What's it worth to ya?

On the topic of taxes, Brock Sides of Signifying Nothing writes:

My opinion as a utilitarian: Fairness is a useful concept for dividing splitting the cost of pizza between friends, but worthless when trying to determine what share of the tax burden an individual should bear. Economist can tell us about the effects of various tax schemes on economic efficiency, i.e. the total size of the economic pie as measured in dollars, euros, or what have you. But any gains in efficiency brought about by making the tax system less progressive may be offset by the diminishing marginal utility of money. If we shift $100 dollars of the tax burden from Bill Gates to some pauper, there?s a net loss in utility, because that $100 was worth more to the pauper than to Bill Gates, who could afford to wipe his ass with $100 bills if he wanted to. Somewhere in the middle lies the perfect tax system that maximizes utility, but we?re not going to find it by bloviating about fairness.

There is simply no proof that the pauper values the $100 more than Bill Gates does. I have known many poor people who valued their marginal dollar little more than as an ass-wiping apparatus; I have known many rich people who valued their marginal dollar like their lives depended on it. There is no way to compare the utility of the $100 for Bill Gates and the pauper. There is no way to add, subtract, multiply, divide, transform, factorialize, or take the square root of utilities of different individuals.

Goods such as money are valued by what ends they help achieve, and those ends are subjective to the individual. Action is taken to pursue by the individual those ends to attempt to reach higher states of satisfactions. A second unit of the same good does hold a lower marginal utility than the first unit, as it is used to pursue less desired ends. However, this comparison between different units of the same good can only be made within the individual. The Law of Dimishing Marginal Utility is only valid when referring to a single individual. This Law does not hold for interpersonal comparisons. Bill Gates might well be happier with his billionth $100 than the menial laborer is with his hundredth. There is simply no way to know.

A truer standard of "fairness" is consent. If we really want to "maximize utility", the best thing to do is allow voluntary exchanges, not coercion. Coercion destroys utility.

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First you say: There is

First you say:

There is simply no proof that the pauper values the $100 more than Bill Gates does. I have known many poor people who valued their marginal dollar little more than as an ass-wiping apparatus; I have known many rich people who valued their marginal dollar like their lives depended on it.

Immediately afterwards you say:

There is no way to compare the utility of the $100 for Bill Gates and the pauper. There is no way to add, subtract, multiply, divide, transform, factorialize, or take the square root of utilities of different individuals.

It seems to me that in the first quote you are making an interpersonal utility comparison. Your evidence indicates that the miser values his marginal dollars more than the pauper values his. So interpersonal comparisons of utility are not impossible, even if they are difficult.

I don't know if you're the charitable type, but if you are, would you donate $100 to the orphanage, or mail $100 to Bill Gates? (Of course, Bill would probably just turn around and donate it to the orphanage, but let's suppose for the sake of argument that he's a stingy miser.)

Donation don't enter in'o

Donation don't enter in'o it. We are talking about economy here. We are talking about paupers and prime movers here. There is a good chance that Bill Gate's dollar is going to used to move the economy along in some sort of high ROI enterprise. The pauper is probably going to invest in Marlberos and Jack Daniels (since that is how he ended up a pauper in the first place -- poor business decisions.)

We know what fairness is,

We know what fairness is, you know what fairness is, you have done since childhood, but here you are trying to argue that it's something else entirely and to contradict the instinctive notion that everyone has.

Indeed, it may turn out that the world is overall a better place if the children of the rich inherit riches and the children of the poor inherit nothing, and it may be that such a situation is consistent with the highest possible ideals of justice and economic advance.

But don't try to make out that it's "fair"!

We all know life in general isn't fair, and it won't suddenly become so if all transactions are based on consent only. Guy X will still slip on a banana skin, or get a disease, or get the girl, that guys Y and Z miss. This isn't fair, and no amount of uncoerced exchange of goods, services and monies will make it so.

Anyway, you *agree* with Brock that the basic notion of "fair shares" (which probably has a rather deep justification in game theory) isn't much use when it comes to allocation of resources, so I don't see why you should want to end up by redefining "fair" in a way that contradicts our basic notions.

Just accept it: the system you prefer, like life, will be unfair!

It seems to me that in the

It seems to me that in the first quote you are making an interpersonal utility comparison.

I disagree. I am making statements about how each one values his own marginal dollar, using my own personal value of scale to compare the two. The interpersonal comparison is based on my own subjective appraisal, not any sort of objective measurement.

I don't know if you're the charitable type, but if you are, would you donate $100 to the orphanage, or mail $100 to Bill Gates?

It depends. If my standard for donating was, "Whom would value it more?" (and for this example, I will replace the "orphanage" with "orphan" because orphanages don't value things, only people do.) If that was my standard, I would try my best to evaluate which individual would value it more. Perhaps my evaluation yields the belief Bill Gates would be incredibly ecstatic in being able to use that $100 to replace the memory card of his digital camera, and that the orphan would only be mildly amused at using the $100 to use for his school supplies. In that scenario, if my standard was, "Who values the $100 more?", I would give the $100 to Bill Gates. In other evaluations, the result might be the opposite.

If, OTOH, if my standard was, "Whom do I believe will benefit, based on my own subjective evaluations of the situation, from the $100?", I might give it to the orphan. Perhaps I believe that the marginal gain in education for the orphan from school supplies will result in a society I like better than one in which Bill Gates can take more digital pictures. In that scenario, and under that standard, I would give the $100 to the orphan. But only in that specific scenario. Other scenarios would yield different actions on my part.

Note that in my actions by the second standard, it is my subjective evaluation that is driving my decision, not any sort of "objective societal net utility gain".

We know what fairness is,

We know what fairness is, you know what fairness is, you have done since childhood, but here you are trying to argue that it's something else entirely and to contradict the instinctive notion that everyone has.

Umm, no. I don't see how what Brock is saying is fair at all. Instinct can be useful, but it can also mislead. Instinct told most people at a point in the past that heavy objects fall faster than lighter ones, and that frogs come from muddy soil. I prefer strict methodology to instinct.

We all know life in general isn't fair, and it won't suddenly become so if all transactions are based on consent only. Guy X will still slip on a banana skin, or get a disease, or get the girl, that guys Y and Z miss. This isn't fair, and no amount of uncoerced exchange of goods, services and monies will make it so.

When did I say that a system of uncoerced exchanges will make things perfect? I only claimed that my standard of fairness was "truer" than Brock's.

Anyway, you *agree* with Brock that the basic notion of "fair shares" (which probably has a rather deep justification in game theory) isn't much use when it comes to allocation of resources, so I don't see why you should want to end up by redefining "fair" in a way that contradicts our basic notions.

It may contradict your basic notions, but it does not contradict my basic notions of fairness. It seems eminently fair to me that people be allowed to engage in free choices to pursue their own subjective ends. It seems rather unfair for one person (or a group) to force some people to make choices against their will for a particular subjective view of a utilitarian outcome that the person (or group) doing the forcing desires. That would be selfish.

Just accept it: the system you prefer, like life, will be unfair!

Absolutely.

I only claimed that my

I only claimed that my standard of fairness was "truer" than Brock's.

Jonathan: Let me make it clear that I do not claim that a utilitarian society would be a fair one.

What I object to are attempts to hijack the notion of fairness to serve a preferred system of sharing the overall tax burden, such as Will and Cowen's implicit appeal to fairness in my original blog entry.

There was a letter in my local paper a few days ago which claimed "The only fair tax is a sales tax." (The author was railing against a proposed county payroll tax.) How absurd!

TomD: Yes, the notion of fair shares does have a game theoretic analysis. It's a Schelling point, which negotiating parties can agree upon quickly, eliminating unproductive negotiation. Which makes what it so useful for splitting the cost of a pizza. Of course, when the number of parties grows too large, negotiation is inevitable, and we call it "politics".

The interpersonal comparison

The interpersonal comparison is based on my own subjective appraisal, not any sort of objective measurement.

Jonathan: I don't understand the subjective/objective distinction you're appealing to here. Is it an epistemic one, or a metaphysical one?

Surely you're not saying that "X values his marginal dollar more than Y" is "subjective" in the way that "Vanilla is the best flavor for ice cream" might be called "subjective".

Schelling points are hella

Schelling points are hella cool.

If I'm correct on the usage

If I'm correct on the usage of the terms, it's an epistemic distinction.

For someone to say definitively that "$100 is worth more to the pauper than to the Billionaire", one has to have an objective scale of utility, and the ability to measure each's utility along that scale.

If such a scale does not exist, or the ability to measure objective utility is not present, then one cannot be definitive on who values it more.

Jonathan's (and my own) position is that, correctly, interpersonal utility comparisons are a priori invalid because personal utility is ordinal and not cardinal, so there is nothing that can be transformed into mathematics and thus rendered by computation, analyzed, etc. Its the old "apples and oranges" dilemma.

What Jonathan *is* doing, is looking at the situation and making his *own* subjective judgement, taking into account some anecdotes, and saying that "it may be possible that the rich man places having $100 higher on his internal order of preferences than does the pauper."

That is quite different from saying that there exists an objective scale of utility and that based on starting wealth, utility of each and every new dollar can be computed- therefore we can say with certainty/objectively that the pauper values the $100 more than Bill Gates.

Brock, I suspect it?s an

Brock,

I suspect it?s an epistemic one. My belief is that there is no such thing as objective economic value. And by economic value I do not mean value in the sense of ideals, such as ?I value integrity,? but rather economic value of scarce goods. No good ? money, gold, food, clothing ? has objective economic value. Rather, economic value is subjective.

How much value does a glass of water have? It depends on the individual, his circumstances, and his goals. Further, it depends on how many units of the good he already possesses. To me a glass has little value compared to a ring of gold. Yet, if I was dying of thirst in the desert, I would gladly trade in my ring of gold for a glass of water. My ends ? enjoying a cold, refreshing glass of water while writing on my blog in my apartment vs. sustaining my life in the desert ? is what determines the value I place on the glass of water. If instead I was fed up with life at all, I might not value that glass of water even if was dying of thirst in the desert.

How much value does $100 have? The answer given by many economists is ?$100?. But that answer is circular, and it begs the question ? how much value does $100 have? People value money for the same reason they value other things like glasses of water ? it helps them achieve their own personal goals. $100 might be worth more to me today when I have the urge to buy a PS2 to satisfy my own yearnings to play Grand Theft Auto, but tomorrow, when the urge goes away, the $100 might be worth less. It?s the subjective fulfillment of individual ends that determines the value of the $100.

Yes, each successive unit of the good is worth less and less to the individual, as it is used to satisfy less desired ends. The first glass of water in the desert might quench your thirst. The second glass of water might be used to fill your canteen for future use. The third glass might be used to drench your head. Etc.

But the actual subjective satisfactions each glass of water (and $100) is something very individualized in nature. No comparisons can be made across individuals. There is no ?state of satisfaction thermometer? we can use to quantify the value placed on items by different individuals.

It is just as possible that Bill Gates values the $100 more than the pauper as vice versa. It is just as possible that Bill Gates received more satisfaction with that $100 than the pauper as vice versa.

TomD: Yes, the notion of

TomD: Yes, the notion of fair shares does have a game theoretic analysis. It's a Schelling point, which negotiating parties can agree upon quickly, eliminating unproductive negotiation. Which makes what it so useful for splitting the cost of a pizza. Of course, when the number of parties grows too large, negotiation is inevitable, and we call it "politics".

I don't like the construction of fairness as Schelling Points, unless it comes with the strict consent of everyone involved. Otherwise, ethics is thrown out the window. "Politics" seems to defy this standard.