Cardinal Schmardinal, Ordinal Schmordinal

The most common objection made to interpersonal utility comparison in this debate (Glen's roundup post) has been that utility is ordinal, not cardinal, and somehow this makes IUC's impossible. I will attempt to disprove that assertion, and demonstrate that the key is whether or not you can do specific comparisons to find equality points, not whether utility is cardinal or ordinal.

First, let us assume that utility is cardinal, and that (as many of the IUC opponents have admitted), you can approximately measure someone else's utility function. Now in order to do IUC, you still need a zero point. That is, if an apple gives me 2 more utils than an orange, and a bagel gives you 3 more utils than a donut, I still don't know whether an apple gives me more utils than a bagel gives you unless I have some kind of basis. A nice property of cardinal utility is that I only need a single basis in order to make any IUC. That is, if I know that in this situation, an orange would give me the same utility as a donut would give you, I can deduce that my apple will give me one less util than your bagel, and so on for any other comparison.

My claim is that while ordinal utility makes weaker statements, it can still make statements based on the same data. Suppose that I only know that for Apples, Bananas, Carrots, Durians, and Elderberries, my preference goes A > B > C > D > E, and that for Figs, Gooseberries, Honeydew, Iodine, and Jicama, your preference goes F > G > H > I > J. Let's start with a single basis, as we needed with cardinal utility - suppose that I will enjoy a Carrot as much as you enjoy a Honeydew. Unlike with cardinal utility, this does not let me do full IUC's, but it does let me make definite statements about interpersonal comparisons, like "I will enjoy a Banana more than you will enjoy some Jicama". That is, tying two ordinal points together limits the possible orderings of the combined list. This is an indisputable mathematical fact.

It is true that this is only a small amount of comparison, but consider how silly it is to postulate only one such basis point. If I can find one, I should be able to find others, and the more I have, the more I know about the order of the combined list. If I also know that I will enjoy a Banana less than you will enjoy some Gooseberries, and that I will like a Durian more than you will like some Jicama, I can now answer quite a number of questions about whether I will like X more or less than you will like Y[1]. It's true that I can't make cardinal statements like "I will enjoy X twice as much as you will enjoy Y", but the uses I've seen for IUC are mostly ordinal. They are things like "Is it a net win if I do X and you do Y" - which is an ordinal question[2].

Thus it seems to me that if interpersonal utility comparison has a problem, the problem is in the comparison. To me, the comparison seems reasonable, just like approximating someone else's utility function, but I can see how someone might object to it (more on that in another post). But (unless I've made an error), it sure looks to me like this whole cardinal/ordinal distinction is a red herring. Ordinal utility requires more equality points, and it results in weaker statements, but you can do IUCs with it just like you can with cardinal utility. So feel free to argue about whether interpersonal comparisons are possible, but it is mathematically erroneous to say that ordinality is the issue.

Next, a demonstration of deriving cardinal from ordinal...

[1] Note that ordinal utility comparison can feed on non-equal comparisons, ie I like X more than you like Y also gives us meaningful data about the possibilities for the merged list.

[2] If this is not quite obvious, note there are two ways we can get it. First, if we can get basis comparisons of the form "I like X as much as you don't like Y", then we can make statements about the order of merged list of my preferences and your anti-preferences, in the same way as with seeing who will like something more. But one can argue, with some justice, that this is assuming what we are trying to discover. However, one can cleverly avoid this by using the intrapersonal comparison of asking you to come up with Z s.t. you like Z as much as you dislike Y. This can be done by finding a Z such that you are indifferent between doing both Z and Y vs. doing nothing. Now to see if me doing X and you doing Y is a net win, we see if I like X as much as you like Z.

Related posts:

Why IUCs?
Encoding Happiness
IUCs and the Law of Large Numbers
No Soul Suggests IUCs
Love and Intrapersonal Utility Comparison
What color does a submarine weigh? (True or False?)
Exploding IUCs on the roadside
Interpersonal Utility Comparisons
Pareto Efficiency and Justice
Can the Paradox of the Non-Comparability of Interpersonal Utility be Resolved?

Share this

It doesn't work. I think

It doesn't work. I think Mises addressed this but I don't know where. First off my ordinal changes over time. Plus depending on what I am doing and what I have in my possession the combinations of ordinals have different values. I may not be so keen on ice cream or bananas but I may really like banana splits. If I already have a banana then the ice cream has more appeal to me. If I don't and none is available then it doesn't. The utility that Austrians talk about has these kinds of attributes. They are volatile and dependent on other factors.

If you have kids you will see these kind of dynamics in play. They do try to gauge each others utilities and often get them wrong. You are put in the middle trying to gauge both. Often your decision will not only fail to please one but will fail to please both. They both view their own utility function as superior to what they gauged for the other based on past experience. Often they are actually trying to be fair about it too. Ever use a siblings toy you know they don't play with to fish something you value highly out of the toilet? Ever notice the reaction when this is discovered? It becomes their most valued possession.

Catallarchist child A: “Daddy, I feel sick”
Catallarchist child B: “He always feels sick. If we stop now we are not going to have time for my movie”.
Catallarchist Parent: “What do you mean, ‘I feel sick’?”
A: “Car sick”
Parent: “Wait a second. I’ve got to make this turn.”
B: “Hurry daddy. I don’t want to miss the beginning”
Parent: “Do you think you can make it?”
A: “I think so.”

Two minutes pass

A: Blooort….Splush! "Sorry, daddy.”
B: “You always ruin everything! Whaaaaaaa!”
Parent: “Why didn’t you tell me to pull over, or roll down the window. Now we have to stop and clean up this mess and no one sees the movie”
A: “I did tell you to pull over!”
Parent: “No you didn’t. You said you could make it. ”
Catallarchist Child : “Well, I didn’t judge my IUC properly with regards to my sibling B’s need to get there and against your need to stay on the road. I took all your current ordinals as judged by me, sorted them then found items that were clearly of more utility to me than you and vice versa, generated the cardinal order and made my decision. I then felt a little sicker, there was another turn, and I had to start the calculation all over again from scratch. This causing me to postpone my needs to the point of catallarchy catastrophe. Besides I get car sick when I do math while traveling in the car.”
Parent:Damn you should know that IUC’s are fraught with danger! You’re getting punished when we get home.”

This whole debate is off

This whole debate is off focus. What matters is that to apply mathematics in a meaningful way, there must be functional relationships between two quantities such that one quantity is precisely, uniquely, and predictably determined by another. Without this necessary condition, you do not have mathematical reasoning. You do not have functions. You have mathematical symbols dressed in mock precision.

The same problem would occur whether or not a scale of valuations is ordinal or cardinal: even if a G-dlike Catallarchist could divine my (cardinal or) ordinal scale of valuations at a single moment, is there any reason to believe that this momentary constellation of valuations will remain in any way constant such that a precise, unique, and predictable relationship may be found with anything else? Is there any reason to believe that my IUC "function" is in any way capable of being falsified?

How would one go about "measuring" a scale of valuations independently of an individual's actions? A questionnaire? But the problem of "revealed preference" is known to anyone who has ever tried getting a dirty movie off their hotel bill. Cognitive analysis using advanced FMRI and CAT Scans? But unless one was (redundantly) measuring these physiological responses while an individual conducts an actual catallactic exchange, one is still not measuring the right quantity: the scale of valuations an individual experiences in the moment of praxis. That scale, at the moment of action, is the only determinant of whether or not an exchange will take place, and under what terms.

If you wish to study IUC's, you are left with examining economic history and making statements like, "in this transaction on Friday the 23rd of June 2006, Bob valued $50 more than his carton of cigarettes, and John valued the carton of cigarettes more than his $50; otherwise the exchange would not have taken place at these terms." This is insightful into the necessary conditions for exchange, and capable of dispelling many fallacies, but it is not the foundation for an attempt to divine the will of a man through symbols.

Patri, "suppose that I will


"suppose that I will enjoy a Carrot as much as you enjoy a Honeydew"

How do we know such a thing? Suppose we don't know it, but you think so. What makes you think so?

"suppose that I will enjoy a

"suppose that I will enjoy a Carrot as much as you enjoy a Honeydew. Unlike with cardinal utility, this does not let me do full IUC’s, but it does let me make definite statements about interpersonal comparisons, like “I will enjoy a Banana more than you will enjoy some Jicama". That is, tying two ordinal points together limits the possible orderings of the combined list. This is an indisputable mathematical fact."

Lovely. Everything you say is true. Except for "suppose that I will enjoy a Carrot as much as you enjoy a Honeydew." How do we even say this? In the world of ordinal utility, all my rankings tell me is that, for me, consuming A is better than consuming B, and so on. We have no quantities attached to these ranks (i.e., A is better than B, but as you note, we can make no claim as to the degree of improvement between getting an A and getting a B). Since all we have are ranks (which have no absolute values outside of ordering my preferences), how can we say that Carrots delight me "as much as" Honeydews delight you?

Put forthrightly, I object to the supposition that you can find that I enjoy a Carrot as much as you enoy a Honeydew, because this concept of "as much as" implies some measurement (thus back to cardinality) of utility, or a comparison of the ranking systems (which is similarly impossible).

[And, aside from the tedium of this ongoing debate, I am genuinely interested in Patri's ordinal-cardinal transformation, even if it relies upon the supposition to which I object.]

Indeed, Patri is supposing

Indeed, Patri is supposing the very conclusion he needs. You might as well start with: Suppose interpersonal utility comparisons are valid. Q.E.D.

Starting from the

Starting from the meta-theoretical point that we need to start with the obvoious and work to the less-obvious, I have to ask a simple question: Does anyone (who has been in a Long Term Relationship, or had kids) have any question that they do make IUC judgements, or that they are basically correct. My speding $ on this Remote Control Car is worth less happiness than my wife spending the same $ on a spa or my 2yo spending the $ on another darn doll.

I would assert that in practice, every one of us makes these IUCs every day and that we assume (accurately most of the time) that these are not controversial. I think that anyone arguing against the possibility of IUCs has to say that what 4 billion people (all married, semi-married, or parental) do every day is bogus. And on an obviousness standard...I think that's something of a steep argument to climb.

You don't think billions of

You don't think billions of people act on the basis of bogus reasoning every day?

I think that when most

I think that when most people (including most of the people posting arguments) do something as a matter of course, the bar to insist that we're all full of hooey is a bit higher than when people don't do it as a matter of fundamental everyday interpersonal behavior.

Edit : When most of the

Edit : When most of the people posting arguments on both sides of this issue are implicitly accepting that IUCs work in their everyday lives AND when 4.5 billion other people accept the same, I think it trivial to claim that the bar is higher for claims against IUCs than for claims pro-.

And further...if someone

And further...if someone expects an argument on the topic (on the anti-IUC) position to have any chance of succeeding, said person must explain why our experience of daily successful IUC comparisons are a) Wrong, or b) not relevant to the argument.

We can use shortcuts that

We can use shortcuts that for the practical purposes of 4.5 billion people act like IUC's, even if they aren't IUC's. If we've internally symlinked "Kid A values toy X more than Kid B values toy Y" to "I would value toy X more than I would value toy Y," then we'd probably make the correct judgment in around the same number of cases as the number of cases in which people actually do make the correct judgment.

We've evolved thousands of mechanisms for faking it, so the fact that just about every human can seemingly make IUC's bears no relation to whether they are, in fact, possible.

And further…if someone

And further…if someone expects an argument on the topic (on the anti-IUC) position to have any chance of succeeding, said person must explain why our experience of daily successful IUC comparisons are a) Wrong, or b) not relevant to the argument.

They aren't IUC comparisons. They're not wrong, either. The choices people make reveal their own preferences, their own values. In any case a parent isn't trying to maximize his child's utility, but rather is trying to maximize things about the child that he, the parent, values, which sometimes but not always is to maximize the child's utility. For example, the child may prefer ice cream to spinach, but the parent will give him spinach against his will and keep the ice cream under control.

That point was dodged before, so I'll mention the dodge: the parent supposedly is looking at the child's future preferences and giving the child what the child will prefer to have gotten in retrospect. My answer is: why does the parent give preference to one preference scheme over another? Surely because he agrees with it. The parent undeniably has his own set of wishes with respect to the child. And if the child grows up and continues to differ with his parent, the parent may start nagging the child. For example, one common point of contention between parents and their grown children is the issue of the child getting married and having children.

I mean they aren't IUCs.

I mean they aren't IUCs. "IUC comparison" is redundant.

Daniel and Constant suggest

Daniel and Constant suggest that IUCs are not possible, even though everyone does things that resemble them all the time.

The argument I read was:
Parents aren't making IUCs, they are instead:
a) comparing what they would prefer
b) not operating based on comparison of others values, but basically selfishly

I would once again suggest that this flies in the face of the experience of 4.5 billion people.

Do parents sometimes choose what they would prefer? Yes. Do parents sometimes choose in order to get better outcomes? Yes.

However, parents will also make choices on: will Annie like a doll more than Bill will like a toy truck, where neither of the above critiques are appropriate. Neither parents goals nor what the parent prefers will be a basis for choosing. So, still looks an awful lot like an IUC.

Married folks also, but don't need more examples yet.

Arguing that this doesn't happen gets into the same traps as psychological egoism. Once you argue that people who think they are doing IUCs, who seem in normal english to be doing IUCs, gets the question of Real IUCs to be irrelevant.

If 4.5 billion peeople think that IUCs exist, and rely on them every day, why should I accept some wierd contorted definition of IUCs that will define them out of existence in order to make some pet philosophical point of someone's now seem to be true? Again seems more likely the wierd definition is the problem.

Another thing. I

Another thing. I certainly do not draw up ordinal rankings of my preferences in order to act.

It seems to me that the Austrian use of ordinals is not giving you any indication of utility outside of the immediate choices. I may choose to have vanilla over chocolate ice cream at this time but that does not tell you my preference for strawberry if that was not a choice available. The type of temporary ordinal information the Austrians postulate in no way indicates:
1) The actual process I used to make the choice.
2) Any full ranking of my utilities
3) Pleasure derived
4) Future desires
5) Past desires
6) Desires if a different set of choices were available

You just cannot take the Austrian notion of ordinals to derive a set of cardinals which contains information lacking in the original ordinals. You can never know if I would have preferred pistacho ice cream, for instance.

The only way to derive such cardinals by the proposed process is to have full ordinality which is not present in the Austrian ordinals.

One method to get full ordinality would be to present every person with total wish granting abilities. They would have to be able to wish whatever they wanted. Then we would observe what every person did with that ability.

Then we still wouldn't have the answer since we would not know in what order to put minor desires. So we would have to go back and eliminate the exact wish that the person made and have them wish again add see what they wish for.

So perhaps on my first wish "I wish to be the center of attention at an orgy full of beautiful women, including Rachel Welch (Bolivian) at her prime, Denise Richards, Ashley Judd, Olivia d'Abo at the age she was in Conan the Destroyer, Jennifer Connelly, ..." Well that only tells you want I want at that moment. Now you have to reverse time and redo the wish and say, "That is not allowed exactly as stated. Try again" what would be the next best thing. I guess the same wish except I'll take Abo at her current age. Then repeat this for all possibilities. Some of them include Richard Simmons being present, some don't. Most of them do not involve orgies.

That is the magnitude of the problem that this full ordinaity problem has to tackle. It's impossible. I can think of no way to do it without time travel and magical wish granting.

Which is why we have phrases like "How could you possibly know what I want?!"

Seems to me that if IUC were

Seems to me that if IUC were accurate we'd all know what each others preferences were with regard to the issue of IUCs and there would be no need to argue about it. It's not that you continue because you are trying to change my preference either. If you knew my preferences and therefore deduced that you could change my mind then why isn't it working? Presumably you have some information I don't that would quickly flip me if only I knew it. If that is the case then well produce that information and stop wasting time telling me things I already know.

People argue on the most trivial of issues, where each side is as fully informed as the other. This shows that our IUC calculators really aren't that good. They don't work in these most trivial of cases.

Most of you are nerds, otherwise you wouldn't be spending time here arguing about IUCs. At least that's what my IUC tells me. Nerds are notoriously bad at doing IUC calculations. We don't know what the cool fashions are, what the coolest music is, where to be seen and with whom. Heck if our IUC caluclators were so reliable we wouldn't even have the notion of the entrepreneur.

I don't even know if I agree with calling the processes we use to make decisions an IUC Calculator. I actually don't believe we do IUCs.

If I were to punch you in the nose I can pretty much tell you that you are not going to like it. I don't need to do anything like calculating your utility function for a bloody nose to figure out you are not going to like it. There's no cardinality let alone ordinality involved. I know you won't like it because I don't like it. I don't have to calculate whether you like it better or worse than a purple nurple. Nor do I attempt to gauge how much utility you get out of the punch to the nose relative to how much I do.

That I know that Johnny doesn't like dolls or boys in general don't like dolls does not require an IUC with a girl.

That we try to predict each others reactions and valuations I can agree to. How we go about it is quite a different issue.

If I pulled fifty dollars out of my pocket right now and had to choose whether to give it to my oldest son vs. my youngest based on who would get more utility out of it I can tell you right now I don't have an answer. Why should I be making such decisions on utility? How do I calculate utility?

Heck if I knew my oldest was into crack cocaine then I would base the decision on the precise opposite of what some people have claim. My rough idea of what you guys mean by utility would mean that my oldest would have the higher function by far. Crack is extremely pleasurable to the point where people who use it choose it over almost anything else. Certainly this shows a very high utility function. In fact, using my non-IUC calculator I can tell you that for any one of you the likelyhood is that if you tried crack for a couple weeks you would certainly rank it above your other concerns.

I am doing here what some of you would call calculating the utility of other people but what I would call predicting other peoples behavior. Which includes propensity to act on whims, tendency to be irrational, belief in an afterlife, scientific background, and so forth.

Do you think I could have predicted what Thomas Edison was going to shop for down at the hardware store when he was working on his inventions?

That we can predict certain simple behaviors in other people is true, but even then we are not accurate. Some of the most important things motivating people way more complex. If we have internal IUC calculators then they are cheap pieces of garbage that can't do anything past addition and subtraction and even then get things wrong.

Kyle, To counteract your


To counteract your argument via numbers I'll say two things:
1) It's fallacious
2) Well you know 4.5 billion people also believe in free will. Note that the theory of free will says that you CANNOT accurately predict what others are going to do. Their choices are free at any point and not subject to following some IUC formula.

So who do you listen to? The first 4.5 billion people or the second 4.5 billion people?

If 4.5 billion peeople think

If 4.5 billion peeople think that IUCs exist

Nobody believes that. Ask them. Ask exactly this. Do not change the words. Ask them, "Do you believe in IUCs?"

I guarantee you that people other than people engaged in this discussion will say, "What's an IUC?"

At that point I know what's going to happen. You're going to explain to them what an IUC is, but you're going to do it in the way that surveys so frequently do: you're going to do it so as to elicit the answer that you want to get.

I guarantee you that I can defensibly translate IUCs into standard English so as to elicit the answer that I want to get.

Here is how I would translate it: utility is a way of talking about choice. So let us talk about choice. Consider two alternatives, A and B, and ask yourself, would you choose A over B. If you would, then you would choose A over B, given the choice. And meanwhile, you can imagine that someone else might choose B over A, given the choice. Suppose, then, that you would choose A over B and someone else would choose B over A, given the choice. My question to you, then, is, would there be an objective choice between A and B?

The other person would say, "huh?"

I would explain. I would say the only thing I could say. "Would objective reality choose A over B or B over A, given the choice?"

The other person would answer, "that doesn't make sense." Translated into philosophical terms, that would be the same as saying, "the question makes a category error."

Did you hear anyone around here in this discussion talking about category errors? You did? Bingo.

The argument I read

The argument I read was:
Parents aren’t making IUCs, they are instead:
a) comparing what they would prefer
b) not operating based on comparison of others values, but basically selfishly

No. You have both points wrong.

a) comparing what they would prefer

By making a choice - no matter what the choice, no matter how selfish or selfless - they are establishing what they prefer. By definition, a person cannot choose what he does not prefer. Preference is defined by choice. No matter what kind of thinking goes into making the choice, the choice establishes their preference and so by definition they choose in accordance with their preference.

b) not operating based on comparison of others values, but basically selfishly

No, a preference can be selfish or selfless. Preferences are not automatically selfish. If you spend your dollar to feed the homeless, then that establishes that you prefer to spend the dollar on the homeless. There is no way for your choices to escape your preference.

You are operating with a mistaken concept of preference. Both of your points reveal that you are using a mistaken concept of preference. You are confusing the economic concept of preference - which is based on choice - with common "folk psychological" ideas that people use to think about themselves and others. And that's why you believe that everyone makes IUCs.

I can say, "I don't like vegetables as much as I like ice cream but I am going to eat vegetables anyway because I know they're good for me." The concept of "like" is thus shown to be distinct from the concept of choice. You are likely confusing utility with concepts such as the concept of "like".

If we were talking about the

If we were talking about the views of ordinary people we would not all be using the term "IUC". The very fact that we are using that term which is invented for this discussion and similar discussions demonstrates that there is no ordinary English term for it, which makes it unlikely that ordinary people have any belief about it whatsoever.

People have beliefs which they express in ordinary terms. The reason we are not all using the ordinary terms rather than using the term "IUC" is that we all recognize that the ordinary terms do not quite cover it.

Talk about utility is a way

Talk about utility is a way of restating talk about preference and therefore about choice. To say that for Bob, the utility of X is higher than the utility of Y, is to say nothing other than that, given the choice, Bob would choose X over Y. That's what it means to say that the utility of one thing is higher than the utility of something else. It is a statement about a choice that a person would make.

So if we compare utility across people, *if* we are using the *same concept*, we must be talking about a choice that a person would make. That is, if we want to say that the utility for Bob of X is higher than the utility for Bill of Y, and if we are using the same concept of utility as above, then we are necessarily talking about the choice that someone would make. Not might make. Would necessarily make, given the choice.

The problem is that there is no chooser aside from Bob and Bill. And Bob's choices tell us his utility function and Bill's choices tell us his utility function. There is no person whose choices give us a cross-person comparison of utility.

None of this contradicts folk psychology. Folk psychology *seems* to some people in this discussion to be contradicting it, but only because they are confusing different concepts.