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

It is a cornerstone of the subjective theory of value that utility, in particular the marginal utility that determines what potential exchanges are allowed to come to fruitition, cannot be compared between individuals or between different points in time for a single individual.

I am requesting input, including possible changes in the title, that deals with this issue, as described below.

Assume that Bill Gates buys a small Pacific Island and causes 100 identical houses to be built. All 100 are hermetically sealed and filled with an inert gas, Argon, for example. After he leaves the day to day operation of Microsoft, he retires to the island and opens up one of the houses and begins to live in it. He then invites 99 of his most random acquaintances to join him on the island. However, he doesn't allow them to live in the houses, but requires them to live in tents on the beach.

The $64 question --

Given that we have no way in either theory or practice to compare the utility of the houses to Bill Gates with the utilities of the houses to the other 99 inhabitants of the island if they each possessed them, which distribution of the houses produces a greater benefit to the island society as a whole? Provide a theoretical economic justification for your answer. (or not)


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This seems to be simply a

This seems to be simply a variant on the dictator-Pareto problem (i.e., that Pareto optimality is a necessary, but not a sufficient, condition of distributive justice, since an allocation where a dictator owns everything is itself Pareto optimal, even if it is not "just").

One approach is to remember that, but for Bill Gates, there would be neither houses nor tents on the island, so what right does anyone have to say that Gates' restrictions are "suboptimal"?

Kip, This seems to be simply

Kip,

This seems to be simply a variant on the dictator-Pareto problem (i.e., that Pareto optimality is a necessary, but not a sufficient, condition of distributive justice, since an allocation where a dictator owns everything is itself Pareto optimal, even if it is not “just")....

This may be true in part, but I'm not interested in justice of any kind here.

Regards, Don

_Given that we have no way

_Given that we have no way in either theory or practice to compare the utility of the houses to Bill Gates with the utilities of the houses to the other 99 inhabitants of the island...._

Of course there is a way, intuitive empathy. We make rough and ready comparisons of interpersonal utility all the time, and we are no doubt right in our assessments more often than not. People who are utterly unable to empathise with the subjective values of others are known as psychopaths. My guess is that most people would prefer sitting on a cushion to sitting on a spike and that most people prefer living in houses to living in tents on the beach and that Bill Gates does not have peculiar and abnormal desires about owning empty argon filled houses on desert islands.

If Bill has forceably taken

If Bill has forceably taken them to the island, then it does boil down to a Dictator problem, the 99 have nothing to offer as there are no options available except swimming with the sharks. If we assume that the decision to come to the island is by choice, and if we assume that Bill wants people on his island, as expressed by his invitation, then we now have a market. Bill wants friends. The currency is either time or housing (tents/houses). The market is the best vehicle for improving the overall utility of each individual without sacrificing the utility of any individual as compared to the implied third option of whatever life they currently have prior to coming to the island. Each individual could blace binding bids (time, services, etc) on their time to Bill in exchange for housing (tent, room, whole house) and he could pick and choose which to honor/take until the marginal utility of friendship is lower than that of empty houses.

The same could be said in the coercive case, but game theory would suggest that it would require the threat of suicide (the third option) to be sufficient to motivate Bill to offer a house up.

What Paul said, plus this.

What Paul said, plus this. We do in fact have a way to think about the utility of other people. They are largely genetically programmed, and we share 99% of our genes with everyone else. Thus, we can infer things about other people, generally. For example, that sugar will diddle their pleasure centers roughly similarly. Why? Because it triggers similarly designed nerves via some genetically determined chemical triggers, resulting in similar nerve pulses, which end up in similar pleasure centers of the brain, etc etc.

Consider a similar experiment to yours, except where the 99 random people were 99 random alien beings from across the galaxy. In this case we'd be a lot less certain that moving them into human houses would really make things better overall.

Important question: did

Important question: did Gates let his acquaintances know they would be forced to sleep in tents before coming to the island?

Who cares? They're Bill's

Who cares? They're Bill's houses and how he uses them is none of our business.

Huh. I think you're lead

Huh. I think you're lead astray because you think of utility as a sort of quantity associated with each individual. Maybe I'm wrong. I think it's preferable to think of utility not as a quantity but as a degree of preference satisfaction. (But instead of going "on a scale from 1 to 10" we go "on a scale from 1 to infinity"...)

Now, subjectivism holds that each of us has a subjective scale and not only don't we share a common measuring unit but the units are not convertible.

Your puzzle looks vague to me. You ask of "greater benefit to the island society as a whole" but since I'm not an utilitarian or a collectivist, I don't know what's that. People have preferences and benefits, not islands or communities or whatnot.

The issues of the Social Welfare Function. I'm totally against such a construct partly because I think it's incompatible with the root of subjectivism. If instead you ask of the Pareto criterion, things are clear.

I don't think you'll success in deriving a "best" distribution of wealth out of value theory alone, be it subjective value theory or otherwise simply because you need further presuppositions regarding the weight of an individuals degree of preference satisfaction (even if meaningful, the SWF can be more or less egalitarian).

Anyway, in a market setting you get revealed preferences and willingness-to-pay which help you translate some preferences into cash. That should be enough for most sensible policies.

The issue of inter-subjective comparisons of utility is a hard one for utilitarians, at least some of them, those that need to add and subtract incommensurable units of different scales.

Also, we should keep in mind that the "ban" on inter-subjective comparisons is a scientific one. I can't *scientifically* compare your pain with mine, but outside the strict criteria of science, of course I can. We do that all the time. There's some work on this, derived from Wittgenstein's ideas on language, sensation and inter-subjective issues.

I agree with Gabriel on the

I agree with Gabriel on the social welfare function.

However I want to add one point and that is a point that I've seen neglected in other discussions: whatever we decide should be treated as something that was predictable before the beginning of the hypothetical case - because in the end whatever we decide (in reality) would be a precedent and would affect society for an indeterminate period. For example, if we were contemplating a redistribution of houses so that everyone would get a house, we should treat this as something that Bill Gates knew was going to happen, which would have affected whether Bill Gates built the houses.

I have seen economic discussion of law in hypothetical situations which seemed to me to be marred by a failure to back up to before the beginning of the hypothetical case, so I thought that was worth bringing up.

To elaborate on the matter

To elaborate on the matter of the social welfare function. The scientific function of economics is surely to explain and to predict. Science does not say what is better and what is worse. Scientists may say that they were unhappy that science led to the atom bomb, but science itself does not say whether atom bombs are good or bad, it only shows us how they work. Similarly, I think, with economics. If you say what should or should not happen, you may be using economics (to help you predict the consequences of your decision) but your assessment itself stands outside of economics, just as scientists' assessment that the atom bomb was a tragic invention stands outside of physics.

I don't think you're asking

I don't think you're asking a question. Or rather, if you define the following, I think you'll find the answer is included in that definition.

greater benefit to the island society as a whole

Your "paradox" isn't really a paradox. It's the natural confusion caused by trying to optimize an undefined measurement. There IS NO "society as a whole" that benefits from any decision or allocation. There is only a set of individuals, who individually prefer various choices they can make.

Personal utility in the strictest sense isn't even a scalar - it's just an ordering of options at any given point in time. We can tell which option an individual prefers based on what choice she makes. And it stops there. We can't tell what option was second place, let alone how much better the best choice was deemed to be, let further alone what choice might be made in a later situation or by a different individual.

In your scenario BillG owns the island, and each squatter can choose to live in a tent, to leave, or to revolt in some way (possibly just by buying a house, but possibly by trying to redistribute the property through violence or appeal to sympathy). There's still no optimization of any greater whole, except in the mind of each actor who gets to make his or her individual choice.

I suggest you change your title to: Is there a reasonable definition of "collective benefit"?

I think Gabriel and Dagon

I think Gabriel and Dagon hit the nail right on the head. I hadn't really thought about this much before, but there is really no such thing as a "cost to society" or "benefit to society." I'd already figured out there was no such thing as collective responsibility or group justice; I just hadn't extended it to any form of group benefit. That's kind of huge, because it means all these people trying to calculate "cost to society" etc. are really just masturbating. And sometimes sp00ging on other people in the process when they try to dictate policy. What a bunch of wankers :)

Ok I took the masturbation analogy way too far. :behead:

It seems to me, though, that

It seems to me, though, that a lot of attention is paid in economics to this. One reason may be that economists are often employed by the state in order for them to tell it what to do, and they need some basis on which to tell the state to choose one policy over another, when every alternative policy harms someone and benefits someone else.

Sean, I believe cost and

Sean,

I believe cost and benefit "to society" is simply a rough and ready shorthand for "costs and benefits in the aggregate" so I don't think anyone is actually engaged in mental masturbation here.

Steven, I think Sean's

Steven,

I think Sean's point, and Gabriel's and Dagon's point, is that costs and benefit can't be aggregated. As Gabriel writes:

Now, subjectivism holds that each of us has a subjective scale and not only don’t we share a common measuring unit but the units are not convertible.

If there isn't a common measuring unit then they can't be aggregated. And as Dagon writes:

Personal utility in the strictest sense isn’t even a scalar

If it's not scalar then it can't be added, so it can't be aggregated.

All, A good set of comments.

All,

A good set of comments. I won't try to indicate where assumptions about my outlook were not correct.

It is clear that most people would believe that the distribution of the houses just seems to make sense, even if no possible measurement can validate that.

However, there seem to me to be at least two ways in which the distribution is supported without any need for interpersonal utility comparisons.

First, there is nothing in this problem as stated that rules out MBVE (Mutually Beneficial Voluntary Exchange.)

There is every reason to believe that BG might well be willing to exchange a house for the services of a goumet cook, a gardener, or a handyman who promises to mow the lawn and re-align the satellite dishes after a storm, etc.

I don't think that there is any question that if all 99 argon-filled houses change hands as the result of MBVEs, then it would be hard to argue that the island society would not be better off, although I see no reason to necessarily bring optimality into the equation.

The second approach is too eccentric to cover in a comment, but it relates to the fact that the 99 argon-sealed houses do not likely really have real, direct (marginal) utilities for BG. If they have no utility, then no question of interpersonal comparisons exists. If a good has utility, that means that it is useful as a means of achieving an ordinally ranked subjective end or goal. Only some economic goods at some times satisfy this condition.

If we set aside production factors, there are two categoties of economic value, subjective use-value and exchange-value, with the larger of the two being the economic value of the good at a given point in time. While something with exchange value can be considered to have a marginal utility for the purpose of including it in a MBVE, this is not sufficient if there are no subjective use-valued (AKA consumer or first order) goods
available to later exchange for.

I believe that there is at least some degree of acceptance of the fact that a society almost universally benefits from an increased supply of economic goods. However, this doesn't apply to exchange-valued goods, as is seen by the ultimate exchange-valued good, i.e. money. As Austrians never tire of repeating, any supply of an existing money provides all of the services that money can and does provide. All that happens is that the exchange value of the monetary unit changes in the opposite direction of the change in supply, although not directly proportionately.

If I am considering exchanging a good, it is by definition an exchange-valued good as its subjective use-value is not high enough to rule out the exchange. This means that almost all exchanges not involving money are of exchange-valued goods for subjective use-valued goods for both parties to the exchange. This means that both goods are converted from exchange-values to subjective use-values. This increase satisfies the starting assumption that society benefits from an increase in subjective use-valued goods. If money were involved, then only one conversion takes place.

As an example, when BG exchanges a house for the services of a gourmet chef, both the house and the services are converted from exchange-valued goods and benefit society due to the two new subjective use-valued goods.

Regards, Don

Steven: What Constant said.

Steven:

What Constant said.

Don, you're still not

Don, you're still not addressing the base problem of what you mean by a society being better off.

Your proposed voluntary exchanges make the participants better off (well, at least they expected each exchange to make them better off, and who am I to disagree?) All voluntary actions have a higher utility than the action not chosen. But that utility for each individual simply cannot be added up to a utility for any group or subgroup.

if all 99 argon-filled houses change hands as the result of MBVEs, then it would be hard to argue that the island society would not be better off

It would be impossible to argue, because we don't know what you mean by the phrase. It would be just as hard to argue that if all houses were burned to the ground that that the fnargle wouldn't be wooply as well.

Use-value and exchange-value are irrelevant to this fundamental question. In both cases, the value to the maker of a decision (whether it's to enjoy the existence of my matched set of 99 argon-filled houses, or to trade one for some other service or good) is purely internal to that actor.

Dagon, Don, you’re still

Dagon,

Don, you’re still not addressing the base problem of what you mean by a society being better off.

Try this:

A society in state B is better off than in state A if state B adds a new supply of consumer goods without reducing or redistributing the existing supply.

Regards, Don

Don, your basic point is

Don, your basic point is that while left unoccupied the houses are not consumer goods but if they were to be redistributed then they'd become goods for the new owners.

You are right in that redistributing them you make them available for consumption, but it doesn't follow that Bill Gates is not worse off than before.

If something is a "good" to me that means I'd rather have it than not, all thing being equal, and it's a "consumer" good because its main/official/regular use is consumption rather than further production/refinement.

It is true that most discussions of utility, especially in economics circles, is related to Consumer Theory, but this doesn't mean that one can't "obtain utility" from non-consumer goods. (One can have preferences regarding non-consumer goods: If u(A) > u(B) then A preferred to B, where A and B are world states that are different only in my having or not of a non-consumer good.)

Gabriel, You are right in

Gabriel,

You are right in that redistributing them you make them available for consumption, but it doesn’t follow that Bill Gates is not worse off than before.

Nowhere did I say anything about redistribution other than by means of MBVEs.

Regards, Don

Sean, "Who cares? They’re

Sean,

"Who cares? They’re Bill’s houses and how he uses them is none of our business."

Likewise bars, restaurants, places of employment, airplanes...