Exploding IUCs on the roadside

Continuing the recent discussions on interpersonal utility comparisons, I will follow the pattern and disagree with my fellow Catallarchist Brandon Berg's shocking assertion that interpersonal utility comparisons (IUCs) are possible. As such, and since I will not have much good to say below about the argument, I will first point out that Brandon is an excellent thinker and that with the final salient point of his post (that redistribution is not justified by IUC) I heartily agree- and that as always, my contention is with the argument, not the arguer.

That said, pace Brandon, one of my least favorite arguments about political economy is the suggestion that IUCs are possible. Not the least because it happens to be absolutely false (cannot be done theoretically or empirically), not simply 95% false or 99% false, or any other concession one is willing to make. But also because it usually involves, by parts, irrelevancies, category errors, and bad faith argumentation. Part one will deal with the former objection, while part two (tomorrow) will address the latter.

Primarily, the reason that IUCs are impossible is that for it to be possible at all (in a rigorous/economic sense), several properties must simultaneously be true:

1. Utility is cardinal.
2. Utility rankings are constant within individuals over time.

3. Utility can be measured objectively.
4. Following 1, 2, and 3, Happiness/Utility[1] can be measured on an objective, absolute scale through summing cardinal utilities and comparing like to like.

Starting with the first proposition- The consensus of economists for over a hundred years has been that utility is ordinal, not cardinal (one thinks the marginal revolution took care of that idea). Not that a consensus tells us much, but following the work of Mises & Rothbard, it is theoretically & abundantly clear that all utility is marginal/ordinal[2] and not additive. This, of course, dooms IUC from the beginning, but let us continue.

Moving down the list, constancy/consistency is an assumption that is plainly contradicted by everyday experience. People demonstrably do *not* have constant utility rankings or preferences, in fact people's tastes change all the time with different rankings. I'm not even sure that diminishing marginal utility (a principle claimed to support the possibility of IUC) could even exist[3] if preferences were constant.

A favorite rebuttal is that subjective states have been measured; thus,
the old, unscientific subjective feeling of heat has given way to the objective
science of thermometry. But this rebuttal is erroneous; thermometry does
not measure the intensive subjective feelings themselves.
It assumes an
approximate correlation between the intensive property and an objective
extensive event—such as the physical expansion of gas or mercury. And
thermometry can certainly lay no claim to precise measurement of subjective
states: we all know that some people, for various reasons, feel warmer or
colder at different times even if the external temperature remains the
same. Certainly no correlation whatever can be found for demonstrated
preference scales in relation to physical lengths. For preferences have no
direct physical basis, as do feelings of heat.[4]

[Emphasis added]

Just as thermometry cannot tell you if you're hot or cold, neither can converting some preferences to dollars allow one to say 'voila, utility is measured'- no, dollars are being measured and any connection to individual utility is indirect and, as time passes, increasingly erroneous. Converting some preference lists to dollars does not bridge the gap to measuring utility directly, nor can it claim to objective comparison since, as we know prior, preferences and utilities are not constant (unlike laws of physics). Trying to reduce things to probabilities does not solve the problem, either. That simply makes the position of the "possibilists" less distinct, while leaving the problem of subjectivity unaddressed.

Lest Rothbard be accused of some dualism in his last sentence, some clarification is in order. The corpus of work done in neuroscience, cognitive science, and even happiness studies all support the idea that there is significant and meaningful difference between individuals in how they process pain, pleasure, thoughts, etc. While there are realms of generality and areas of the brain that are often associated with X, Y, or Z phenomena (they light up on fMRI scans and what not when faced with X, Y, or Z), what is clear is that you cannot see "a thought" or a feeling via imaging (despite it being mediated by the physical network of the brain) and that what does light up is unique in particulars from brain to brain. The same regions don't light up the same way between people and often even over time within the same person. Thus Rothbard's assertion is essentially correct- there is no constant direct physical basis, even within individuals over time, to say "aha, that blip there in the frontal cortex is a preference and it is X intense vs. Y".

And the happiness literature overwhelmingly suggest that happiness is a relative phenomenon and not absolute. Few things will keep people demonstrably happier over some baseline over time, regardless of how much or how varied they may be; hedonic adaptation is the word. Thus since empirical biology & psychology, as well as economic theory all deny any sort of additive/absolute nature of happiness or utility, and given the theoretical and empirical refutations of the other necessary conditions, interpersonal utility comparisons are flatly impossible, and always have been.

-----------------------------

fn1. Despite being separate concepts, the two are often, unfortunately, conflated.

fn2. Contra Caplan, who (unconvincingly, IMO) posits that (a) neoclassical economics allows cardinal utility and (b) Rothbard allowed it too, and was just mistaken.

fn3. In an economically relevant way.

fn4. Rothbard, Murray. "Toward a Reconstruction of Utility and Welfare Economics," pp19-20


Related posts:

Why IUCs?
Cardinal Schmardinal, Ordinal Schmordinal
Encoding Happiness
IUCs and the Law of Large Numbers
No Soul Suggests IUCs
Futilitarianism
I-CDDFP
I-CUP
Love and Intrapersonal Utility Comparison
What color does a submarine weigh? (True or False?)
Interpersonal Utility Comparisons
Pareto Efficiency and Justice
Can the Paradox of the Non-Comparability of Interpersonal Utility be Resolved?

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Both sides are right,

Both sides are right, they're just arguing different things.

Utility cannot properly be compared among different individuals/situations/timepoints. Expected utility IS compared all the time, by most people.

The key is that those people who make the comparisons aren't comparing actual preferences (aka utility), they're comparing the results of a model of their own and others' preferences, and then sometimes checking their predictions against actual expressed preferences. Some people have better models than others, and some people have more confidence in their models than others, but in all cases it's just a simplified model, and will contain errors.

When TyroneBrandon claims it's an unconvincing argument against redistribution, he's right. Many people overinvest in their models of the world, and even forget that the model is different from reality. You invariably get into arguments about how predictive the model is, and what kind of error rate is reasonable to accept before deciding the model is "good enough".

Worse, the normal empathy-based model contains incorrect-but-annoying-to-refute assumptions like the bizarre mix of "all people have equal weight for their preferences" and "all 'legitimate' preferences are similar to my own".

So I'm agreed with both y'all. Interpersonal (and intertemporal) utility cannot be compared, and this is not the best argument against redistributive systems.

The best argument against redistribution for me is that it fucks up the motivation to do things that people think are important enough to pay well. Second-best is that it's a violent act, and I prefer to minimize the amount of coercion to which I am party.

Brian, ... I’m not even

Brian,

... I’m not even sure that diminishing marginal utility (a principle claimed to support the possibility of IUC) could even exist3 if preferences were constant.

Diminishing marginal utility says that interchangeable means will be sucessively applied to lower subjectively ranked ends and, as a result, the marginal utility of any of the means will be set by the lowest ranked end that the available quantity of means can be applied to. I see no requirement for constant or non-constant preferences.

Regards, Don

I'm fairly sure that

I'm fairly sure that Rothbard deals with von Neumann's notion of continuous cardinal utility fairly decisively in the paper I linked. Prior to the text I quoted is the extensive takedown of that position:
[Emphasis added for the critical point]

The errors of this theory are numerous and grave:

(1) None of the axioms can be validated on demonstrated preference
grounds, since admittedly all of the axioms can be violated by the
individual actors.
(2) The theory leans heavily on a constancy assumption so that
utilities can be revealed by action over time.
(3) The theory relies heavily on the invalid concept of indifference of
utilities in establishing the numerical scale.
(4) The theory rests fundamentally on the fallacious application of a
theory of numerical probability to an area where it cannot apply.
Richard von Mises has shown conclusively that numerical probability
can be assigned only to situations where there is a class of entities,
such that nothing is known about the members except they are
members of this class, and where successive trials reveal an
asymptotic tendency toward a stable proportion, or frequency of
occurrence, of a certain event in that class. There can be no numerical
probability applied to specific individual events.39

Yet, in human action, precisely the opposite is true. Here, there are no
classes of homogeneous members. Each event is a unique event and is
different from other unique events. These unique events are not repeatable.
Therefore, there is no sense in applying numerical probability theory to such
events.40 It is no coincidence that, invariably, the application of the neocardinalists
has always been to lotteries and gambling. It is precisely and
only in lotteries that probability theory can be applied. The theorists beg the entire question of its applicability to general human action by confining their
discussion to lottery cases. For the purchaser of a lottery ticket knows only
that the individual lottery ticket is a member of a certain-sized class of
tickets. The entrepreneur, in making his decisions, is on the contrary
confronted with unique cases about which he has some knowledge and
which have only limited parallelism to other cases.

(5) The neo-cardinalists admit that their theory is not even applicable
to gambling if the individual has either a like or a dislike for gambling
itself. Since the fact that a man gambles demonstrates that he likes to
gamble, it is clear that the Neumann-Morgenstern utility doctrine fails
even in this tailor-made case.41

(6) A curious new conception of measurement. The new philosophy
of measurement discards concepts of “cardinal” and “ordinal” in favor
of such labored constructions as “measurable up to a multiplicative
constant” (cardinal); “measurable up to a monotomic transform”
(ordinal); “measurable up to a linear transform” (the new quasimeasurement,
of which the Neumann-Morgenstern proposed utility
index is an example).

This terminology, apart from its undue
complexity (under the influence of mathematics), implies that
everything, including ordinality, is somehow “measurable.” The man
who proposes a new definition for an important word must prove his
case; the new definition of measurement has hardly done so.
Measurement, on any sensible definition, implies the possibility of a
unique assignment of numbers which can be meaningfully subjected
to all the operations of arithmetic. To accomplish this, it is necessary
to define a fixed unit. In order to define such a unit, the property to be
measured must be extensive in space, so that the unit can be
objectively agreed upon by all. Therefore, subjective states, being
intensive rather than objectively extensive, cannot be measured and
subjected to arithmetical operations. And utility refers to intensive
states. Measurement becomes even more implausible when we realize
that utility is a praxeologic, rather than a directly psychologic,
concept.

von Neumann-Morgenstein

von Neumann-Morgenstein showed how utility functions need to be continous when you add risk-aversion into the mix.

Utility is not cardinal, and Caplan didn't claim this, because there's an infinity of continous functions that can stand for the same preferences so there's no unique scale. Any monotonic transformation of a contious utility function represents the same preferences.

So, it depends on what you mean by cardinal. In a sense, it's cardinal but not in the sense that those numbers are meaningful beyong "u(A) > u(B) < => A prefered to B."

I agree that there are no

I agree that there are no clear scientific methods of measuring happiness. First of all, there are many different views on what kind of "happiness" is most valuable. Some people think inner peace is the best, some people think exhileration, etc. (The same obtains to comparisions of the strength of preferences.) If we are going to attempt to measure happiness we need to chose a specific standard which gives weight to certain states. There might be many possible standards, but that doesn't mean one does not exist. The choice of standard doesn't have to be formal; we can have semi-subconcious ideas of what exactly happines is and what weight to give to different kinds of happiness.

Neither, as this post points out, is happiness directly observeable. However, we can look at signs of happiness and give weight to different signs. We can listen to people talk about how they feel, we can use empathy, and we can look for smiles and other behaviors associated with happiness. We can then insert our observations into our standard for measuring happiness, and come out with a real value.

I think the major criticism of this is that there is no clear way to establish a standard of measuring happiness. Any standard could theoretically be as good as any other. I think that is true that logic cannot tell us which model to use; chosing a standard is an essentially normative judgement. The comparision of happiness really only has normative goals, so it makes sense that the actual process of comparison is normative as well. (Not that I think it matters, because agreement is not necessary for something to be moral, but I don't think our standards of measuring happiness will wildly differ either.)

This does pose problems for more scientific attempts at measuring happiness, but I do not think these are insurmountable; simply present the data and let people make up their own minds, or use a model and state that this is one you think fits with the moral intuitions of yourself/others. More importantly, it becomes obvious that certain people are more happy than others, and if we have a choice between curing someone of malaria and giving someone a diamond ring, we should chose the latter, because it promotes more happiness.

Brandon- In turn: 1. I agree

Brandon-

In turn:

1. I agree that utility can be precisely and objectively measured only as an ordinal. But that we can’t measure a quantity doesn’t mean that it doesn’t exist, and I do think that utility has magnitude. I’m not sure how to go about arguing for or against such a proposition, though.

The argument over the nonexistence (or more correctly, irrelevance) of quantity of utility does not depend on the assertion that it can't be measured. Having its character shown to be ordinal and not cardinal should be sufficient argument.

Can we agree, at least, that utility has a sign which can be detected through revealed preference? That is, can we objectively and unambiguously distinguish between utility and disutility, and thus make an IUC where the signs differ?

This is the biggie. You can say that for person 1, his preferences among three alternatives are ranked A>B>C. For person 2, her preferences are ranked C>B>A. When these preferences are demonstrated by action, all we know is that for person 1, A>B and A>C, and for person 2, C>B and C>A. Knowing the 'sign' of the preferences doesn't get us any closer to figuring out who values B less or whether A>C or C>A between these individuals.

Also, you arguing that the very idea of an IUC is incoherent because of the way utility is defined, or merely that we can’t perform them because we don’t have tools that can measure utility?

Both. :) But the first logically implies the second, and my point is ultimately the first.

2. I agree that utility rankings vary over time, but I’m not sure why this is relevant. My weight fluctuates over time, and yours probably does, too, but no one would argue that you can’t compare our weights.

Weight is the interaction between mass and gravity, both of which are based upon constants of the universe that do not fluctuate. Utility to an individual is not constant at all, its highly dependent upon context and time. Given that its so infrapersonally variable I can't see how the leap can be made to compare interpersonally.

3. I agree that utility can’t be measured objectively. All I’m saying is that we can sometimes make a reasonable guess at the order of magnitude.

See #1. But further, I don't believe that magnitude matters (explained more in my next post), not on a demonstrated preference basis. A quick analogy that may or may not be analogous- there are many variables that influence how a woman gets pregnant and whether it implants into the uterine wall, but when it does, you either are or are not pregnant. You're not "really pregnant" or "982 pregils worth of pregnant" such that you can compare one pregnant woman to another and meaningfully say "these two women are both at equivalent gestation times, yet woman A is *more* pregnant than woman B". That is nonsense.

Likewise when the rubber hits the road and choice has to be made (the only point of relevance to economics) you either do or do not, following Yoda. There is no magnitude.

When I say that we can make IUCs, I don’t mean it in a rigorous mathematical sense. It’s a very fuzzy comparison which can only be made at the extremes. Furthermore, we can never be 100% certain, and we can’t even assign a definite numeric probability to being correct, because we have no way of figuring out what that probability is.

I don't think you're comparing utility, I think you're comparing several orders down the road of calculation piled on consideration where you come up with an idea that its better for A to have something than B. Thats ethics and philosophy, not economics and mathematics, and I don't think probability comes into it at all. Its sort of a "myth of certainty" that results from trying to attach a mathematical sign or function to something. In analysis we ought not begin with a myth.

Also, DMU can exist even if preferences are constant. You can demonstrate this by asking a person if he’d rather have an apple or an orange. Supposing he says he’d rather have an apple, you then ask him rather he’d rather have two apples or an apple and an orange. Then three apples or two apples and an orange, etc., until he finally chooses an orange over one more apple.

Yeah, brain fart on that one. Don set me straight too.

Brian: Thanks for the

Brian:
Thanks for the thoughtful response, but I think you're rebutting a much stronger claim than I actually made. More on that after my answers to your objections:

1. I agree that utility can be precisely and objectively measured only as an ordinal. But that we can't measure a quantity doesn't mean that it doesn't exist, and I do think that utility has magnitude. I'm not sure how to go about arguing for or against such a proposition, though.

Can we agree, at least, that utility has a sign which can be detected through revealed preference? That is, can we objectively and unambiguously distinguish between utility and disutility, and thus make an IUC where the signs differ?

Also, you arguing that the very idea of an IUC is incoherent because of the way utility is defined, or merely that we can't perform them because we don't have tools that can measure utility?

2. I agree that utility rankings vary over time, but I'm not sure why this is relevant. My weight fluctuates over time, and yours probably does, too, but no one would argue that you can't compare our weights.

3. I agree that utility can't be measured objectively. All I'm saying is that we can sometimes make a reasonable guess at the order of magnitude.

When I say that we can make IUCs, I don't mean it in a rigorous mathematical sense. It's a very fuzzy comparison which can only be made at the extremes. Furthermore, we can never be 100% certain, and we can't even assign a definite numeric probability to being correct, because we have no way of figuring out what that probability is.

Also, DMU can exist even if preferences are constant. You can demonstrate this by asking a person if he'd rather have an apple or an orange. Supposing he says he'd rather have an apple, you then ask him rather he'd rather have two apples or an apple and an orange. Then three apples or two apples and an orange, etc., until he finally chooses an orange over one more apple.

The joke about comparing apples and oranges is left as an exercise for the reader.

Utility can be demonstrated

Utility can be demonstrated by action (and, economically, is the only way to demonstrate utility). That is surely not outside the realm of normal perception. The fact that human cognition is highly interdependent and simultaneous in action both eliminates the possibility of “demonstrating utility with physical laws” and of interpersonal utility comparisons of a quantitative sort. But human brains are built on and subject to physical laws…

Please demonstrate some function of the brain that is purely ordinal in nature, some function that is reliant on a construct of logic as opposed to a physical quantity of some thing.

Arguing, as you seem to be, that you can know the order and magnitude of utility, is akin to someone suggesting that you can simultaneously know the position and speed of an electron, physics be damned.

I would turn this against you: you are in essence arguing that the electron can be known without having any electron to be measured whatsoever.

Steven, It would seem that

Steven,

It would seem that the whole comparison is a category error, since its not a matter of ordinality or cardinality when one neuron hits another, but of sequence. And I'm sure there are plenty of processes that depend on the order in which they are struck and not by how often they are (a pathway of A to B to C that yields D consequence is not cardinal in any sense). If you want to get very picky neuron activity is binary and not subject to "mostly fired" or "mostly not fired", so cardinality is completely out of the picture at that level of detail. Whether some processes differ qualitatively depending on quantity of neurons fired in a particular network, I don't know; but from what I have seen it would seem in theory that for any given person a similar output can from from any number of different network arrangements, rendering comparisons of "mass of neurons fired" completely moot- if the base of your comparison is not a constant phenomenon then you're wasting your time trying to measure.

And that turnaround is just silly. I have always stated that the way to know what preference order is, is to observe action. That is called revealed preference/demonstrated preference depending on who you ask. Thats also the basic rule of quantum indeterminacy- you have no idea what the state is *until* observation, which is essentially what utility is. Speaking to what the state is prior to observation is pointless.

(RE 1) A sort of queerness

(RE 1) A sort of queerness argument: if utility is ordinal merely, it is a beast unlike any other. In order to have a solely ordinal utility measure we must suppose that there is no quantity. However, in supposing that there is no quantity, we must also abandon any hope of demonstrating utility consistent with physical laws and, as such, outside the realm of normal perception. Thus if utility exists as ordinal merely, it must require a sort of perception unlike all others.

Note that this is not the same as "hot and cold" versus thermometry, which is a canard: we have every reason to suppose that "hot and cold" refer to an internal cardinal measure, not an ordinal, as we can pinpoint the temperatures at which we feel either.

Steven, Your second&third

Steven,

Your second&third sentences do not follow the first sentence.

However, in supposing that there is no quantity, we must also abandon any hope of demonstrating utility consistent with physical laws and, as such, outside the realm of normal perception. Thus if utility exists as ordinal merely, it must require a sort of perception unlike all others.

Utility can be demonstrated by action (and, economically, is the only way to demonstrate utility). That is surely not outside the realm of normal perception. The fact that human cognition is highly interdependent and simultaneous in action both eliminates the possibility of "demonstrating utility with physical laws" and of interpersonal utility comparisons of a quantitative sort. But human brains are built on and subject to physical laws...

Arguing, as you seem to be, that you *can* know the order and magnitude of utility, is akin to someone suggesting that you can simultaneously know the position and speed of an electron, physics be damned.

You can get ordinals from

You can get ordinals from cardinals but you can't get cardinals from ordinals. For example, you can order people by their weight, getting an ordinal (their position in the order) from a cardinal (their weight). But if all you know is where people are in a line then while there *may be* some cardinal lying behind that ordinal which you might be able to guess at, the ordinal itself, their place in line, does not yield you that cardinal. It's possible that they were simply shuffled and then placed into line, and in that case any cardinal you "recover" is almost certain to be spurious.

You can "fake" a cardinal by arbitrarily assigning units to ordinals. For example, you can say that the first person in line "measures" one unit of this supposed cardinal, the second person in line "measures" two units, and so forth. But here you're clearly just pulling a cardinal out of your -.

We get preference from choices, and that gives us an ordering and therefore an ordinal, not a cardinal. Those who claim that there is nevertheless a cardinal are in essence conjecturing that there is some cardinal lying behind the ordinal. Just as it may be that people were put into line on the basis of their weight, a cardinal, so might it be (one may conjecture) that the choices that people make are made on the basis of some cardinal. However, that is a conjecture that I see no reason to subscribe to myself. Moreover, even if the ordering of men in a line has in some instance been based on their weight, it does not follow that their order in line is in fact a weight. Similarly, even were it true that people made their choices on the basis of some cardinal, it would not follow that their preference - and therefore their utility - was itself a cardinal. It is still an ordinal.

Whether the ordinality of

Whether the ordinality of utility is an argument against the-argument-for-redistribution-from-i-u-c depends on the audience. (Ordinality of utility is not an argument against redistribution, it is only an argument against a particular argument for redistribution.)

I follow Popper's rule of arguing. If someone makes a weak argument, I strengthen it before replying. If someone argues for redistribution on the basis of IUC, I strengthen the argument before replying. Let us postulate, as a given, that it is more moral for a given dollar to be used to better the condition of the poor than to better the condition of the rich. I allow this as a postulate for the sake of argument for one reason: that I know it is an unshakable conviction on the part of the person I'm talking to (as I said, of course, it depends on the audience). At least, I am not going to shake it.

And in that way I skirt around the issue of IUC. (I think I do anyway.)

So what do I do for an argument instead? I talk about consequences. I point out that if you don't allow "exploitation of labor" in some country what you end up with North Korea. (Not necessarily in so many words - what I say depends on the audience.)

I'm morally opposed to any robbery whatsoever. While I feel for the poor, I draw the line at robbing the rich - thus while I like charity I like the charity to be voluntary. But this is my moral position and I don't put my foot down about it (depending on the audience).

So, why is the first line of

So, why is the first line of the first paragraph indented in the comments, but nothing else? That seems odd.

My argument for property and

My argument for property and against robbery (my name for what others here have euphemistically called "redistribution") depends on the audience but in my own mind my most basic argument is that:

a) In a contest over property between the producer and some third party who did not produce it, clearly the producer is the rightful owner the challenger is a would-be parasite.

b) In a contest between two people who have cooperated on the production of something, clearly they are bound by the agreement they have made with each other - e.g., the employment agreement between employee and employer.

c) In a contest over natural resources, initially it is not clear who owns what but once someone has invested significantly in developing a resource that no one before him developed then to take that resource from him by force becomes a robbery.

Now while I am sure there are hypothetical scenarios that put the above points all to a severe test, but I think in the real world most of the *political* contests over property are clear-cut attempts to rob. There is of course gray area - for example I have observed contests over borders between neighbors where it was not at all clear to me who was right. But this is not the sort of contest that generally makes up political controversies.

Brian: Insofar as the idea

Brian:
Insofar as the idea of an IUC is logically incoherent, then we're talking about two different things, and this is mere semantic quibbling. Desires and preferences have intensity, and that intensity has magnitude, not just ordinality. Even if we can't measure the intensity, it's real.

Knowing the ’sign’ of the preferences doesn’t get us any closer to figuring out who values B less or whether A>C or C>A between these individuals.

Do you mean that we can't distinguish between utility and disutility? So, for example, if X hauls something to the dump and mentions this fact to Y, whereupon Y decides to go to the dump to retrieve it, we can't say that Y values it more than X, since X was willing to expend considerable effort to get rid of it?

Weight is the interaction between mass and gravity, both of which are based upon constants of the universe that do not fluctuate.

In people, mass does fluctuate. If my scale says 200 one day and 201 the next, it's because my mass has increased, not because G has increased.

I'll come back to 3 after I've read the follow-up.

I don’t think you’re comparing utility, I think you’re comparing several orders down the road of calculation piled on consideration where you come up with an idea that its better for A to have something than B.

My claim is purely positive---that the subjective benefit to A is greater than the subjective benefit to B. Probably. No normative judgment (I've got your softening 'e' right here :mrgreen:) can be made based soley on this fact.

>>Can we agree, at least,

>>Can we agree, at least, that utility has a sign which can be detected through revealed preference? That is, can we objectively and unambiguously distinguish between utility and disutility, and thus make an IUC where the signs differ?

>This is the biggie. You can say that for person 1, his preferences among three alternatives are ranked A>B>C. For person 2, her preferences are ranked C>B>A. When these preferences are demonstrated by action, all we know is that for person 1, A>B and A>C, and for person 2, C>B and C>A. Knowing the ’sign’ of the preferences doesn’t get us any closer to figuring out who values B less or whether A>C or C>A between these individuals.

I think that signed preference is the key to IUCs. The problem with your response is that you don't compare A, B and C intrinsically. Suppose that A, B and C each contain only one good, which we will call "kiddie porn" (KP for short). A is 0 units of KP, B is 1 unit of KP and C is 2 units of KP. Say that person 1 and person 2 were each endowed with 1 unit of KP (they each have basket B). We can now say that the marginal utility to person 1 of an additional unit of KP would be less than the marginal utility to person 2 of an additional unit of KP because for person 1 it would give him to the less preferred basket C while for person 2 it would give him the more preferred basket C. So IUCs are possible, just probably only for special cases.

So, for example, if X hauls

So, for example, if X hauls something to the dump and mentions this fact to Y, whereupon Y decides to go to the dump to retrieve it, we can’t say that Y values it more than X, since X was willing to expend considerable effort to get rid of it?

Of course we can say that, but only because we are using an idiom which no longer refers merely to utility. We can say the same thing in any market exchange: if I sell something to you, then of course we can say that you value it more than I do, in the sense that you value it more than the amount you paid me for it, and I value it less than the amount you paid me for it. That's not an interpersonal utility comparison.

Or if you think it is an IUC then why didn't you, long ago, say, "people make exchanges in the marketplace, therefore they are performing IUCs, QED"? My guess is the reason you haven't long since said this is that you recognize that that isn't an IUC.

Joe- Argh. Utility is

Joe-

Argh. Utility is ordinal and thus non comparable. For it to be cardinal you have to do a lot more work than you've done here (and argue against a very large corpus indeed). I cannot sum up A>B>C in any meaningful way, and thus what you're asking for is impossible. You're not measuring what you think you're measuring.

Constant, you wrote: "Or if

Constant,

you wrote:

"Or if you think it is an IUC then why didn’t you, long ago, say, “people make exchanges in the marketplace, therefore they are performing IUCs, QED“? My guess is the reason you haven’t long since said this is that you recognize that that isn’t an IUC."

I assert that there are 3 conditions for a rigorous IUC:

1) The basket of goods under consideration must be inherently comparable. That eliminates the potential for IUCs in exchanges, which inherently involve two goods and in which each party gets more of one good and less of the other. I can say $50 > $20 in an absolute sense but I can't say {$50, a big mac} > {$20, 2 big macs} in the same sense. The only way that you can get comparable baskets is if one contains more of every good than the other. The simplest way to achieve this is to limit the baskets under consideration to contain only one good, but I'll be general.

2) One of the people has to value the basket with the higher quantities over the basket with the lower quantities, and the other person has to value the low quantity basket over the high quantity basket.

3) each person's utility has to be monotonic for these goods.

Then it should be clear that person who values the higher quantity basket has a higher marginal utility for these goods than the other person. Don't you agree?

Joe, The marginal utility of

Joe,

The marginal utility of a good (or a "bad" in the other person's case) can be positive or negative. Meaning: a person can prefer to get one more of a good, or he can prefer to get one less of the good (or prefer not to get one more of the good if you like).

That is a property of *ordering*. In ordinals, there are positive directions and negative directions. If you go in the direction you prefer, that's positive. If you go in the direction you don't prefer, that's negative.

So as far as I can see all you're doing here is pointing out that ordinals have the greater-than/less-than relationship. But that is simply the defining property of ordinals, that's what "order" means.

So I don't really see how this example gets us anywhere. It illustrates that ordinals are ordinals.

It seems to be a rather convoluted way of pointing out what I don't think anybody would deny, which is that of course we can compare *direction* between two sets of ordinals with a greater than/less than relationship.

If I'm missing something I'll need more clarification.

Constant: The dump scenario

Constant:
The dump scenario isn't analogous to market exchange. If you sell me something, that doesn't mean that you don't value it; it just means that you value the money you receive more than you value the thing you're selling.

But if you're willing to expend time, effort, gas, etc. to haul something to the dump, this is a pretty strong indication not only that you don't value it, but also that having it is actually a disutility to you. Hence the sign of its utility to you is negative. Conversely, if I'm willing to expend the same resources to go and pick it up from the dump, that's a pretty strong indication that the sign of its utility to me is positive.

You may deny the possibility of interpersonal comparison of utility when the sign is positive for both people, but what if the sign is positive for one and negative for the other?

Constant, I don't know what

Constant,

I don't know what one would mean by comparing two people's utilities other than that you say that person 1's marginal utility for good G > person 2's marginal utility for G. That was how the original point was phrased: A billionaire's marginal utility for $1K is supposedly less than a pauper's marginal utility for $1K.

If both people have positive or negative marginal utility for G, then there is no way to compare them. I agree with the comments you have written which make that point. However, when you consider a case where the marginal utilities have different signs, then comparison becomes possible with no loss of logical rigor.

In real life it can get messy because you start thinking about trade-offs and multiple goods and that makes IUC impossible, but if you just hold everything else constant and only vary G and find that one person optimally wants no G while the other person optimally wants infinity G, then you've found two people with comparable utilities, at least for G. And I think that you can make a relatively strong case for redistribution in that situation. If the person who wants no G has lots then giving it to the person who wants infinity G can only increase their combined utility.

If both people have positive

If both people have positive or negative marginal utility for G, then there is no way to compare them. I agree with the comments you have written which make that point. However, when you consider a case where the marginal utilities have different signs, then comparison becomes possible with no loss of logical rigor.

Yes of course, and I stated that, when I wrote, "It seems to be a rather convoluted way of pointing out what I don’t think anybody would deny, which is that of course we can compare direction between two sets of ordinals with a greater than/less than relationship."

But in that very limited case please realize that there is obviously no need for coerced redistribution. The person who gas G and doesn't want it will gladly give it to the person who wants it, might even pay him to accept it.

You may deny the possibility

You may deny the possibility of interpersonal comparison of utility when the sign is positive for both people, but what if the sign is positive for one and negative for the other?

As I have stated to Joe, "what I don’t think anybody would deny, which is that of course we can compare direction between two sets of ordinals with a greater than/less than relationship."

Obviously you can compare positive and negative - if you have a positive and negative direction. (To get technical, if one set of ordinals has a relationship east versus west, and another set of ordinals has a relationship north versus south, then there is no way to compare the directions unless you arbitrarily assign, say, east to north, but here of course we are talking about the same relationship, i.e., preference.)

And by the way, I do think that this point is captured in every market trade, contrary to what you have said. In a trade, if I sell you A in exchange for you giving me B, and you agree to the exchange, then the marginal value of the change in property "A - B" (one more A, one less B) to me is positive, while it is negative to you, and the opposite change "B - A" is negative to me and positive to you. Please compare:

But if you’re willing to expend time, effort, gas, etc. to haul something to the dump

Compare the above with:

But if you're willing to expend time, effort, gas, etc. to go to the market...

Quickly looking at my above

Quickly looking at my above comment, I think I got A and B backwards. But you know what I mean.