David R. Henderson  

Tyler Cowen on Interpersonal Utility Comparisons

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One of the things we are most sure of in economics is that you can't compare utility, marginal or otherwise, across individuals. Utility is ordinal, not cardinal.

Which is why I don't understand Tyler Cowen's post this morning. He leads off fine, writing:

1. You cannot build and sustain a polity on the idea of redistributing wealth to take advantage of differences in the marginal utility of money across varying wealth classes.

He's right. You can't. But the reason you can't is that you can't measure differences in the marginal utility of money across people. Why? Go back to my second introductory sentence: Utility is ordinal, not cardinal. So there's no such thing as a "difference" to measure.

But that's not Tyler's reasoning. He writes:

2. The ideas you can sustain a polity around often contradict the notion of socially arbitraging MU differences to try to boost total utility.

This makes sense only if you can measure differences, which makes sense only if there are differences to measure. There aren't. If you doubt that, ask yourself this: what's the difference between 1st and 4th?


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CATEGORIES: Economic Philosophy




COMMENTS (42 to date)
Nick writes:

I agree that there are good arguments for why we shouldn't compare utilities. But to say that this is one of the things economists are most sure of misses a lot of the debate behind the topic.

Yes, utilities are supposed to capture ordinal preferences, and I agree that this makes naive utilitarian sorts of calculations where we sum up everything incoherent.

But there are other approaches to thinking about how we might construct a social welfare function. For example, we might consider the (ordinal) preferences people would have behind the veil of ignorance. Depending on their preferences people may be expected utility maximizers, with the expectation computed by putting equal weight on each person in the world, and then our resulting social welfare function looks a lot like summing up over utility functions.

How reasonable this exercise is can be debated of course, but it's not inconsistent with economic conceptions of utility since it's derived from ordinal preferences.

And of course empirical economists often do welfare analysis which involves summing utility, so it is used in practice as a way to evaluate policy decisions.

David R. Henderson writes:

@Nick,
And of course empirical economists often do welfare analysis which involves summing utility, so it is used in practice as a way to evaluate policy decisions.
Not true. We sum values, not utilities.

Steve Brecher writes:

The ineluctably subjective nature of utility, happiness, well-being, etc. makes quantification and interpersonal comparison or summation of magnitude impossible, and makes utilitarianism incoherent.

MG writes:

I chose to interpret Tyler's point as supporting a broader political economy claim. In this case, I thought he could had substituted marginal propensity to consume, instead of marginal utility, and still made the same point -- the fragility of a polity based solely on this objective. My questions are, do you also have a technical objection to comparing propensity to consume across peoples? And, can Tyler's point be applied to the futility of arbitraging other inter personal marginal functions?

Humans are rationally ignorant about most subjects. Pragmatists in democracy see this and write for intellectuals, for secondhand dealers of ideas, not for academic specialists.

Tyler writes at this margin, unless I am mistaken.

roystgnr writes:

"ask yourself this: what's the difference between 1st and 4th?"

If I'm in 4th, and I would be ambivalent between a 25% chance of taking 1st or a 50% chance of taking 2nd, then I can say (U(1)-U(4)) = 2(U(2)-U(4)).

That still doesn't help with interpersonal comparisons, since all such observations are independent of affine transformations of U, but it's at least a big step up from *ordinal* utility.

Kevin Erdmann writes:

I believe that Zach Weinersmith had the last word on this.

CA writes:

I'm quite sure that you can compare utility and marginal utility to some degree in many situations. And we are implicitely comparing utility when we vote for or against certain public projects and decisions.

Josiah writes:

The idea that you can't make interpersonal utility comparisons seems pretty weak to me.

For one thing, everyone does in fact make interpersonal utility comparisons all the time. Even economists do it. It's hard to see how you could avoid this if you want to interact with or care about other people.

For another, the arguments against making utility comparisons between different people would seem to also apply to making utility comparisons for the same person at different times.

Levi Russell writes:

Josiah,

Are you sure you're not talking about value?

John Z writes:

David - it seems to me that the fact (if it is a fact) that you can't make interpersonal utility comparisons is a deliverance of philosophy, not economics.

If it's a deliverance of economics, something we are 'most sure of', then how do you get to that conclusion through economic reasoning? What's the proof?

That economists don't know how to make interpersonal utility comparisons hardly shows that it cannot be done.

Nick writes:

@David R. Henderson

There are many well-known research papers that maximize over a social welfare function obtained by summing up utilities. For an old example, see equation (7) in 'An exploration in the theory of optimum income taxation', James Mirrlees, Review of Economic Studies. For a recent empirical example, see section C of 'Moral hazard versus liquidity and optimal unemployment insurance', Raj Chetty, Journal of Political Economy.

I think it was Scott Alexander who once quipped that interpersonal utility comparisons were one of those things that are hard in theory but easy in practice.

I can't find the link, but as I recall, the example he gave was giving up your bus seat to an old lady. You do it because it increases her utility more than it decreases yours, and people perform this sort of comparison correctly all the time.

Craig Richardson writes:

This is one of those things that seems "obvious"- of course we can see if some people are happier than others. Don't you like chocolate ice cream more than I do? Sure. But's it a bit more complicated.

Here is the issue that gets confusing. Economists have something they call the marginal rate of substitution which measures people's willingness to trade off one good for another at the margin (small changes). So let's say we have two goods: bananas and chocolate chip cookies.

Joe is willing to trade, at the margin, 1 cookie for 3 bananas that he has. Mary is willing to only trade 1 banana for 1 cookie.

Aha, you might say, this shows that Joe likes cookies more than bananas!.. aren't we comparing utility now? Mary must like bananas more than cookies.

Nope, while we're comparing the rate of "trade" between two goods, we don't know how happy cookies and bananas make Joe vs. Mary in total.
Mary might care very little about both, as she is on a paleo diet, whereas Joe cares a lot. But we can't glimpse inside people's brains to truly know what that utility is though. There is no blinking number inside to tell us.

The rate of trade doesn't tell us about total happiness from consuming them both.

If you've had intermediate micro, you can think of indifference curves as "altitude" lines (like a topographical map) up the hill of happiness as we move in a NE direction. But just because we can measure rates of trade, that doesn't tell us at what level of utility we are at. It's sort of like looking directly down at two people standing on two hills from a helicopter. We can see their relative positions, but we can't guess their altitude.

We can intuitively *feel* like we can do it, but as Robbins (1932) points out, there is no scientific basis to measure it.

Hope that helps!

Toby writes:

@Thomas Colthurst,

Thinking that we make interpersonal utility comparisons doesn't make it so. Take the example of giving up the seat for the old lady. All it shows is that you value that she sits more than you value that you sit. Nothing more, nothing less.

David R. Henderson writes:

What Craig Richardson said. Thanks, Craig.
@Thomas Colthurst,
I can't find the link, but as I recall, the example he gave was giving up your bus seat to an old lady. You do it because it increases her utility more than it decreases yours, and people perform this sort of comparison correctly all the time.
My gut feel is the same as yours. But I can’t prove it. And there’s also Toby’s point.
@Nick,
I’ll check out those papers, but I must say that I have a strong prior, based on Paul Samuelson’s work, that you can’t do this. Of course, they can assert it by positing a cardinal utility function. If I’m on a desert island without a can opener (as Reggie Miller would say), I can assume a can opener.

awp writes:

I feel like your argument is equivalent to

One of the things we are most sure of in economics is that you can't use it to predict the reactions of individuals to changing incentives/constraints. Individuals are idiosyncratic.

Therefore since we can't predict the reactions of individuals it is silly to argue that we can predict the average response across a population.


While I completely accept that Utility is ordinal, I am also pretty sure that on average the poor gain more "happiness" (even if I can't measure it) than the rich with the increase in consumption of an additional dollar's worth of goods. This I accept because I accept that consumption has decreasing marginal utility for individuals.

Ryan writes:

"My gut feel is the same as yours. But I can’t prove it. And there’s also Toby’s point."

My impression is that this would be questionable for a few reasons:
1) Radical unknowability of the workings of other people's minds would undermine our ability to socially function. So, either we can know what/how other people think (and thus likely estimate their utility) or we cannot and empathy, social intelligence, transactions and everything else cannot get off the ground.

2) Radical unknowability of other people's minds also has no compelling philosophical force. It violates common sense, and the level of skepticism is similar to that of doubting whether other minds and their subjective valuations actually exist. If we can accept other minds as existing due to common sense, then why not accept utility estimates of those other minds based upon the same common sense?

3) In theory, couldn't these questions be empirically resolved? Utils ultimately tie back to brain states. Unless the brainstates are radically different across individuals, utils should also be comparable.(Note: I will accept that this isn't a smoking gun due to the state of our research on neurology, but flat denial may still seem implausible.)

I mean, I end up thinking that strong versions of the inability to make utility comparisons are largely dogmatic. It's hard to really argue against dogmas, but it isn't incumbent upon others to accept them.

Tiago writes:

I disagree. The fact that you cannot measure it well does not mean you don't measure it.
The whole point of cost-benefit analysis is to reach a conclusion over which course of action is better than the others. And this means "maximizing utility", however people name it. One proxy for it may be maximizing value in dollars; a different one could be assigning different weights for dollar gains or losses according to income distribution, like Nathaniel Hendren proposes. But you will always need to make interpersonal comparisons for policy purposes. So while you are at it, you might as well have a previously agreed, reasonable and transparent method, even if necessarily flawed.

Levi Russell writes:

Thomas Colthurst and David Henderson,

Another interpretation of the bus seat example is that "helping other people" is a good that you value and you value the next unit of "helping other people" more than you value sitting in the seat.

Charlie writes:

Cardinal utility has a long established history in economics.

http://en.m.wikipedia.org/wiki/Cardinal_utility

Guess you aren't a Von Neumann fan. You just ruled out almost all his work on decision making under uncertainty, which can't be done with only ordinal utility,

Though people could have cardinal utility that wasn't comparable across people. This whole post is muddled.

Bob Murphy writes:

Good post David. Something similar happened in 2011, which I noted at my blog, regarding Dan Klein's essay in the WSJ.

This whole situation is weird because *obviously* Tyler Cowen is familiar with the standard argument against Interpersonal Utility Comparisons. So I don't know why he so casually invokes them, in a way that I used to specifically bring up in class to get students to see the problem with the conventional understanding.

If a certain physicist thought Einstein was wrong and that you could easily go faster than light, it would be weird if he said on his pop blog, "You can't sustain a solar system polity with rockets going five times faster than light, because eventually the fuel costs will be astronomical," without at least giving a nod to the fact that many of his colleagues would think he is speaking nonsense.

david writes:

Yup. Expected utility theory re-admits cardinal utility.

What's more, even interpersonal utility makes a return under the representative agent. Mirlee's 1977 paper that Nick mentions straightforwardly says: "Individuals have identical preferences..." and has the planner sum over the continuum of individuals.

David Friedman writes:

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?

David R. Henderson writes:

@David Friedman,
Thanks. I would appreciate it if you would provide the cite where Von Neumann shows this.

Justin writes:

But aren't Von-Neumann utilities still ordinal in the following sense: I can multiple my VN-M utility function u(.) by c>0, and u'(.)=c*u(.) is a utility function which represents the same exact preferences as u(.). Thus even though the second representation gives "more" utility," it is describing exactly the same person who uses the first.

Brian writes:

David,

Here is a not-too-old paper by Ken Binmore that talks about the work of Von Neumann and Morgenstern and discusses (in sections 5 and 6) how John Harsanyi builds on it. I agree completely with David Friedman that this idea of personal utilities not being comparable, though widely held, is out of date and not really believed by anyone on a practical level.

Let me make an analogy to show why an outright rejection of interpersonal utilities is certainly wrong.

Consider human perception of color. We can all look at the sky and call it blue, or grass and say it's green, but there's no way to know whether my perception of sky blue is the same as yours. We might all agree on where the color lies on a ROYGBIV scale, but such a scale is an ordinal ranking. Your perception of blue might be more like my perception of green, but we'd have no way of knowing as long as we are consistent in what we term blue and green. (Consider the recent controversy over a dress--is it white and gold or blue and black?) Color is subjective.

But scientists have known for a long time that color corresponds to an intrinsic property of light, whether we call it wavelength or frequency or photon energy. Color is cardinal property, and the retina, with its cones, is constructed to change that cardinality into a perception. How well we do that will vary from person to person, but a correctly operating eye and brain merely add noise to a cardinal property. Color perception, then, must be mostly cardinal.

A similar analysis can be applied to utility. It may seem like all we have is an ordinal ranking for each person, so that absolute utilities and therefore comparisons are impossible. But note that personal preferences ultimately have a biological and, indeed, chemical basis. If we associate utility with pain and pleasure, specifically, then a given perception of utility will be associated with certain levels of endorphins (to kill pain) and dopamine and serotonin (to create pleasure). The preferences we show in terms of pain and pleasure correspond to our brain's perception of the chemical levels in our body, just as our perception of color corresponds to the wavelength of light. Utility is a cardinal property, with noise.

What this means is that interpersonal comparisons of utility certainly are not only possible but also precisely definable, as long as we recognize that noise will put a limit on how useful those comparisons are. This idea puts a clearer light on the point David Friedman makes with his pinprick/torture example.


Nick writes:

@David R. Henderson

I wouldn't have had a problem with your post if the first sentence had been instead

One of the things we are most sure of in economics is that you can't objectively compare utility, marginal or otherwise, across individuals.
It's possible to construct a social welfare function by summing up utilities, we may even think it is meaningful, but economists recognize that this at some point involves making a moral judgement about how to weight people. Often we assume everyone has the same utility function since it seems fair.

I don't think Tyler Cowen was addressing his post to people who believe that utility is objectively measurable and comparable, rather he was addressing it to people who believe that that is the right social welfare function to maximize.

Hazel Meade writes:

I am not sure what you are trying to say here.

Are you saying that there's no way to know whether the an extra a dollar objectively matters more to a rich person or a poor person, so we shouldn't care which one of them gets it?

I think that's a really terrible position to take. And I'm usually on your side. Yes, it's possible that some people's default comfort level is higher and thus marginal increases in wealth make more of a difference to them than poor people whose default comfort level is lower. But the fact that someone is born into comfort and thus is more sensitive to deprivation doesn't mean society should endorse their desires and treat them as objectively more important than (say) raising the comfort set-point of poorer people. There are a lot of people who just don't know how good they could have it because they havn't experienced what life is like with a higher income.

OIn other words, maybe they are happy living at the poverty line, and the upper-middle-class trust fund babies aren't, but that doesn't mean society should prefer to satisfy the desires of upper-middle-class trust fund babies.

Hazel Meade writes:

Addendum...
Ok, I realize your saying society should have no preference who gets the extra dollar. But I still say that's a terrible position. You can't treat marginal utility at the poverty line where there are steep gradients of basic things like health and nutrition equivalent to "this cabbage patch kid makes my spoiled middle-class brat really super happy." If only because the poverty line kid really has no idea what his life would be life if he was in that middle-class kids shoes.

David R. Henderson writes:

@Hazel Meade,
I realize your [sic] saying society should have no preference who gets the extra dollar.
No, I’m not saying that at all. All I’m saying is that you can’t make interpersonal utility comparisons.

Hazel Meade writes:

All I’m saying is that you can’t make interpersonal utility comparisons.

Really? I look over the fence and see that the grass is greener all the time.

Human being do make interpersonal utility comparisons every day. I'd rather be a first quintile earner than a 4th quintile earner. I look at my co-workers and I compare the size of their houses to mine. I compare what kind of car they drive to mine. I compare how many vacations they take, and where they are going. I'm pretty sure I can tell who is better off than me in economic terms, and it's pretty strongly correlated to how much money they have.

David R. Henderson writes:

@Hazel,
Notice that all of your examples are of things that you think would make your utility higher or lower. They aren’t interpersonal at all.

Hazel Meade writes:

Nope, while we're comparing the rate of "trade" between two goods, we don't know how happy cookies and bananas make Joe vs. Mary in total.
Mary might care very little about both, as she is on a paleo diet, whereas Joe cares a lot. But we can't glimpse inside people's brains to truly know what that utility is though. There is no blinking number inside to tell us.

To put it another way...
Let's say Joe comes from a rich family and he's used to driving a Mercedes. Mary comes from sub-saharan africa, and she's used to riding a donkey. So we really can't tell whether utility is more maximized by giving Joe a Porsche than by giving Mary a Toyota Camry? I mean, Joe might subjectively care a LOT about driving that Porsche, right? And poor Joe might really seriously psychologically suffer if he doesn't have a chaffeur, whereas Mary is totally content riding around on that donkey in the sunshine.

Hazel Meade writes:

Notice that all of your examples are of things that you think would make your utility higher or lower. They aren’t interpersonal at all.

Sure, because other people's utility functions are a total mystery to everyone else. How am I supposed to know that guy in the four bedroom house on the three acre lot doesn't secretly long from a mud-brick hovel in the Congo?

David R. Henderson writes:

@Hazel,
Sure, because other people's utility functions are a total mystery to everyone else.
Exactly!

Hazel Meade writes:

Then why is it that other people seem to be bidding up the price of the same things I want, like nice houses on large lots? That's just a huge coincidence that has nothing to do with other people having similar utility functions to mine?

David R. Henderson writes:

@Hazel,
Then why is it that other people seem to be bidding up the price of the same things I want, like nice houses on large lots? That's just a huge coincidence that has nothing to do with other people having similar utility functions to mine?
It's not a coincidence. That's a separate issue from whether one can make interpersonal utility comparisons.

Hazel Meade writes:

This is getting really silly. If someone has a similar utility function to me, then I can compare their lifestyle to mine and estimate their utility and compare it to mine. That's an interpersonal utility comparison.

Lots of people want similar things. Lots of people have similar utility functions. It's easy to imagine yourself in someone else's shoes and get a good estimate of what an extra dollar means to them.

And even if I'm wrong, I still see that richer people have a bunch of stuff that I want, so it's hardly going to make me less likely to support redistribution to think that maybe none of that stuff actually makes them happier. It's like you're saying "It's impossible to know whether that yauht really makes that millionare any happier than you, so you shouldn't mind that he has it and you don't!"


Brian Holtz writes:

I would love to see David Friedman's points debated further. They seem pretty strong.

pgbh writes:

Any time you decide to save money instead of spending it now, you are in effect making an interpersonal utility comparison. Saving is a decision that the utility your current self receives from current consumption is less than the utility your future self will receive from deferred consumption.

Sure this isn't technically "interpersonal", but you don't have perfect knowledge of your future self's utility function - just like you don't have perfect knowledge of other peoples'. In both cases all you can do is infer them from current observations.

pgbh writes:

@Hazel

You shouldn't mind that someone else is better off than you, unless you have some good reason to suppose that a more equal distribution would be more just or overall beneficial.

A failure to follow this rule is called "envy" and has been condemned in most cultures throughout history.

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