08 Nov 2011

Modern Utility Theory and Interpersonal Utility Comparisons

Economics 66 Comments

I want to elaborate on my earlier post in which I temporarily ceased being The Fonz of Economics due to a problematic question that Dan Klein had used to separate the men from the boys among the libertarians. First, let me be clear: Tyler Cowen clearly knows about everything I am going to say in this post, but for some reason (perhaps he thought it was obvious or he was just in a rush and didn’t want to confuse things) he let it go. I am less sure about how to handle Klein on this issue, because he (I believe) wrote the list of questions in the first place.

Anyway, to refresh your memory, Klein had asked people whether or not they agree with this statement: “A dollar means more to a poor man than to a rich man.” Klein thought the answer should clearly be yes, so much so that he said “c’mon people!” to those who disagreed.

I just double-checked and yes, I disagree with Klein on this so much that I actually devote a whole section of my introductory textbook to saying why the above statement is meaningless. Now you can see why I am taking this so seriously, and why it makes me lament the state of economics that we can have such huge disagreements. (Note, I am not saying Klein is a bad economist and I’m a good economist. I’m saying, economics as a discipline is in sorry shape if Klein dreams up a question to test basic economic literacy, that I use an example of economic illiteracy in an introductory textbook.)

So for those who want more (both of you), here is the discussion from my textbook, Lessons for the Young Economist. And keep in mind as you read the following that I am aiming this at junior high or even younger students, so that’s why I engage (for once) in puerile humor.

Preferences Are Subjective

Because preferences are tied to specific individuals, we say that preferences are subjective. Loosely speaking, the difference between a subjective versus an objective statement, is akin to the difference between an opinion versus a fact. It makes sense to say, “Mary prefers vanilla ice cream to chocolate, but John prefers chocolate ice cream to vanilla.” These two statements are perfectly compatible, because preferences (in this case, preferences for ice cream flavors) are subjective and can differ from person to person.

In contrast, it does not make sense to say, “The ice cream has 300 calories for Mary, but 280 calories for John.” The number of calories in a serving of ice cream is an objective fact; it can’t differ from person to person. Mary and John might disagree with each other about how many calories the ice cream has, but in that case at least one of them is simply mistaken. Yet both of them could be simultaneously “correct” when Mary says, “Vanilla tastes better than chocolate,” while John says the opposite. To repeat, Mary and John can disagree with each other about which flavor of ice cream tastes better—with neither one nor the other being wrong—because preferences are subjective. There is no “fact of the matter” concerning which ice cream tastes better, the way there definitely is an objective way to demonstrate how many calories are in a serving.

Warning! Many critics of economics—both from the progressive “left wing” as well as the religious “right wing”—totally misunderstand what economists mean by saying that preferences are subjective. These critics think that economists are somehow endorsing moral relativism, or that they are saying no one can judge the actions of anyone else. But these complaints are without merit, because economists aren’t saying those things at all!

Remember, we are simply tracing out the logical implications of our decision to classify observed behavior as purposeful action. If we see Mary go up to the counter and choose vanilla ice cream, while we see John go up to the counter and order chocolate, we won’t get anywhere in our understanding unless we realize that Mary and John have different tastes when it comes to ice cream flavors. As we will see more clearly in Lesson 6, the only satisfactory way to explain market prices is to first recognize that preferences are subjective. This recognition in no way condones the preferences of particular individuals.

For example, an economist can’t possibly explain the price of tobacco without acknowledging that some people prefer to spend their money on cigarettes, rather than on other products. After the economist states this fact, he can—with perfect consistency—then ground his teenage son when he catches him smoking in the garage with his hooligan friends. If you’re still not seeing the distinction between professional analysis versus personal beliefs, forget about economics and consider an FBI profiler. To track down a serial killer, the profiler needs to “think like the killer,” and try to understand what desires are causing the killer to act the way he is. Obviously this analysis doesn’t mean that the profiler is neutral with regard to the actions the killer takes, or that murder “is a personal choice.”

To sum up: When people engage in purposeful actions, they are motivated by desires that are not necessarily identical from person to person. In order to explain exchanges, economists must recognize that preferences are subjective.

Preferences Are a Ranking, Not a Measurement Using Numbers

Because preferences are tied to a person’s exchanges, the preferences can only reveal a ranking of goals. When Mary chooses vanilla over chocolate ice cream, this purposeful action only indicates that she prefers vanilla. We can’t determine “how much” Mary prefers vanilla over chocolate; indeed, that statement doesn’t even make sense in terms of strict economic logic.

In everyday conversation, we all know what it means to say that “Mary really prefers vanilla over chocolate but her sister Jane only slightly prefers vanilla to chocolate.” But it’s important for you to see that this type of talk makes no sense in terms of the preferences that we use in economic reasoning.

After all, what does it really mean—from the standpoint of pure economic logic—to say that Mary has a preference for vanilla over chocolate? All it means is that, faced with a choice between the two flavors, Mary would pick vanilla. But that is the same thing we can say about her sister Jane, whose friends would testify that she has only a “slight” preference for vanilla. Jane too, when faced with a choice, would pick vanilla over chocolate. So in terms of logical deductions that we can make based on a person’s purposeful actions, all we can say as economists is that both girls exhibit a preference for vanilla over chocolate.

We can take this train of thought further to drive home the lesson. Even if Jane announces, “I just barely prefer vanilla to chocolate!” that wouldn’t give an economist the ability to conclude that her preference for vanilla is “less intense” than Mary’s. No, it would merely allow the economist to conclude that Jane preferred to yell that particular sentence, versus yelling something else or keeping her mouth shut. Remember, we are using the notion of a person’s subjective preferences to explain the concrete actions that the person takes. If someone utters a statement, that informs economists about the person’s preferences all right, but only because the utterance itself is a purposeful action!

To help you remember the points of this lesson, consider the analogy of friendship. For example, Sally might have three friends, and so we could say that in her mind she holds feelings of friendship for each of them. We can push it further and ask Sally to rank her friends. She might say that Bill is her best friend, that Mary is her second-best friend, and that Joe is her third-best friend. Such talk is perfectly meaningful.

But what if we then asked Sally how much better a friend Bill was than Mary? Now things start to sound a little strange. And if we asked her, “Does Bill possess at least 30% more friendship than Joe?” we would have entered the realm of the absurd. The moral of this story is that it makes sense to rank friends, but even so there’s still no such thing as an objective “unit of friendship” behind the scenes, driving our ranking.

The same is true with preferences in general, at least as we use them in economics. As you will learn in upcoming lessons, to understand and describe exchanges, we need to assume that people have a ranking of goals or ends. People take actions to satisfy their most important preferences, or to achieve their highest goals. We do not have to say that people have a mathematical “utility function” that they seek to maximize, even though such talk is commonplace in other economics textbooks. This alternate approach is only useful in coming up with specific answers to contrived numerical problems; it doesn’t actually shed more understanding on the process of exchange. In fact, the use of mathematical utility functions is very harmful when learning basic economic principles, because it often causes the student to forget where the notion of preference comes from in the first place.

An Alternate View

Even professional economists do not always heed the principle that preferences are a ranking, not a measurement. For example, economists often use the term utility to describe how much pleasure or satisfaction a person gets from a particular situation. Therefore they might describe our scenario by saying, “Mary chose vanilla ice cream because it gave her more utility than the chocolate ice cream would have given her.”

So far, so good. But then many economics textbooks push it further and start assigning numbers to measure how much utility, so that (say) Mary gets “55 utils” from vanilla but only “34 utils” from chocolate, and so in order to “maximize utility” she obviously chooses the vanilla. If you are taking a Ph.D-level class, the textbook will explain that “utils” don’t really exist, the way “kilograms” are an objective unit of weight and “meters” are an objective unit of height. Instead, the Ph.D.-level textbook will explain, economists can use mathematical utility functions just as a convenient shortcut to describing preference rankings. So when the function assigns “55 utils” to a bowl of vanilla ice cream but only “34 utils” to the chocolate, all that really means is that Mary would choose the former over the latter. The utility function could just as well have assigned “18.7 utils” to the vanilla and “2.3 utils” to the chocolate; the important thing is that Mary acts “as if” she is maximizing this arbitrary mathematical function.

In this book, we will not be using the confusing terminology of “utils,” and we won’t be performing calculus on “utility functions” the way other economics textbooks do. These practices, though common, are dangerous because they can mislead you into thinking that we are measuring the amount of psychic satisfaction an individual derives from particular actions.

It may be that one day neuroscientists come up with an objective way to quantify various degrees of happiness, such that they can coherently talk about Mary being “three times more satisfied” than Bill. But even if this happens, our point here remains the same: In the field of economics, such talk is meaningless. In economics, we use terms like “preferences” as a way to explain or describe the purposeful actions of individuals. When someone chooses one thing over another, all we can conclude is that the person preferred the chosen item over the discarded item. Psychologists or neuroscientists (or even common sense) might shed more light on the event, but economic logic per se can go no further. The economist isn’t claiming to have all the answers; far from it! The economist is actually being humble here by admitting the limits of what economic reasoning can say about a given event. In Lesson 6, we will see how subjective preference rankings interact to yield objective market prices. At that time, you will understand better why we are stressing these points in this lesson.

Different Individuals’ Preferences Can’t Be Combined

If preferences are subjective to each individual, and cannot even be measured or quantified for each individual, then obviously it would make no sense at all to try to combine or aggregate individual preferences into “social” preferences. Unfortunately, even professional economists often engage in just this type of reasoning. Many people (try to) justify progressive income taxation, for example, by claiming that “a dollar means more to a poor man than to a rich man.” The idea is that taking $1 million from Bill Gates won’t lower his utility very much, whereas handing out $1,000 to a thousand different homeless people will greatly boost each of their utilities. Therefore, the typical argument goes, total or “social” utility has been increased by the redistribution of some of Bill Gates’s wealth.

In Lesson 18 we will examine the consequences of progressive income taxation. For now, we point out that the typical justification for it is absurd. You can’t add up different amounts of utility from various people. In fact, if you use the alternate term preferences it will be more apparent why combining them from different people is an impossible task. It makes sense to ask, “What is the total weight of the population?” or “What is the average age of the population?” It does not make sense to ask, “What is the total preferences of the population?” or “What is the average amount of utility per person?”

To make sure you understand just how nonsensical it is to (attempt to) perform arithmetical operations on different people’s preference rankings, once again let’s switch to the analogy of friendship. Suppose that Sally and Larry have the following “friendship rankings”:

Friendship Rankings

53_img01.jpg

Before continuing, make sure you understand the table: Sally has five friends total. Her best friend is Bill, her second-best friend is Mary, and so on. Larry, on the other hand, only has two friends. His best friend is Joe, and Bill is his second-best friend. Notice that even among their shared friends, Sally and Larry don’t have the same ranking order. Sally thinks Bill is a better friend than Joe, while Larry thinks that Joe is a better friend than Bill. There is nothing strange about this, because preferences are subjective.

Now suppose a busybody school administrator comes along and says, “This is terrible! Poor Larry doesn’t have as many friends as popular Sally! I have a great idea to make things fairer. I’ll write a note in Sally’s handwriting that says, ‘You smell!’ and put it in Adrian’s lunch bag. This will cause a big fight between Adrian and Sally, so he won’t be her friend anymore. Then I’ll arrange it so that Adrian sits near Larry on the school bus. They will eventually become friends. I can’t predict whether Adrian will become Larry’s 1st, 2nd, or 3rd-best friend, but no matter what, he will be ranked higher as a friend of Larry than he was as a friend of Sally. Through my benevolent intervention, I will have increased the total amount of friendship among the children.”

Obviously the above story is quite silly. But we have used a silly story to demonstrate the silliness of trying to add up subjective, individual preferences. Hopefully you can now see that trying to increase “social utility” by taking money from a rich man and giving it to a poor man, is simply nonsensical. Perhaps proponents of progressive taxation can justify it on other grounds, but appealing to the economic concept of preferences (or utility) doesn’t get the job done.

66 Responses to “Modern Utility Theory and Interpersonal Utility Comparisons”

  1. Gene Callahan says:

    “But these complaints are without merit, because economists aren’t saying those things at all!”

    Well, they oughtn’t to be, but we know Mises often said just such things. (This is a point on which Rothbard had him to rights.)

  2. noiselull says:

    I’ve read LFTYE from cover to cover and this is the only part I didn’t feel I absorbed. Why can’t utils be real? If it is true that “It may be that one day neuroscientists come up with an objective way to quantify various degrees of happiness”, why can’t economists use utils? Even if the economists don’t know the actual number, they can still assign numbers to clarify the utility function. It seems that Rothbardians like to deny that utility functions exist so that they can claim Hayek was an idiot and that even infinite knowledge can’t help a central planner. What’s funny is that Murphy seems to accept the Kirzner solution to the Mises-Hayek expressions of the calculation/knowledge problem. This requires utility functions with utils. It even seems reasonable to me that a “central” principal might be doing the school good if he finds a more effective manner of redistributing friends. (Perhaps this will result in bad incentive effects. Landsburg can do a piece on that one.) The utility monster is a ridiculous distraction.

    Incidentally, are there any Mises quotes that put him firmly in the camp against IUC?

    • Bob Murphy says:

      This isn’t an Austrian thing. It’s a modern utility theory thing, that (for some reasons) Austrians harp on. For example, look at this 1958 William Baumol article and its citations. This is mainstream stuff, with summation signs, vectors, set theory, and everything.

      And like I’ve been saying, any good graduate level micro book will derive utility functions from ordinal preference relations. Even von Neumann Morgenstern utility functions (which are derived from preferences over lotteries) respect this, though people sometimes think they are less ordinal than generic utility functions. (They’re not, to be clear. But sometimes people think they are.)

      • noiselull says:

        But-b-but, But Rothbard said! (in his welfare econ piece)

        • Bob Murphy says:

          I get that you are being amusing, but in case you think I am contradicting you somehow: Of course Austrians are big into this stuff, I guess because they co-founded modern utility theory. But my point is, my “dogmatism” on ordinal preference rankings being the foundation of utility theory, isn’t some crankish Austrian view. I would be extremely surprised if we can’t find Mises quotes that are explicitly anti-IUC, but by the same token I know we can find Hicks quotes, Baumol quotes, Efe Ok (the cutting edge mathematical utility theorist at NYU when I was a student) quotes, micro grad school textbook quotes, Bryan Caplan in his “Why I’m Not an Austrian” quotes, etc. etc. saying that mainstream economics doesn’t rely on IUC.

          • noiselull says:

            That’s just an appeal to authority. Mainstream economists can be wrong too. I’m not actually using the argument that since only Austrian cranks believe something it must be false. On the other hand, I’ve seen (though I have to look these up) quite convincing demonstrations that a mathematical utility functions requires that utilty must “exist” at some level. Certainly Austrians who argue against Hayek as being allied with Mises support that position.

            • Major_Freedom says:

              I don’t get it. You say that Austrians are saying this and that about utility, and then Murphy says no, it’s very mainstream to insist that utility is ordinal, and he goes out of his way to give you examples of mainstream economists who say that economics doesn’t rely on IUC, and you come back with “that’s appeal to authority” because mainstream economists can be wrong too?

              Wow.

    • marris says:

      I’ve thought about this. For example, we now have the technology to do scans of people’s brains and see regions become active. Someday, we may have tech to figure out precisely what neurons are involved when a given brain enters mental state X.

      However, I don’t think that actually solves the “cardinal utility” problem. For one thing, I don’t think you’ll get arithmetic. You could _define_ the happiness level of neuron X firing and neuron Y firing as the “sum” of the happiness of neuron X firing and the happiness of neuron Y firing. But it’s not clear that this “happiness” definition will have any relation to the subjective happiness that the mind feels. I think neuron fire patterns will not be composable in happiness terms.

      Now it’s still possible to develop some kind of neuron-fire-pattern to subjective-survey-answer map. For example, for each fire pattern, you may ask the person being scanned how they “feel”… given enough responses, maybe you could build out some information. But by introducing this subjective analysis, I think your back to square one. It’s not clear whether some person’s subjective responses are comparable with those of another person going through “similar” fire patterns [it will not be exact since the brains will be different].

      For a while, I thought it might be possible to get around even this restriction by creating copies. For example, I think if I clone Bob’s brain on a molecular basis, I could create something that feels like Bob [modulo it's soul if you're religious]. However, it’s not clear why this would be useful. The cloned brain/mind would still be offering subjective responses. And I don’t think I can somehow “emulate” Bob’s brain, where part of me could “run” it while another part of me sticks around as a “subjective mind reader.” I don’t think this is a coherent idea.

      • Gene Callahan says:

        I did not know the great Roger Marris also does neuro-economics!

      • marris says:

        Yes, I also do parties

  3. joshua says:

    Can’t do interpersonal utility comparisons blah blah blah, ok. Something I thought about long after I passed my game theory class…. Why can’t we convert both guys’ utils into a common currency? Like time, for instance… I bet the poor guy would be willing to trade more time, if such a thing were possible, for that dollar than the rich man would. Is there any way that kind of thinking could work?

    • Joseph Fetz says:

      Utils???

      Oh, no. Please, not “utils”.

    • Bob Murphy says:

      Joshua sure you could do that. But it wouldn’t allow you to make interpersonal comparisons, unless you assumed that each man valued an hour the same. But then you’re right back where you started.

      • noiselull says:

        Of course, you can’t simply assume that people have the same given utility/disutility functions, add in their wealth, and get IUC. It is an empirical question. But why would you assume that the initial utility functions are probably so vastly different so as to possibly render a poor man’s appreciation of a dollar lower than that of the rich man? To put it in another way, a dollar must be worth more to one person than to another. Chances are, given DMU, it is worth more to the poor person.

        • Dan says:

          Why must a dollar be worth more to one person than to another?

        • marris says:

          I think there are several issues here:

          (1) Although utilitarians often treat utility as a cardinally measurable thing can be allocated to one or more “human vessels,” this is typically not how economists think of it. Formal economic models typically _define_ utility in terms of agent choices. The model simply does not extend to multiple agents.

          (2) It may be possible to define some kind of “utility proxy” which _is_ measurable. For example, we may measure how much money I need to give Gene or Bob until each of them smiles. Or jumps for joy. Or expresses happiness in some other way. We can certainly apply any _given_ measure to a population and see what the results are. but we should not read too much into this. We’re not measuring happiness. We’re just measuring our proxy.

          (3) Depending on the population and the heuristic, we may find that the rich person values $1 more than the poor person. For example, if you took $1 from Scrooge, then he may scream louder than some poor person. And if that loudness is your proxy measure, then we’ll conclude that Scrooge values the $1 more.

        • Bob Murphy says:

          noiselull wrote:

          To put it in another way, a dollar must be worth more to one person than to another. Chances are, given DMU, it is worth more to the poor person.

          Do you think there must be a percentage surplus of friendship units, in between your best and second-best friends?

          • noiselull says:

            Friendship is only valuable due to utility. What makes up utility must be left to neurologists. (BTW, I suspect reading Dennett contributed to my position.)

      • Tel says:

        But it wouldn’t allow you to make interpersonal comparisons, unless you assumed that each man valued an hour the same.

        Look, it’s a model of behaviour, so it doesn’t have to be strictly accurate, it merely needs to be a reasonably workable predictor of behaviour. There’s nothing weird about that. All models are wrong, even models in physics — when was the last time you calculated magnetogravity while lining up a pool shot in a bar?

        If you presume that typical human lifespan is the same for all people, and everyone gets one lifespan to spend, it’s not an entirely unreasonable position to base each person’s calculation on how much of their own life it costs to obtain the things they want.

        This model delivers quite decent results. Let’s suppose you are a plumber, how much time does it cost you to fix a tap? Not a whole lot, because you:

        * already have all the tools.

        * already know what you are doing.

        * have plenty of spare washers and bits on hand.

        Let’s suppose you are not a plumber, and you want to fix a tap, well the cost in time is considerably higher because you either need to go and learn about taps and plumbing, and get the tools, and get the parts, etc, or you need to work some job long enough to earn the money to pay both the plumber and whatever transaction overheads are involved (e.g. transport, tax, phone call, etc).

        You will probably find some corner case that it doesn’t cover, and it doesn’t apply particularly well to personal stuff like how many friends you might have (although it can partly apply), and no doubt some guy is going to just let his taps drip all day cos he cares about other things… I accept all that.

        Mind you, if you extend the model to presume that people can spend their money in ways that extend their lifespan it gets a bit recursive, probably not intractable.

        • Major_Freedom says:

          Did everyone watch the movie “In Time” over the weekend or something?

          Tel, it is unreasonable to assume that people’s lifespans being roughly similar has anything to do with utility, since as Murphy said, different people would value time differently, so there is still not common denominator.

          To say that because time can be measured, it can somehow explain utility, is just the labor theory of value making another appearance in economic discourse.

          • Tel says:

            I have a brilliant answer to that one, I just can’t afford the time to write it.

  4. Silas Barta says:

    Wow, pretty neat (or frustrating) that you used the exact phrase in your text that Klein did!

    • Joseph Fetz says:

      I would tend toward frustration. Kind of like beating myself in the head repeatedly with a big, black, steel-toed boot of funky foot-smell frustrating.

    • Bob Murphy says:

      Silas, right, now you see why I was so astounded at the whole thing.

  5. Gene Callahan says:

    “What’s funny is that Murphy seems to accept the Kirzner solution to the Mises-Hayek expressions of the calculation/knowledge problem. This requires utility functions with utils.”

    No, that is not true. Kirzner does not even bring utility functions into play in his “re-homogenizing” work at all.

    • Joseph Fetz says:

      Gene, do you have the title of the book/article related to this work of Kirzner? I am not challenging you, I just want to know for further study.

      Thanks.

      • Gene Callahan says:

        Joseph, my Kirzner library isn’t with me at the moment. Bob, do you recall where he does the most Mises-Hayek discussion?

        • Joseph Fetz says:

          Gene, I think I may have found it due to clues in your last comment (and, a handy google search). Does this sound familiar?

          ‘The Meaning of Market Process: Essays in the Development of Modern Austrian Economics”

          • Gene Callahan says:

            Sounds about right.

            • Joseph Fetz says:

              Cool. Thanks.

          • Bob Murphy says:

            I think that’s the book I reviewed (at mises.org?) back in 1999 or 2000 maybe. I remember that I said it contained “some of the very best of Hayekian thought” and he told me he didn’t like that term, since it implied he wasn’t a Misesian.

    • Bob Murphy says:

      Yikes good catch Gene. Yeah noiselull, what the heck are you talking about? (a) Kirzner doesn’t say that and (b) where did I endorse this? Are you talking about my review of Kirzner for mises.org?

      If you want to retract my nomination as today’s Bastiat, I understand.

      • Joseph Fetz says:

        That “today’s Bastiat” thing is so completely stupid.

        Sorry economic profession, hate to break it to you, but Bastiat was Bastiat and that is that. There is no “today’s Bastiat” because Bastiat is dead. Now, if one of you would die today or just kill yourself, then you would be only one tiny step closer to being “today’s Bastiat”. Until then, no dice.

      • noiselull says:

        (a) The very idea that a central planner can solve equations to solve for resource distribution requires cardinal utility. Rothbardians seem to believe so. That’s why they say you can’t solve it even in principle. (Not referring to your argument about number of equations, which I don’t understand because I am bad at math) (b) Yes

        • Dan says:

          “(b) Yes”

          That’s a weird answer to the question where did I endorse this.

        • marris says:

          What is “The very idea that a central planner…” ?

          Something that Bob said? Or your thoughts?

        • Bob Murphy says:

          noiselull, I truly have no idea what you are talking about. You can do modern welfare economics without using cardinal utility functions. You can define Pareto optimality, etc. etc. without cardinal utility.

          • Bob Murphy says:

            noiselull, I should pull back some of my remarks. There are certain things they do in welfare analysis that might rely on cardinal utility. But, I don’t think any of that is necessary for the stuff they would need from mainstream economics, to do the “central planner’s solution.” There wouldn’t be a unique outcome, but the central planner could always reach an “efficient” outcome only relying on ordinal preference relations.

          • Tel says:

            Pareto optimality is oft talked about but rarely used. It would imply that you had complete agreement from all parties concerned (including the person being taxed) and all parties affected by the transaction (which is everyone on Earth if that transaction was in US dollars).

            You could argue that most of those people can be ignored because the effect on them is small, but that’s not Pareto anymore, that’s the common quasi-Pareto-as-I-feel-like-today optimum which might sometimes be similar to Pareto.

  6. Utility Man says:

    Neuroscientists will never be able to contribute to utility theory by quantifying satisfaction because utility /=/ satisfaction.

  7. Bharat says:

    Perhaps this could have fallen under Shameless Self-Promotion as well? :D

  8. David Friedman says:

    “Because preferences are tied to a person’s exchanges, the preferences can only reveal a ranking of goals.”

    That simply isn’t true. As Von Neumann showed, if individual choices under uncertainty meet certain fairly modest consistency conditions, individual preferences can be assigned cardinal utilities, arbitrary only up to linear transformations (i.e. changes in the unit and zero point), and individuals will then choose among uncertain outcomes on the basis of their expected utility.

    So one can, in a non-arbitrary way, assign cardinal rather than ordinal utilities to individual preferences.

    Interpersonal utility is a harder question, but I agree with Dan Klein. For one thing, people routinely give gifts to those they care about, especially their children. If utilities are entirely incomparable between people, how could I possibly decide how to spend my limited resources on gifts intended to make different people happy? More generally, while I agree that we don’t have any mechanism for measuring interpersonal utilities comparable to the mechanism of revealed preference for evaluating a single individual’s preferences, does anyone seriously doubt that the disutility to one person of being tortured to death is greater than the disutility to another of a mosquito bite?

    What is less clear is whether the marginal utility of a dollar to a rich person is predictably less than to a poor person. The question there is why one is rich and one is poor. If we imagine that people are chosen at random and varying amounts of money dumped on them, then on average the prediction holds, because of individual declining MU. The same is true if the reason for differing incomes is differing productive abilities. But if the reason for differing incomes is differing utility functions, the conclusion reverses–I will leave the proof as an exercise for the reader.

    • Bob Murphy says:

      Dr. Friedman, I realize this is like challenging Superman to an armwrestling contest, but I think you are wrong about vNM utility functions. We obviously don’t disagree on the math, we disagree on the philosophical interpretation. But for example have you read Baumol’s 1958 paper on this? I don’t want to waste your time, but I’m pretty sure he is exactly disagreeing with you? (Don’t read the whole paper–if the first 2 pages don’t sound like it’s relevant, then stop.)

      • David Friedman says:

        I’m not making the philosophical claim that cardinal utility corresponds perfectly to intensity of preferences, but I think it is at least related to it. If I prefer B to A only by a little but C to B by a lot (intensity of preferences), I will prefer a lottery between A and C to a certainty of B even if the probability of C in the lottery isn’t terribly high. Do you disagree? That implies a connection between VN utility and intensity of preferences, even if not an identity. To put it differently, it shows why VN utility tells you more about intensity of preferences than a simple ordinal ranking of A, B and C would.

        I don’t at the moment have access to the full Baumol paper; the first page doesn’t sound as though it is going to convince me to change my view.

        The question of ordinal vs cardinal is separate from the question of interpersonal comparisons. I think doing the latter ultimately depends on knowing enough about human beings, through being human beings, to be able to deduce things about what is happening inside other people’s heads from what we can observe outside their heads. We can’t do it perfectly, perhaps we can’t do it very well, but I think it is clear that we can do it to some degree, and routinely do–as in my example of choosing gifts.

        • marris says:

          > If I prefer B to A only by a little but C to B by a lot (intensity of preferences), I will prefer a lottery between A and C to a certainty of B even if the probability of C in the lottery isn’t terribly high. Do you disagree?

          YES. What if I hate lotteries? I can have all sorts of subjective feelings about your procedure which interfere with the data you’re trying to get from it.

    • marris says:

      > That simply isn’t true. As Von Neumann showed, if individual choices under uncertainty meet certain fairly modest consistency conditions, individual preferences can be assigned cardinal utilities…

      Well, hold on. It’s true that VNM can be used to assign cardinal utility values such that certain conditions are met. It is _not clear_ that these cardinal numbers represent anything else. X may get a cardinal utility of 1 and Y may get a cardinal utility of 2, but VNM _does not_ say that Y provides twice as much satisfaction as X. VNM just gives us numbers that play nicely with probability expectations.

      > If utilities are entirely incomparable between people, how could I possibly decide how to spend my limited resources on gifts intended to make different people happy?

      I dunno. Is it possible that you’re just ranking anticipated responses to your gifts? Or maybe you’re just picking some objective fairness criteria [equal monetary value, equal number of things, whether each recipient will respond in a similar way, etc] and just going off that?

      > does anyone seriously doubt that the disutility to one person of being tortured to death is greater than the disutility to another of a mosquito bite?

      It possible to “normalize” individual responses so that you can tell when someone is slightly happy vs. really happy. But we have no way of knowing whether the “really happy” for two different people are the same thing. We can only form our own heuristic estimate using response criteria that we select. We probably revise our heuristics as we get better feedback from others. After all, other people often just _tell_ us when they’re really happy. Much of the time, I think we just accept that at face value.

      • marris says:

        > But we have no way of knowing whether the “really happy” for two different people are the same thing.

        That’s probably too strong. I’ll just say that _I_ have no way of knowing… But I, like everyone else, use heuristics to do the type of gift allocation which you describe.

    • Adrian Gabriel says:

      One question I have for Mr Friedman is if he has even taken the time to thoroughly understand subjective value theory and ordinal rankings, or if he is like Selgin and White with their thorough unwavering decision to be pedants. If so, Mr Friedman is a sucker for a monopolized education and is not demonstrating any individuality in his thinking. He seems to be regurgitating what the State has fed him through his university teaching. Sometimes I wonder about you Mr Friedman, because your father was a huge sucker for statism and inflation. I remember reading your blog about Rothbard and how he correctly showed your father’s monetarism as a tool of the State, and how you got all offensive. Maybe you should read up further on Austrian Economics and stop relying on the mechanics of the State. Other than that, at least you try being Anarcho-Capitalist. Yet I suggest reading up more on Rothbard, unless of course you will continue to envy his superiority to you….

      • marris says:

        Dude, calm down. Why don’t you respond to the analysis rather than make Yo Papa jokes? Calling someone a crazy statist is not an argument.

      • Major_Freedom says:

        Gabriel, this is not the way to treat Dr. Friedman on Murphy’s blog. It’s highly rude and without class.

      • Joseph Fetz says:

        Adrian, stick to the arguing the subject matter, man. We can have disagreements, but it makes no sense to attack people, especially somebody that many of us would love to have back to debate certain topics in the future. It has nothing to do with kissing anybodies tukhus, it has to do with common respect and decency.

      • Wonks Anonymous says:

        David Friedman claims to have never taken an economics course for credit (his degree is, I believe, in physics). So it wasn’t the State that fed him economics. It was more likely the dinner table plus a good dose of autodidactism.

    • Major_Freedom says:

      That simply isn’t true. As Von Neumann showed, if individual choices under uncertainty meet certain fairly modest consistency conditions, individual preferences can be assigned cardinal utilities, arbitrary only up to linear transformations (i.e. changes in the unit and zero point), and individuals will then choose among uncertain outcomes on the basis of their expected utility.

      Von Neumann did not show that cardinal utility is what individuals are actually utilizing. He only showed that under certain assumptions (which don’t always hold, which makes it less explanatory than ordinal utility), ordinal preferences can be assigned certain mathematical values the calculation and outcome of which mimics the outcome of ordinal utility ranking comparisons.

      If utilities are entirely incomparable between people, how could I possibly decide how to spend my limited resources on gifts intended to make different people happy?

      By ordinally ranking the various alternatives for dispersed gift spending available to you, and then choosing the one dispersed gift spending pattern that is most valuable to you.

      “Should I spend equal amounts on everyone, or should I spend more on some than on others? If the latter, should I spend more on the older family members and less on the youngest?”

      Etc

      More generally, while I agree that we don’t have any mechanism for measuring interpersonal utilities comparable to the mechanism of revealed preference for evaluating a single individual’s preferences, does anyone seriously doubt that the disutility to one person of being tortured to death is greater than the disutility to another of a mosquito bite?

      I doubt it, in fact I reject it. For the rhetorical question presumes a valid common denominator for making such comparisons. The common denominator being presumed in that rhetorical question is simply not valid.

      When people ask these rhetorical kinds of questions, they are really presenting themselves in their own mind as the needed common denominator, which actually relates to a mutually exclusive, unique ranking unrelated to the rankings ostensibly being considered. They think to themselves that it would be far worse for themselves to be tortured to death compared to themselves being bitten by a mosquito. That ranking is valid because the individual themselves serves as the common denominator.

      But an error is made when this ranking is then split into freely floating elements that no longer apply to the same person, but instead single elements are applied to single individuals other than the individual thinking in this way, where one element (say being bitten by a mosquito) now applies to one person, another person, and the other element (say being tortured to death) now applies to a third person. Then you incorrectly think “Aha, this person would feel much greater disutility in being tortured to death than this other person would feel disutility in being bitten by a mosquito.”

      Yes, it makes sense if you said that YOU prefer being bitten to being tortured, but the whole meaning of such a ranking that requires a common denominator, namely you, in order to even make sense, is totally lost when you take the elements in that ranking and strip them away conceptually from each other, after which you then plant each element onto an individual, and pretend that the same common denominator, namely you, applies. But it doesn’t apply any more. You’re now talking about two entirely new individuals and thus two entirely new common denominators, each with their own ordinal value scales that can only be comparable to each other using themselves as individuals as the common denominator.

      What is less clear is whether the marginal utility of a dollar to a rich person is predictably less than to a poor person.

      This question suffers from the same error as above.

      The question there is why one is rich and one is poor. If we imagine that people are chosen at random and varying amounts of money dumped on them, then on average the prediction holds, because of individual declining MU.

      What is actually holding in that thought experiment is DMU for the individual, not the hypothesis that IUC is valid.

      • David Friedman says:

        “He only showed that under certain assumptions (which don’t always hold, which makes it less explanatory than ordinal utility)”

        No. That means that it explains less about some things (people whose preferences don’t fit the axioms), but more about others (the choices under uncertainty of people whose preferences do fit the axioms). So it is neither more nor less explanatory.

        I find it amusing that you take it for granted that “less explanatory” describes an unambiguous ordering, but are confident that interpersonal comparisons provide no ordering at all.

        I asked:

        “how could I possibly decide how to spend my limited resources on gifts intended to make different people happy?”

        You responded:

        “By ordinally ranking the various alternatives for dispersed gift spending available to you, and then choosing the one dispersed gift spending pattern that is most valuable to you.”

        And how can I rank the alternatives if my objective is to benefit the recipients and, according to you, it is absolutely impossible for me to know whether one allocation of gift money does that better than another?

        If I asked “how can I square the circle” would your answer be “by squaring the circle?”

        • Patch says:

          If you have two people to choose between, Hobo Bob and Richie Rich, and your goal was to give the money to who you think needs it most, most people would not hesitate and give the money to Hobo Bob. You give the money to Hobo Bob because the compassion earned by helping him out is greater than the compassion felt by helping out Richie Rich. If you know that Hobo Bob is going to spend the money on warm food because he is starving while Richie Rich will blow it on a new car, then you make the decision based on your own value scale where you say Hobo Bob’s survival is more important than Richie Rich’s new car. Who “needs” it more is completely arbitrary-there is no positive law stating a life is more important than material objects. Only our ethical and moral systems make that choice.

          I don’t think the above statements require interpersonal utility comparisons. You are basing your decision off of your own subjective value scale, not on whether Hobo Bob’s “utility” is greater than Richie Rich’s. Your value scale based on what you subjectively decide is more important. Its impossible to know who “benefits” more. In fact, I could argue the opposite, saying that Richie Rich needs my money because I want him to have a car collection, or something else. In both cases I am dispersing with my money based on my own value scale, and that value scale is based on what I arbitrarily decide is more important (Hobo Bob’s survival or Richie Rich’s collection). Neither group “needs” the money more in the value free sense.

        • Adrian Gabriel says:

          Mr Friedman, take a lesson from the man that makes your analysis look futile:

          http://mises.org/daily/3638

          Mathematics is for physics, not economics. Stop with the statism please.

          • Joseph Fetz says:

            Adrian, no disrespect, but I am sure Dr. Friedman is quite familiar with Murray’s works.

          • Contemplationist says:

            The arrogance of an idiot who imagines David Friedman is not familiar with Rothbard is very amusing. And an anarchist like Friedman is also a statist! Statists left and right, statists everywhere I look! Go back to your rat-infested cave. In the real world people have disagreements, many of them honest. If you are so sure of what you know is Right and True, and anyone disagreeing is a heretic, then please start a Church, and leave us all mortals to feel Doubt.

        • marris says:

          > I find it amusing that you take it for granted that “less explanatory” describes an unambiguous ordering, but are confident that interpersonal comparisons provide no ordering at all.

          An unambiguous ordering of the former kind is a nice mental tool, but I’m not sure we really need it. We just need a ranking model which permits choices between two alternatives, and one which permits selection of a highest ranked item from a set of candidates. A full ranking is useful for defining higher order abstractions, like demand schedules.

          But not every analysis requires demand curves. Or if you really wanted to use demand curves, you may define them differently [e.g. from indifference curves]. Or just assume individual demand schedules as _primitives_ in your conceptual model. It’s totally up to the economist.

          > And how can I rank the alternatives if my objective is to benefit the recipients and, according to you, it is absolutely impossible for me to know whether one allocation of gift money does that better than another?

          MF’s point is that this _is_ impossible. As in “cannot be done.” So you’re going to have to settle for something else. Like estimating the response pattern for each gift allocation and then ranking the patterns from “the one I’d most like to see” to “the one I’d least like to see.”

          This is just one example. Each giver can rank the various allocation patterns by whatever observable criteria he wants. Or the criteria need not be observable. A gift allocation may be rejected because the giver feels that he will have “regrets” about it later, regardless of the recipient responses.

          > If I asked “how can I square the circle” would your answer be “by squaring the circle?”

          I think this is a qualitatively different question. For someone to show you, there would already need to be inter-subjective criteria which both parties share.

          If that shared criteria is in place, then I could try to present a procedure, you could poke holes in my presentation, etc.

          For IUC, MF is claiming that shared utility norms are _not_ in place. The gift giver must resort to _other_ criteria [responses, knowledge of customs, etc]. Most people are happy to use these other criteria _in place_ of IUC when they do gift allocation.

          • David Friedman says:

            “Each giver can rank the various allocation patterns by whatever observable criteria he wants.”

            And how does the rational giver choose observable criteria when his objective is to make the recipients happier? He does it by using those criteria that he believes correlate with increases in happiness. You are arguing that it can’t be done, I’m pointing out that people routinely do it. Human beings are not impenetrable black boxes, especially from the point of view of other human beings.

            The donor could, of course, have some objective other than making the recipients happy. But, as I think you could easily discover, either by asking people or by introspection, people do quite often have as one of their objectives increasing the happiness of other people they care about, and take actions for that purpose.

  9. Bill Woolsey says:

    Perhaps this was already mentioned in the thread, but I think term utlitiy is being used in two ways.

    One way, relevant to philosophy, is that it means happiness or maybe a net hedonic balance. It doesn’t necessailty have to do with the preferences people have. It is at least possible to think abuot self-destructive behavior. And comparisons between people are possible. Not very precise, of course. Dimiishing marginal utility would have to do with the pleasure or happiness from considering alternative amounts of consumption of a good. And you have the ice cream story.

    The other use of the term is to mean individual preference ordering. And that has come to be the dominant use in economics. Using utility to describe preference orderings (as oppose to saying perhaps people’s preference orderings are based on what they think will make them happy,) doesn’t tell us too much about self-destructive behavior or allow interpersonal comparisons.

    Diminishing marginal utility, or dimininishing marginal rates of substitution, more exactly, have to do with consistency in ordering. Actually, I still like the simple–first things first approach to diminishing marginal uitlity. (As opposed to the shape of the more prefered set.)

    The words are used in two ways because classical economists played an important role in the development of utilitarian philosophy. Utilitiarian philosophers played an important role in classical economics. JS Mill, most obviously.

    Personally, I think it is a terrible mistake to take subjectivism, which makes some sense in economics, and try to carry it over to moral philosophy. Just as I don’t think that the concept of utility appropriate to moral philosophy should be carried over into economic analysis.

  10. Patch says:

    I know Neoclassicals have derived their utility functions ordinally, but is modern welfare economics (take for example, Cost Benefits Analysis) free of cardinality/IUC? The notion of consumer surplus and measuring the quantifiable changes in agent’s welfare to see who benefits from a specific policy “more” has always struck me of utilizing cardinality, or at least assuming that each agents “value” the same dollar “equally”. For example, slapping a tax on a good to correct for a negative externality, and weighing the losses in consumer and producer surplus, and then comparing them with the increase in government revenue to see if society accrues net benefits.

    I’m hesitant to rely on Rothbard;s comments on consumer surplus for this, mainly because people have criticized his view on utility functions (and his view that the Tangency Condition implies cardinality).

  11. Adrian Gabriel says:

    Patch, just because Rothbard is critsized for his accurate perspective does not make him any less c orrect than he has proven himself to be. This would be like saying Jesus Christ was a nut because everyone tortured him, or that Ron Paul is an idiot for demonstrating accuracy. Bad excuse for not understanding his mechanics. To make such broad assumptions in cardinal utitilty functions is absurd. With numbers place upon values, one makes the large mistake of thinking we are drones. I do not understand how anybody thinks cardinal utility can have any place in a world where diversity is important for amplifying ideas and innovation, as well as increasing human’s tandard of living.

    http://mises.org/rothbard/toward.pdf

    • Contemplationist says:

      Hey retard

      To point out again, this isn’t a church. If you want to honestly argue, you can do so. Its cliched but reality is mostly not black-and-white. In the real world, there are approximations that help deal with uncertainty. Math can help in this instance. Whether cardinal utility is useful or not is an open debate. Dr. Friedman argues that it is definitely of some use.
      In short, what’s missing from your zeal of a convert is DOUBT, and NUANCE. This isn’t some pansy code for equivocating on evil or whatever. We are not talking ethics or values. We are talking about concepts to understand the world. There will be disagreement, and doubt. There exists tremendous uncertainty. Sometimes the tools created by economists or mathematicians can help deal with this. Sometimes, it cannot. This should be the debate, not your religious citations.