Thursday, May 26, 2022

The Need for 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. He defined an economic improvement as a change whose total value was positive, meaning that the value to those who benefited by it was greater than the disvalue to those who lost by it. He offered the concept as an imperfect proxy for a utility increase on the grounds that although a given amount of money might represent more utility for one person than another 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 so, in almost all circumstances, something is a potential Pareto improvement if and only if it is a Marshall improvement.[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.

[1] 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).



Jon Leonard said...

Aren't willingness to pay and utility fundamentally different? If I'm using what I think of as the standard definition of utility, I may value my next dollar differently than someone else would, and I definitely value my next dollar differently than I would if I had substantially more. Von Neumann's insight about probability and utility lets us model utility fairly well as a real-valued function. (Imperfectly, since people sometimes have nontransitive preferences, but the model is still useful.) It's not unique, since multiplying utility by a positive constant or adding a constant doesn't change the results: If I claim I enjoy everything good twice as much as someone else does, that can't be proven or disproven, and interpersonal utility can't be compared in that sense. But willingness to pay is much easier to work with, using things like second-price auctions. It's not clear that that's fair (utility-wise) between rich and poor, but Marshall's definition doesn't really depend on interpersonal comparison of utility.

Gilbert said...

And why should economics conclude on what is good for a country?

I think the more usual presentation and the only one that can be taken seriously is that it will conclude who will gain and loose how much and then note that value judgements are beyond science and economics in particular.

Frankly the argument you present here sounds a bit like a fairly vicious leftist straw-man of what a Libertarian would think. Basically (1) Value judgements, mostly ones favorable to Libertarianism, fall out of economics (2) only if we buy into the provably meaningless idea of interpersonal utility comparison (3) and operationalize that meaningless idea in a way that assumes the interests of the rich are more important than those of the poor (because a rich man can and therefore will pay more to avert the same bad thing) (4) and therefore we should believe these absurdities. I mean horse carriage much?

Also I haven't read Marshall, so I'm not sure how simplified your summary is. My folk-historical understanding is that he did actually believe in a naive cardinal utility which was an understandable and productive confusion at the time. But if he seriously thought that "although a given amount of money might represent more utility for one person than another such differences would usually average out for changes that affected many people" the parts simplified away better include an answer to (3) above.

David Friedman said...

As I wrote (about Marshall):
"He offered the concept as an imperfect proxy for a utility increase on the grounds that although a given amount of money might represent more utility for one person than another such differences would usually average out for changes that affected many people."

Your point is why it is an imperfect proxy, as Marshall recognized.

The usefulness of Marshall's concept depends on interpersonal comparison — without that, why do we care whether something increases value as Marshall defines it?

The point of what I posted, which is part of a much longer chapter, is that in order for concepts such as efficiency to be of use one has to accept interpersonal utility comparisons, that the Paretian and Hicks-Kaldor approaches don't solve the problem. I'm arguing for Marshall's approach, which makes its utilitarian basis explicit, over alternatives that hid it.

You are correct that one can't deduce interpersonal comparisons from observing choices, even under uncertainty, for the reason you give. Nonetheless we do in practice make interpersonal comparisons all the time, whether or not philosophers approve of it. I'm about to post that piece of the chapter next.

David Friedman said...

It's true that one can do economics as a wertfrei project and the information produced is sometimes useful to people, but if economists are not trying to reach conclusions about what is good for a country, or the world, why do they waste their time with efficiency theorems?

It's at least a curious coincidence that so many economists are free traders.

Jon Leonard said...

I'd misunderstood the point you were trying to make. That is, if you try to do economics without reference to utility, and substitute willingness to pay instead, you get a model that's about as useful as a model based on utility. (And like many models, partially wrong or incomplete but still useful is a fine outcome.) If we insist on anchoring it to some concept of utility, you can still get ordinal comparisons though "which would you pay more for?" exercises. I'd thought you were saying that neglecting utility was still useful, as opposed to saying that we need to anchor things more thoroughly in utility.

Anonymous said...

Whose monetary utility did the Fed decrease to increase banks' monetary utility by trillions of dollars during Quantitative Easing?