What\'s So Hot About Pareto, Anyway?

A while back I left a promisory note in the comments to write a post on diminishing marginal utility and interpersonal comparisons; this might that post, but I'm making it up as I go along so we'll see. Terminological hangups aside, I'll stick to the standard economic use of "utility" in what follows.

So: what's the deal with Pareto efficiency? A Pareto improvement is an improvement that makes at least one person better off while making nobody worse off, and a state of affairs is Pareto efficient if there are no Pareto improvements that can be made. Sounds unobjectionable, but actually is: without appealing to dubious Sen-style notions of "equitable distribution," it's easy to show that perfectly benign, everyday economic activity fails the Pareto test.

Consider a small town in which the current state of affairs is Pareto efficient. Then introduce a new person to that town who's very good at widget-making and can do it at a lower cost than anyone else. (Maybe he migrated, maybe he was just recently born there, it doesn't matter.) His entry into the widget-making market makes the current widget-making monopolist in town subjectively worse off, but makes both the widget-buyers and himself subjectively better off. Clearly this is a Good Thing, but it fails to satisfy the Pareto criterion. One could come up with all sorts of similar examples, but you get the point.

So given the barrenness of the Pareto criterion, why does anyone use it? The answer seems to be that it's the only way to gauge efficiency if we treat utility functions as intrinsically non-commensurable. If interpersonal comparisons are ruled out absolutely, then this is indeed the best we can do -- we have no basis on which to say a world where I am made $1 billion richer and you are made $0.01 poorer is more efficient than one in which we're both made $0.01 richer, and indeed must arguably conclude that the former is less efficient.

This isn't a new criticism, and it's the whole reason why Kaldor and Hicks came up with a modified version of Pareto efficiency (with technical refinement by Scitovsky): a change is a K-H improvement if it could be converted to a Pareto improvement by compensation payments from those who benefit to those who are made worse off by the change. (Note that there's no reason why they have to do so: all that matters is that there's a surplus after these payments have been theoretically carried out.) As before, a state of affairs is K-H efficient if no such improvements can be made. This criterion actually does get the right answer to regular economic questions like the example above -- those who gain could, in principle, fully compensate those who lose and still be left better off -- so it's all good, right?

Not quite. Raise your hand if you caught the conceptual smuggling being committed here. If utility functions are non-commensurable, how can it even be possible in principle for the kinds of compensatory payments K-H requires to occur? If we're commited to radical skepticism with regard to the utility values of different people's preferences, then we have no way of knowing what level of transfer payments could possibly be "correct" compensation, even in theory. The K-H criterion, and I hazard to say any sensible criterion of economic efficiency, seems to implicitly require some sort of (indirect) interpersonal utility comparisons.

I want to go further into this with subsequent posts, but for now that's the quick sketch of an argument against radical Paretian skepticism of interpersonal comparisons -- can anyone find fault?

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I believe K-H rests on a

I believe K-H rests on a presumption of perfect substitution that forces comensurability through money because no matter what is desired, it can be bought.

Matt, We will always want

Matt,

We will always want somebody to be worse off every day. An inferior businessman should be competed into oblivion by someone who can better provide what consumers want while employing resources with lower opportunity costs. We certainly don't want to compensate him for his failure as that would just encourage him and his ilk.

Regards, Don

Don, "We certainly don’t

Don,

"We certainly don’t want to compensate him for his failure as that would just encourage him and his ilk."

Obviously, but then nobody is suggesting that we ought to. The talk about transfer payments is just an explanatory gimmick. All that's really necessary for it is that gains to the benefiters* are greater than the losses to the losers. This is heresy to anyone who professes Paretian skepticism, but totally unavoidable for any robustly useful efficiency analysis.

*This would typically be measured in dollars for simplicity, but doesn't have to be; we could do the hypothetical transfer payments using any set of goods.

Utility is "commensurable",

Utility is "commensurable", sort of, via willingness-to-pay. That's what goes into Kaldor-Hicks.

Also, in contemporary, subjectivist theory, utility is not a (metaphysical?) quantity associated with an individual but rather a ranking of consumption bundles or world-states, preferences.

Therefore, utility can be known because preferences can (theoretically) be known, via revealed preference. What doesn't make sense is to compare the numerical value of the utility function built over a set of observations, especially since over a given set of observations there are an infinit number of utility functions that preserve that information. Hal Varian wrote a lot on this, especially the practical econometric issues involved in building an utility function over observed choices.

The notions of "Equivalent variation" and "Compensating variation" are used in analysis, rather than adding or substracting "utils".

Anyway, these things are best suited for positive economics research, not policy. These are really bad tools for policy, as all utilitarianism and utilitarianism-inspired stuff is, because it misses a lot of the picture.

P.S. I'm not sure what

P.S. I'm not sure what you're trying to prove. Interpersonal comparisons of utility are *scientifically* meaningless because there's no observable way of measuring how much more or how much less I *prefer* something versus your preference.

If we have 2 shirts, a blue one and a red one, and I prefer the blue, but you also prefer the blue, there's no *scientific* way of saying _who prefers the blue one more_. Also, this is hardly enough for a policy that would impose the red one to someone and let the other have the blue.

And to return a bit to your criticism of Kaldor-Hicks, there's no inter-subjective comparison because what I compare are the utilities of the same individual in 2 circumstances and try to determine a sum that would make him indifferent between the 2. So, it's about the same person's utility. Only afterwards I compare the _monetary sums_ to see if a payment is possible, a payment that both would prefer, according to revealed preference.

Patri, Suppose I can (for

Patri,

Suppose I can (for free) plant an apple tree, which will make $1 in apples a day, but it makes your apple tree less valuable, now earning $1/day instead of $1.50/day. We agree that this is K-H efficient b/c I could pay you $0.75/day, and now we are both doing $0.25/day better than before. In this scenario, tell me what intrapersonal utility comparison is being made.

Why do you stop at one (free) (instant) tree? Normally you would plant trees as long as the marginal cost of the next tree remained less than its expected marginal revenue. The payment is not accounting for the opportunity cost of not continuing to plant trees.

'Before' is an invalid basis of comparison for at least you since you can improve your lot, likely by more than 25 cents per day, by means of a unilateral autistic exchange for which the benefit or injury to the existing tree owner is of no relevance.

Regards, Don

This seems all wrong to me.

This seems all wrong to me. Two big problems:

1) Pareto efficiency is sufficient, not necessary, for a change to be good. It is a very strict criterion, so the fact that good things are not always Pareto efficient is just a big duh. No one claims it is a necessary criterion.

2) As long as you can get people to reveal the number of dollars which make them indiffferent between the two options, then, ust as Gabriel says, you are comparing the same person's utility. There is no smuggling, and there is no indirect comparison of interpersonal utility.

Suppose I can (for free) plant an apple tree, which will make $1 in apples a day, but it makes your apple tree less valuable, now earning $1/day instead of $1.50/day. We agree that this is K-H efficient b/c I could pay you $0.75/day, and now we are both doing $0.25/day better than before. In this scenario, tell me what intrapersonal utility comparison is being made.

Now, you may argue that it is hard to get people to reveal that amount, which is sometimes true, but this is a criticism of incentive-compatible bidding schemes, not of K-H efficiency.

I think the problem in your

I think the problem in your example (and many others trying to use this principle) is this:

His entry into the widget-making market makes the current widget-making monopolist in town subjectively worse off

If you define competition as harm, you're doomed. Likely-but-not-committed future trades are not property that is lost when a competitor emerges, and shouldn't be considered as a loss for this kind of analysis.

Dagon, Being undercut does

Dagon,

Being undercut does indeed make the other guy worse off. When analyzing economic efficiency we have no principled reason to exclude the effects on anyone from our analysis.

Patri,

Re (1): my question then would be what exactly it's supposed to be good for. What problem does this criterion solve, and why does anyone use it when there's an alternative which gets the right answer in all the same situations that Pareto does, and also in many more?

Re (2): the interpersonal comparison happens when we sum the gains and losses for both you and I in dollar terms. (Gabriel says as much above when he agrees that 'Utility is "commensurable", sort of, via willingness-to-pay.') This seems to implicitly require that dollars and cents have the same utility for both of us. Needless to say there's no a priori reason why this assumption would be true (though it could be, empirically), which is a problem for K-H (though not that big of one in practice, I think), but that's another post altogether...

Gabriel,

I'm happy to leave policy implications off the table while we're hashing out methodology (though I think they'd need to be addressed sooner or later). All I'm trying to prove is that it seems inescapable to indirectly make interpersonal utility comparisons if we want any useful measurement of economic efficiency. Also see above reply to Patri.

You also seem to waffle a bit when you first agree that willingness to pay is a sound measure of preferences and then say that "there’s no scientific way of saying who prefers the blue [shirt] more". But of course there is: willingness to pay as measured in a common unit!

Actually, my second question

Actually, my second question above was the *converse* of the original question, not the contrapositive. So they are two different questions, basically.

Matt -- I mostly agree with

Matt -- I mostly agree with you. But I have to correct you on the following statement: "If interpersonal comparisons are ruled out absolutely, then this is indeed the best we can do – we have no basis on which to say a world where I am made $1 billion richer and you are made $0.01 poorer is more efficient than one in which we’re both made $0.01 richer, and indeed must arguably conclude that the former is less efficient."

That's not right. The former is neither more nor less efficient than the latter. According to the Pareto criterion, the two situations are incomparable (that is, you simply cannot compare them using the Pareto criterion). This is true of any two situations A and B such that at least one person prefers A to B and at least one person prefers B to A. Pareto's inability to make comparisons like these is why it's referred to as a partial ordering.

With respect to Patri's point: It's true, as a simple matter of logic, that the Kaldor-Hicks criterion can rank situations without making interpersonal utility comparisons. But the question is why we should care what this criterion says. After all, we can dream up all kinds of criteria (e.g., situation A is superior to B if and only if there are more total hairs on people's heads in A), but normative criteria only matter if they make some sense in value terms. So what sense does the Kaldor-Hicks criterion make? If some new policy will make you worse off by $10 and me better off by $15 (meaning you'd pay as much as $10 to avoid the policy and I'd pay as much as $15 to implement it), then K-H says the change is superior to the status quo. No interpersonal utility comparisons required. But why is this a meaningful ordering of the new policy and the status quo? Why should we regard my gain as compensating for your loss, if I don't actually have to compensate you? To answer that question, you'll end up importing some form of interpersonal utility comparison, most likely by assuming (at least implicitly) that the marginal utility of a dollar is constant across persons.

I have been puzzling over

I have been puzzling over something for a while now: are there any scenarios in which voluntary transactions are *not* Pareto-improvements? Maybe the contra-positive is clearer: are there any Pareto-improvements that are not voluntary transactions? I am guessing we will need to assume that individuals are not rational and do not completely know their own preferences, which would be kinda absurd since there is no other way to know someone's preferences other than by observing their actions.

@Matt: To get back to your post, I think you were attacking a strawman when you say that’s the quick sketch of an argument against radical Paretian skepticism of interpersonal comparisons, because economists who do use the Pareto-efficiency criterion also hold that utilities *can* be compared through (and only through) revealed preferences.

Thanks, Glen. You're right,

Thanks, Glen. You're right, I misspoke -- what the Pareto criterion says is that the first situation is not an improvement and the second situation is, which seems weird enough.

The point is ... drumroll

The point is ... drumroll ... no welfare economics without substantive normative theorizing! Philosophical imperialism!

I'm sure that scratching my ass in the privacy of my own home is not pareto-efficient, since I'm sure there's somebody who prefers that no one ever scratch his or her itchy ass. Act Paretianism is crazy.

So we rule out and discount all sorts of preferences... "Meddlesome" preferences, the preferences of racists and child molestors etc. Matt and Patri both give examples of "pecuniary externalities," where other market actors affect the market price of inputs to or outputs from production, but don't adversely affect the production process itself--don't create a "technological" externality. We ignore pecuniary externalities because they are why prices work at all. If you have to pay more than you want to for apples, because everybody else is buying them, well, that's exactly what gets apple growers to grow more apples. And if you get less from your apples next year because everybody's growing more because everybody wants them, Etc., Well, that's what makes the world go round.

At the end of the day, we've got an either more or less principled theory about why we're ignoring and discounting some preferences and not others. But Pareto does get the basic structure of justification right: a good set of rules is one that is generally good for each person. A good rule Paretian might even be explain why we ignore some preferences in Paretian terms.

The way I've had it

The way I've had it explained to me by economics professors is that we can assume for the sake of our analysis that different people's marginal utility of a dollar is the same, which in turn allows us to make interpersonal comparisons of utility using dollars as the basis for comparison.

Of course, we know that different people's marginal utility of a dollar is not the same, but we can account for this discrepency better by using marginal tax rates and redistribution transfer payments than we could by taking it into account in every economic analysis we perform. In other words, economists argue that a cost-benefit analysis to, say, determine whether or not we should build a new roadway is a poor tool for addressing diminishing marginal utility of wealth. Better to address it directly with the tax and welfare system.

This puts libertarians who want to use Kaldor-Hick efficiency in their arguments in quite a pickle. David Friedman offers one way out:

Consider, for example, the abolition of a tariff. Suppose we could show (as in many cases we can) that it is an economic improvement--the benefit to those who are better off as a result of abolishing the tariff (workers and stockholders in export industries and consumers of imported goods), measured in dollars, is greater than the loss to those who are worse off (workers and stockholders in industries that compete with imports). Individual gainers and losers may have greatly varying values for a dollar; a change that benefits one of them by six dollars and hurts another by five is not necessarily an improvement in total utility. But both gainers and losers are large and diverse groups, and there is no obvious reason to expect the one group, on average, to value dollars more or less than the other. If the average is about the same for both groups, then a change that produces a gain in value probably produces a gain in utility as well. That was the argument used by Alfred Marshall, who invented the idea of economic improvement, to justify using it as an approximate way of identifying changes that increase total utility.

The approximation should be a good one as long as we are considering situations where there is no reason to expect gainers and losers to have, on average, different utilities for a dollar--different relations between value measured in dollars and utility measured in some absolute units of happiness. In many cases that is a reasonable assumption. Buyers and sellers of apples, lost hunters and owners of locked cabins in the woods, are likely to be similar people--even the same people at different times.

There is one obvious exception. We expect, as a general rule, that the more money you have the less an additional dollar is worth to you, and therefore that, on average, a dollar represents more happiness for someone with very little money than for someone with a lot of money. That is why we rarely give charity to millionaires. We therefore expect that, if gainers and losers have very different incomes, the net change in value will be a poor measure of the net change in happiness.

A change that makes a rich man ten dollars worse off and a poor man nine dollars better off is an economic worsening, but it may well increase the amount of happiness in the world. The same is true for a change that harms a large group of rich people by a total of ten million dollars and benefits a large group of poor people by a total of nine million. The obvious conclusion, and one that many utilitarians have drawn, is that income redistribution is a good thing. Taxing the rich and giving the money to the poor may be an economic worsening, due to collection costs and disincentives, and yet a utilitarian improvement.

My reasons for disagreeing with that conclusion are two. The first is that since the poor are, as a rule, politically weak, they are at least as likely to be the victims of governmental income transfers as they are to be the beneficiaries. That is the point that I made in Chapter 4. The second is that the struggle among groups trying to make themselves beneficiaries rather than victims is likely to be an expensive one, making practically all of us, rich and poor, worse off in a society that permits such redistribution than in one that does not. That is the point that I made in Chapter 38. Those two chapters were a utilitarian attack on one of the chief doctrines that divides utilitarians from libertarians.

- Machinery of Freedom, Chapter 43 "Answers: The Economic Analysis of Law," pp. 188-190

Venu, The answers to your

Venu,

The answers to your questions are yes and probably not, respectively, though the latter depends upon your assumptions. WRT the issue of people not knowing their own preferences, that's a big topic for a whole other post, but I don't think there's anything absurd about it -- it makes models intractable, but it also happens to be true. I also think that the dogma that "there is no other way to know someone's preferences other than by observing their actions" is soothing and works well enough, but needs a great deal of qualification. But again, this is getting into bigger issues...

I also don't understand how you can call it a straw man, when I've seen with my lying eyes (on the comments to this very blog) people make precisely the argument that interpersonal comparisons are strictly impossible. They may not couch it in Pareto terms (cf. von Mises), but the argument is the same.

Will,

I never found the distinction between pecuniary and non-pecuniary externalities very satisfying, because I don't think we have a principled reason for ignoring the former.

Micha,

DDF's arguments are good and important when the analytical rubber hits the policy road, but I have a third one to add: the knife cuts both ways, in that the lower a rich person values an extra dollar then the higher the reward has to be to get the marginal unit of work/risk-bearing out of them. Since economic growth is largely driven by entrepreneurs attracted by potentially huge rewards, and economic growth is good for the least well-off, soaking the rich is the opposite of what we should be doing.

the knife cuts both ways,

the knife cuts both ways, in that the lower a rich person values an extra dollar then the higher the reward has to be to get the marginal unit of work/risk-bearing out of them. Since economic growth is largely driven by entrepreneurs attracted by potentially huge rewards, and economic growth is good for the least well-off, soaking the rich is the opposite of what we should be doing.

I'm not sure this argument holds water. In actual practice, I think it may be the other way around -- that the marginal differential in dollar utility for rich vs. poor/average drives the outsized rewards for entrepreneurship. Most massive risk taking entrepreneurs either a) are not rich when they *start*, or b) only risk a small proportion of their net worth.

The basic problem is that if rich folks marginal utility were such that they didn't need an outsized reward to justify a big risk, then such people would glom onto opportunities (as long as they had enough non-invested funds to be kelly-safe) and lower the expected payoff of such ventures. Ultimately, it's possible that such a development might end up pricing rational poor people out of the entrepreneurial market entirely, particularly if we at the same time, eliminated a guaranteed social safety net (which limits the devastation of a total loss).

In practice, of course, business ideas and the technological and managerial talent to turn them into profit aren't really a commodity, so I have no fears that it would become impossible under a catallarch regime for a poor, talented soul to become rich by becoming an entrepreneur. It's also quite possible that other positive factors would outweigh the concerns of my previous paragraph, making it easier, rather than harder to have a rags to riches outcome. But at best, I think it's unclear whether the utility gap helps or hurts entrepreneurship.

I suppose it's clear even if my predictions are accurate, that it would help innovation in *general*, but it may significantly increase income/wealth disparity which hurts overall utility. Again, whether the additional economic advantage would spread widely enough that we'd see total utility gains is unclear, IMO.