by quoting David Friedman. Quite apropos as Friedman commented on the Henderson article just cited, saying:

Von Neuman showed how to cardinalize utility most of a century ago, so your statement that utility is ordinal not cardinal is long out of date. Rational individuals buy insurance because of declining marginal utility of income, a concept which makes sense only if utility is cardinal.

Cardinal utility does not solve the problem of interpersonal comparison, but I don’t think I know anyone, including David, who really doesn’t believe it can be done. Do you have any serious doubt as to whether the disutility I receive from a pinprick is less than the disutility you would receive from being tortured to death? If not, you believe we can do interpersonal comparisons, just not very well.

Consider the decision to give gifts or charity. If you are completely unable to make comparisons among different people’s utility, how can you decide which of your friends to give a gift to? Why would you give charity to a poor man instead of to a random billionaire?

Henderson responded here, though I think Friedman’s points stand strong.

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