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Utility: Part II
In Defense of Cardinal Utility
The economists of the late 19th treated utility as cardinal, quantitative, able to be represented by numbers,. Early in the Twentieth Century John Hicks showed that everything then being done by treating utility as a number could be done by treating it as an ordering instead, a description of what you preferred to what but not by how much. About ten years later Von Neumann and Morgenstern demonstrated that there was something cardinal utility could do better than ordinal utility: incorporating preferences under uncertainty into the utility function. They showed that one could assign numerical utility values to outcomes in such a way that an individual choosing between lotteries, probability mixes of outcomes, would always prefer the lottery with the higher expected value of utility.
That is one reason to prefer cardinal utility but not the only one. We observe other people’s utility functions from the outside, our own from the inside. Seen from that perspective it is clear to me that some of my preferences are much stronger than others — and in a way that fits at least roughly with Von Neumann’s approach to utility theory. If I not only prefer an orange to an apple, I very much prefer it, I probably prefer even one chance in four of getting an orange (expected value = (utility of orange)/4) to a certainty of getting an apple (expected value = (utility of apple). Cardinal utility, indeed Von Neumann utility, fits our subjective experience of our own preferences
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A third reason to prefer cardinal utility is that it makes it easier to intuit economics. Marginal utility was a central element of the marginal revolution, the collection of intellectual breakthroughs that, at the end of the 19th century, created modern economics. It was a concept that proved useful to explain prices, economic equilibrium, and much else. If utility is only ordinal, an ordering not a quantity, there is no such thing as marginal utility.
Proving that something is true is not an adequate substitute for knowing why it is true; one of the problems with modern economics is the emphasis on formal mathematics to the neglect of economic intuition. One reason may have been the shift from thinking about economics the way Alfred Marshall did to thinking about it the way John Hicks did. The further your mental model is from what you understand, the more you have to rely on formal mathematics instead.
It is easier to understand declining marginal utility than the convexity to the origin of an indifference curve.
In Defense of Interpersonal Utility Comparisons
One of the common criticisms of utilitarianism is that we have no way of trading off utility gains to one person against utility losses to another, no way of knowing whether the net change is an increase or decrease in total utility. That is not a problem for much of economic theory, which can be done not only without interpersonal comparisons but without anything more than individual ordinal preferences. But it is a problem if you want some way of evaluating the overall effect of a change such as imposing or removing a tariff, one that makes some people better off and some worse.
In fact, we not only can make interpersonal utility comparisons we routinely do make them, even if not very well. A parent making decisions that affect his children is implicitly asking himself whether doing something one child wants to do and the other doesn't will increase the former's happiness more than it decreases the latter’s. Someone deciding which friend to give a gift to is doing it in part on which he thinks will be made happier by it. I signal my feelings, including preferences, in facial expressions, voice tones, and the like. Others appear to do the same, giving me some idea of the strength as well as the ordering of their preferences and how it compares to the strength of mine.
I cannot know another person’s preferences with certainty but I have no serious doubt that the disutility to a random stranger of being tortured to death is greater than the disutility to me of stubbing my toe.
Interpersonal Utility in Economics
Alfred Marshall defined the value of an outcome to an individual, positive or negative, as the largest amount he would be willing to pay to get it or prevent it, and defined an economic improvement as a change whose total value summed over everyone affected by the change, was positive. He offered the concept of an economic improvement as an imperfect proxy for a utility increase. Although a given amount of money might represent more utility for one person than another, which is why it is only an imperfect proxy, he argued that such differences would usually average out for changes that affected many people. Put in modern terminology, an economic improvement is an increase in economic efficiency and an outcome is efficient if it cannot be improved.
A Pareto improvement, a concept originated by Vilfredo Pareto, is a change that benefits at least one person and harms nobody, avoiding the need for any interpersonal comparison of amount of benefit and harm. An outcome is Pareto efficient if it cannot be improved. The problem with substituting the Pareto versions of “improvement” and “efficient” for the ones based on Marshall’s approach is that almost no change affecting a significant number of people is a Pareto improvement, hence almost all outcomes are Pareto efficient.
Hicks and Kaldor tried to solve that problem with the concept of a potential Pareto improvement, a change that would be a Pareto improvement if combined with a suitable set of payments from people who gained to people who lost. If gainers gain more than losers lose, making the change a Marshall improvement, there should be some set of transfers that fully compensates the latter while leaving some gain for the former, making it a potential Pareto improvement, so the two concepts are very nearly identical.1 Since the transfers are not actually made, a potential Pareto improvement is not an actual Pareto improvement — some people gain, some lose — so justifying it as a criterion for what changes are good or bad requires the same interpersonal utility comparison as Marshall’s approach.
It just makes the fact less obvious.
In order for economists to conclude that abolishing a tariff or a minimum wage law or practically any other change is (or is not) good for the country, an improvement, they must be willing to bite the bullet, treat utility as interpersonally comparable.2
I describe a situation in which something is a Marshall improvement but not a potential Pareto/Hicks-Kaldor improvement in "Does Altruism Produce Efficient Outcomes? Marshall vs Kaldor." Journal of Legal Studies, 1987 Vol. XVII, (January 1988).