Pareto Efficiency and Justice

From the (at the time of this writing) Wikipedia article on Pareto efficiency:

Pareto efficiency does not necessarily require a just or equitable distribution of wealth. An economy in which the wealthy hold the vast majority of resources may be Pareto efficient.

Amartya Sen has elaborated the mathematical reasons for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge on Pareto efficient, but inequitable, distributions. A simple example is dividing a pie into three equal pieces, and then distributing them among three people. The most equitable distribution is each person getting one piece. However the solution of two people getting one and one half pieces, and the third getting none will be preferred 2-1 over the equitable distribution.

I added to the second paragraph:

example completely ignores the origin of the pie, so it breaks down to the criticism that Pareto efficiency does not really help in determining the optimal allocation of windfalls that nobody involved actually produced, such as a pie miraculously falling from the sky. This allocation is also only weakly Pareto optimal; strongly Pareto optimal solutions would likely involve everyone receiving a piece of the pie. Of course, it does not tell you how much pie to give each person.

Who knows how long this addition will last? The example given also ignores that the people involved may wish to engage in further transactions to adjust the pie allocation.

What I did not mention is that value judgements like what is "just" or "equitable" require interpersonal utility comparisons, which we already know are impossible. Even if a pie did fall from the sky, it seems to me that most people would consider it the property of whoever found it, or if multiple people saw it fall and knew where it landed, whoever got to it first. The person who got to it may decide to give pieces away, but I don't think he would be invoking Pareto in the process.

This would seem to be the fundamental problem with government ownership of natural resources, or in fact with any sort of attempt by government to allocate resources without resorting to a free market price system. You run into situations like in Sudan where the government spends more money on infrastructure in places that are populated by the ethnic group that is currently in power. This of course happens with taxes as well, but at least taxes are paid mostly by the rich, who also generally have the most power in the government, which means the taxes end up getting mostly spent on the rich.

A much better solution in the case of natural resources would be for the government to simply auction them off to the highest bidder. The auction process would tend to ensure that the fewest number of additional transactions took place regarding the allocation of the resource; the primary transaction would be subdivision if the government did not subdivide the resource in the first place. The allocation problem still exists with the money the government receives from the sale, but this is a one time problem rather than an ongoing problem. The government could pay down its debts and/or write everyone the same sized check and be done with it.

Of course, this solution does not only apply to natural resources, but to everything owned by the government. Put it on eBay.

Update: Interpersonal utility comparisons are impossible other than on a "fuzzy"/probabilistic basis.


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Interpersonal Utility Comparisons
Can the Paradox of the Non-Comparability of Interpersonal Utility be Resolved?

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Sean, Pay attention to

Sean,

Pay attention to Coase: dividing the pie in any way is exactly equal to dividing the pie in another way so long as transaction costs approach zero.

The pie example is terrible.

The pie example is terrible. The size of the pie in constant no matter how it's cut, so any distribution is Pareto optimal. The example says "the solution of two people getting one and one half pieces, and the third getting none will be preferred 2-1 over the equitable distribution." That's true, but the fact that a majority is happy with the distribution has absolutely nothing to do with Pareto efficiency. If my only knowledge of Pareto effiency came from that Wikipedia entry, I would be extremely confused. That's the most serious problem with the pie example, and you addition doesn't really address it. Pie division is a commonly used example in economics, but it's confusing and inapplicable to Pareto efficiency.

BTW, I think wrong to claim that a .5-.5-0 split of a pie is not strongly Pareto optimal. Any pie division is strongly Pareto optimal. Whatever the distribution, you can't give to one without taking from another.

You're right to complain about the pie example, but I think you're missing the point.

Sean, I'm with you to a

Sean,

I'm with you to a certain extent here, but this claim

What I did not mention is that value judgements like what is “just” or “equitable” require interpersonal utility comparisons, which we already know are impossible. (emphasis added)

strikes me as, well, overstated. I understand the point that interpersonal utility comparisons are not particularly easy to do and that analogies between my own marginal utility (where I value my 1st dollar more than my 10,000th dollar) and comparative marginal utility (where I'm said to value my 1st dollar more than you value your 10,000th) don't work very straightforwardly.

That said, the claim that all interpersonal utility comparisons are impossible just doesn't follow. After all, we do things very much like this all the time, as, for instance, when I put a dollar into the Salvation Army bucket. I make the determinination that someone else will get more value from my dollar than I will. And I think, by and large, that I'm usually right when I make that decision.

Your objection, I take it, is that it's pretty difficult for me to determine whether, say, you or Brandon would get the most value out of your dollar. And you're right that such determinations are, on their face, pretty difficult to make. I'd still venture that they aren't impossible to make, though. If Brandon is starving on the street and you're getting ready to use your dollar to light up a cigarette, then I'd say it's pretty obvious to me that he'll get more value from the dollar than you will.

I know; you're going to make the standard sort of libertarian move here and talk about what we in the philosophy world call utility monsters (i.e., the odd duck who gets extraordinary value from really trivial things). Here's the thing, though. There aren't really very many utility monsters out there in the world. From the fact that they might exist, you want to claim that interpersonal comparisons of utility are therefore impossible. But that's just silly. It's like saying that you doubt the existence of the world around you because you might be living in the Matrix. Sure, that's a possibility. But it's extremely unlikely. And extremely unlikely things ought not be our default position. The more unlikely something is, the more evidence you need (or ought to need) before you accept it as truth.

The same principle ought to apply to interpersonal comparisons of utility. You can't just say, "Well, someone might value lighting a dollar on fire more than someone else would value not starving to death." Yes, that might happen. But chances are pretty high (approaching certainty in the real world that you and I actually inhabit) that no one will actually hold this sort of preference. Thus we can pretty safely make at least some rough and crude interpersonal comparisons of utility.

I've modified the example.

I've modified the example. The new statement is:

However the solution of two people getting one and one half pieces is also Pareto optimal despite not being equitable, because the only way for the person with the smallest piece to get more is for one or both of the other two to get less, which is not a Pareto improvement.

Clarified: However the

Clarified:

However the solution of two people getting one and one half pieces and the third person getting none is also Pareto optimal despite not being equitable, because the only way for the person with no piece to get a piece is for one or both of the other two to get less, which is not a Pareto improvement.

That’s true, but the fact

That’s true, but the fact that a majority is happy with the distribution has absolutely nothing to do with Pareto efficiency.

Agreed, so I arrogantly went in and changed the article. The point about the majority is a problem of democracy, not a problem of Pareto efficiency.

Joe Miller, You might want

Joe Miller,

You might want to take your discussion over to the entry "Can the Paradox of the Non-Comparability of Interpersonal Utility be Resolved?" because that's where the topic that you address is being discussed.

When I was four, I had a

When I was four, I had a utility monster under my bed. I think he really did derive more utility from scaring me than I would have from not rupturing my bladder because I was afraid to get up and go to the bathroom.

Sean, I'm not going to touch

Sean,

I'm not going to touch it but I suggest either defending or removing the statement:

"This allocation is also only weakly Pareto optimal; strongly Pareto optimal solutions would likely involve everyone receiving a piece of the pie."

If Brandon is starving on

If Brandon is starving on the street and you’re getting ready to use your dollar to light up a cigarette, then I’d say it’s pretty obvious to me that he’ll get more value from the dollar than you will.

There's a difference between wasting cash and wasting assets. If I use a dollar to buy food and then I eat the food, I've consumed $1 worth of assets that are now unavailable to the rest of society. If I burn a dollar bill to light a cigarette, the only asset I've wasted is a tiny piece of paper. But I've also reduced the money supply, thus doing my part to fight inflation and increasing the value of everyone else's dollars. Plus, my cigarette gets lit.

Steven: I did think a lot

Steven: I did think a lot about Coase in the process but I really only wanted to talk about Pareto. It's unfortunate that in reality transaction costs are not only not zero but usually not close enough to zero to entirely neglect. And actually they are not the same in this example because where did the pie come from? Does the person doing the dividing really own it? It's hard to argue that my giving you a pie is the same as my giving you and two other people the same pie.

FXKL: Excellent comment, and I agree with you. I still do not fully understand Pareto efficiency, particularly about my second point, which is why I did not add it to the article.

FXKL and Constant: I have no problem with my statement about strongly versus weakly Pareto optimal being removed because I don't understand it well enough yet to really back it up.

Joe: For someone to take money from you on account of your burning it is no different than taking money from you on account of your spending it on "useless" things like a fourth car. My "impossible" claim is not string because it's easy to disprove: just show one case where you can do it. But you haven't. The "obviousness" of a comparison is not enough, because if there's one thing I've learned it's that what's obvious to one person is not at all obvious to another.

FXKL: I don't think it makes sense to make a distinction between "cash" and assets here. Cash is an asset in that it can be used for transactions.

Pareto Efficeincy, A

Pareto Efficeincy, A Definition Good Enough For Most Instances:

A situation in which something cannot be given to one person without taking it from another.

A More Pretentious Version of Same:

A situation in which the utility of one party cannot be raised without reducing the utility of another party.

Sean, For someone to take

Sean,

For someone to take money from you on account of your burning it is no different than taking money from you on account of your spending it on “useless” things like a fourth car.

Hey, look, there is gray in the world. I guess that means that black doesn't actually exist. Maybe you're reading too quickly or maybe I wasn't as clear as I thought I was, but this response seems pretty much completely to miss the point of my response. My claim is not that I can make interpersonal comparisons in every single case, reliably and accurately, even in instances where the values are close. Rather, my claim is that in some sorts of really extreme cases, we can pretty reliably make interpersonal comparisons. You respond by saying something like, "Yeah, but if I try to extend those comparisons to less obvious cases, then it doesn't work." Well, duh. That's pretty much just what I'd already said.

My “impossible” claim is not string because it’s easy to disprove: just show one case where you can do it. But you haven’t. The “obviousness” of a comparison is not enough, because if there’s one thing I’ve learned it’s that what’s obvious to one person is not at all obvious to another.

This isn't engaging in anything like reasonable debate. It's more akin to sticking your head in the sand and chanting "nyah, nyah" over and over. I gave you a case. Two in fact. One you don't bother to comment on. Actually, you don't comment on either of them. In any event, my whole point is that while it's possible to deny that we can make interpersonal comparisons of utility, it's not really very reasonable to do so. Indeed, to deny the sort of case that I offer is to adopt a position that is seriously counter to what ordinary people actually think and do on a regular basis. I suppose that you can simply claim that ordinary people ordinarily behave irrationally. I'm not sure that sounds like a promising strategy, especially for someone who thinks that economics can explain why people do the sorts of things that they do.

You seem to be saying something like, "If you can't give me a case of X that everyone would accept as indisputably true, then I have a good reason for believing not-X." Besides the fact that such a move commits the ad ignorantium fallacy, it's a rather odd standard to hold. If this is really how you determine what to believe or not believe, then I suspect that you probably don't end up believing in much of anything...including many of the principles of economics, since I'm sure that we can find at least one economist who will reject any principle that you might care to name.

You may well be a utility monster who derives untold pleasures from your fourth car...so much pleasure that it more than offsets the pain that Brandon suffers when he starves to death. I pretty seriously doubt it, though. And I'm pretty sure that you doubt it, too. If you're pretty sure about that fact and I'm pretty sure about that fact, then guess what? We've made an interpersonal comparison of utility. And like I said before (which, again, you don't really comment on), we do exactly this sort of thing every time we give to charity. Or visit a friend in the hospital. Or help a friend study for an exam. Or skip a party to console a friend who just got dumped. The simple fact is that we make these sorts of comparisons all the time. If we get it right at least once, well then we've successfully made an interpersonal comparison of utility. Not impossible at all. Not even remotely.

Sorry, Joe, I cut down my

Sorry, Joe, I cut down my response to you a bit from what I originally intended to post. I had originally talked about slippery slopes, because talk about "obvious" interpersonal utility comparisons put you on one. What if I'm on my thousandth car, and I just leave the cars rusting in my huge back yard? Is it "obvious" that you should take the money that I would by my 1001th car with and give it to Brandon? When do you stop?

Anyway, the reason I didn't respond to your second example was because I hadn't read it. Now that I've read it, I'll respond: that's not an interpersonal utility comparison. When I give a dollar to the Salvation Army it is because I value the satisfaction that giving away the dollar brings more than I value the dollar. Sure, I may conjecture about the value someone else might place on that dollar, but that is not an actual comparison in any rigorous sense; it's just conjecture.

Sean, If that's really what

Sean,

If that's really what you do when you give money to charity, then I must confess that I'm somewhat surprised. It strikes me that that sort of attitude doesn't very well represent what most people do when they contribute to charity. Or at the very least, it doesn't correspond very well with the (admittedly unscientific) surveys that I do of my intro to philosophy students every semester when we talk about charity. Pretty much universally, they all claim to give money because they feel like their money will do more good elsewhere than it will if they keep it.

I agree that we don't make any sort of rigorous interpersonal comparisons, but I didn't ever argue that we do make these comparisons rigorously. Rather, I claimed that we can do so pretty roughly in cases where one thing is relatively trivial and the other is pretty significant. I may be unable to put a number on the comparisons, but it's a comparison nonetheless. Your claim is that any comparison is impossible. My response is that some rough comparisons are possible. You then respond by saying that rough comparisons are not rigorous. I know that, but it's not really the point.

As for the slippery slope, I suppose that I could point out that, properly speaking, slippery slope arguments are fallacies. You can't just assert that there are no logical stopping points; you have to demonstrate that there aren't any.

More to the point, though, you seem to be assuming that I'm arguing for something that I'm not actually arguing for. I'm not offering some sort of argument for redistribution (which is what your slippery slope charge seems to assume). I'm arguing only for a narrow point, namely, that some crude interpersonal comparisons of utility are indeed possible. I'm not arguing that we can do so all the time or even that we can do so frequently enough to justify redistribution. I'm claiming only that we can in fact make some rough interpersonal comparisons, and that, as a matter of fact, we do so pretty frequently.

It is true that my claim entails that redistribution is, in principle anyway, justified. It doesn't follow that redistribution will in fact be a good idea. But it would follow that we could actually know that a particular act of redistribution would in fact maximize utility.

Two things can be done in

Two things can be done in philosophy. We can strive to improve our everyday ideas, possibly dumping them entirely. Or we can enshrine them. Some philosophers do one, some do the other.

Here's an example of an idea which we ought to combat when we see it: the idea of a just price - meaning the true price of a thing which ought to be charged, regardless of what the market actually has set the price to be. This is a pernicious idea which has caused much mischief in the past, and some familiarity with economics may be enough to shake the idea loose. It is nevertheless a persistent idea which rears its atavistic head all too frequently.

A similar idea is the idea that the economic value of a thing is intrinsic to it in the way that its weight or its color is intrinsic, rather than being a product of variable market conditions.

A similar idea is the idea that utility is something that can be compared across people.

People really do compare

People really do compare utility across people. People also really do read horoscopes.

That said, the claim that

That said, the claim that all interpersonal utility comparisons are impossible just doesn’t follow. After all, we do things very much like this all the time, as, for instance, when I put a dollar into the Salvation Army bucket. I make the determinination that someone else will get more value from my dollar than I will.

Charity does not attempt to maximize the recipient's utility, let alone social utility. If charity attempted to maximize the recipient's utility then it would do everything it could to empower the recipient to choose what he prefers. Specifically, they would never give medicine, never give food, never give clothing, in fact never give anything that could not easily be exchanged for something the recipient prefers. They would always give cash. Charities do not do that, at least most of the ones that I know about do not do that.

What charity attempts to do is to (with the recipient's permission) do something to the recipient that the giver wants done. That might involve clothing or medicine or education or food. The giver is not interested in maximizing the recipient's utility, for if the giver were interested in that then the giver would maximize the recipient's power to choose. That is what utility concerns, it concerns choice and preference.

Charities are not interested in the utility of the recipient. They are interested in benefitting the recipient in some way that the giver considers to be a benefit. They reflect the giver's choice, not the recipient's choice, and therefore concern the giver's utility, not the recipient's utility.