Why can't utilities be measured? Because there can be no such thing as a unit of happiness. In the case of distances we can make ostensive definitions of a unit of distance: a meter, we can say, is this long. A pound is this heavy. But we can't say: a util is this happy.
But perhaps one can be allowed to say that he prefers C to A 3 times as much, while he prefers B to A only twice as much. Here we merely state a relationship between the choices. In other words, let A be one util; then B will be 2 utils, and C, 3. Here we seem to have a unit: A. One util is whatever happiness A provides. One can object by saying that it's unclear how to multiply happiness by constants. How does twice as much happiness "feel"? How can any person determine how many utils he is experiencing, even given a unit? How can we know, for example, by exactly how much to discount marginal utilities? So, even this is problematic.
But don't we sometimes say that we would prefer B to A by "a little," while we would prefer C to A by "a lot"? It is an accident of our psychological makeup that we can't divide utilities by each other to find out by what factor we are better off. But if we can vaguely judge "a lot" vs. "a little," then isn't it in principle possible? I believe a standard strategy is to calculate utilities in terms of money. Again, this is problematic, because of differing utilities of money. But it seems that imprecise calculations are both possible and actual.
Rothbard would retort: three times in terms of what? Utility is purely subjective. Even how much one's "three times more" differs from another's.
-Jon
Freedom of markets is positively correlated with the degree of evolution in any society...
To which they say utility functions are equivalent up to monotonic transformation and the equations have the same solutions regardless of which is used.
To which we retort: you can't have an equation regarding something that is purely subjective and resides only in the mind.
And their proof of this would be, what?
Let me rephrase the problem a little bit. If according to subjectivism we can say that C ranks higher than B ranks higher than A, and therefore, to give this a cardinal slant, C/A - B/A > 0, it is ever legitimate to say: C/B - B/A > 0, that is, that C is "much better" than B, while B is only "a little" better than A?
C ranks higher than B ranks higher than A,
to give this a cardinal slant, C/A - B/A > 0,
Why can't utilities be measured? Because there can be no such thing as a unit of happiness.
February 17 - 1600 - Giordano Bruno is burnt alive by the catholic church. Aquinas : "much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death."
I mean, "ranks higher on one's value scale." It's not a figure of speech but a standard expression. It means that at some particular time t A, B, and C are not "co-attainable" (that is, you have to choose one of these desires to satisfy), and that you prefer C to B, and B, to A. From this it could be deduced that you would pick C at t, or, if, for example, you became aware that C was impossible to achieve or satisfy, then you would pick B at t.
I may be equivocating with respect to the sign ">". If we represent "C ranks higher than B" as C > B, then it may not be reasonable to rewrite this as C - B > 0. But the puzzle remains. Can we say that the distance in happiness between C and B is greater than the distance in happiness between B and A?
I mean, "ranks higher on one's value scale." It's not a figure of speech but a standard expression.
It means that at some particular time t A, B, and C are not "co-attainable" (that is, you have to choose one of these desires to satisfy), and that you prefer C to B, and B, to A.
Can we say that the distance in happiness between C and B is greater than the distance in happiness between B and A?
You "rank" alternative ends as "first," "second," "third," etc. The end ranked first is said to be "higher" on the value scale than the end ranked second.
You would measure the distance by feeling it, by sort of introspecting and asking what you want and how much you want it. As I said above, obviously there is no way to assign precise numbers to utilities, but one might be able to do a rough-and-ready gauging of distances. Or how about this: I would be much happier if someone gave me $1,000,000 as opposed to $2, but only a little bit happier, as in my life wouldn't really change, if someone gave me $2 as opposed to $1. On the other hand, it's much more difficult to measure someone else's distances. I suppose a father can decide which of his children will enjoy a present more. But great insight into a soul, whether your own or another's, is required.
Actually, Rothbard writes that "there is no way whatever of measuring the distance between the rankings; indeed, any concept of such distance is a fallacious one." But he adds in a footnote: "We might, in some situations, make such comparisons as historians, using imprecise judgment. We cannot, however, do so as praxeologists or economists." In other words, economists do not spend their time studying people's souls. I suppose that's as good an answer as we will be able to get here... don't you find it annoying that you post a puzzle only to realize in the end that its solution is found in some canonical work?
Dimitri, you might be interested in this: http://libertarian-left.blogspot.com/2008/03/interpersonal-comparisons-of-utility.html
There is a way to assign a dollar value to the degree one prefers one good to another. Let's say you win a door prize and you get a choice between item A and item B. If you prefer item A to item B, the question is by how much? Well, the doorprize administrator can determine in dollars how much you prefer A to B by offering you B+$x. At the point at which you are indifferent between A and B, you prefer A to B by $x.
Now, money is itself just another good, so this really does not solve the problem of measuring units of subjective preference.
One of the easiest ways to see that it doesn't make sense to measure utility in an objective unit is the impossibility of defining exactly what it is that we are preferring. "How many units of happiness does a bottle of water confer?" Well, it depends. If you had been stranded in the desert for the last two days and you came across a heartless merchant who would not give you water for free, you'd probably give anything he asked in exchange for a bottle of water. The happiness you'd derive from that bottle of water would be very, very great.
But most bottles of water you drink give only a very small amount of happiness relative to other things you might consume, such as a vacation in Hawaii, It is not enough to track even the individual preferences of every human in an economy for every kind of good in that economy - you would have to at least track the individual preferences of every human in an economy for every *specific* good in that economy, in every specific situation in which each individual happens to be, or even plans to be.
Assuming we could assign a unit to happiness, the calculation problem is still insurmountable. The Wikipedia article on the economic calculation problem argues that since anything which can be calculated by one universal Turing machine (of which the brain's calculational capacity is an instance) can, in principle, be calculated by any other universal Turing machine, there is no in-principle calculation advantage to 6 billion individuals over one. However, this skirts several serious problems. First, some problems are more amenable to parallelization than others, so that parallelization results in genuine speedup (see Amdahl's and Gustafson's laws). There is good reason to believe that economic calculation is one of these problems. Second, calculation is only half (maybe less than half) the problem - communication is as much or more of a problem. How would a central planner foresee that I could get stranded in the desert and end up in dire need of a cold bottle of water? And failing foresight, how would I communicate this information to the central planner? Any circumstance which cannot be predicted no matter how much computing power is applied (I would argue that most economic particulars cannot be) must be communicated. The economic calculation problem is a genuine problem and the socialists must surmount this problem among many others.
Clayton -
ClaytonB:Well, the doorprize administrator can determine in dollars how much you prefer A to B by offering you B+$x. At the point at which you are indifferent between A and B, you prefer A to B by $x.
Wrong. How do we know you are indifferent?
Mises' version of the calculation argument has to do with ownership first and foremost, does it not, and only derivatively with utitilities?
To be precise, Clayton, if you accept the door prize of B+$x over A, it shows that you preferred to accept B+$x over accepting A. It does not show that you preferred B by $x over A. There's no reason to believe that you would have taken A if the money had not been offerred, at least in your example, nor is there reason to believe that you would not have taken B plus the money if fewer than $x had been offerred. Further, we can't account for the possibility that you are being motivated to accept the bundle of B+$x for reasons besides the general value that you place on B and the $x. For example, maybe the person offerring the door prizes is a cute girl, and you think B is the more macho thing to accept, and you do so even though to be perfectly honest, you like A better than B. Or you might think that if I'm trying to pay you to take B, it must mean I'm running out of A's, so you'll take the B so the people who really want A's can have one, even though maybe you would normally have taken the A over the B+$x. Or maybe you made a bet during dinner that could be settled for less than $x, and you don't have any other money on you, but you really don't want to get hassled by the person you made the bet with until the next time you see them. So at that particular moment, the $x could be really valuable to you, even though in the scheme of things, A would probably have given you more long-term happiness (so in other words, we could be dealing with time preference and situational accidents here). The point is, you can't eliminate all of these things from an observation of a real world event. And if you could, the experimental conditions would need to be so precise that they wouldn't extend to normal observations, and so would only be useful as trivial facts about a particular experiment.
I mean, the problems go on and on, and we could literally go on for hours about everything that makes it so you can't possibly determine anything about a person's tendencies from a particular observation. And then we could go on for longer about all the reasons that you can't infer anything about a person's wellbeing from understanding their tendencies. And then we could go on for longer about all the reasons that knowing about a person's wellbeing wouldn't necessary tell us what to do as social planners. And we could drive it all home by pointing out that if we wouldn't be able to be "correct" or "perfect" social planners even with all this knowledge, we especially can't be "correct" or "perfect" social planners without any of that knowledge.
Sorry for bumping this ancient thread, but I'm still not quite satisfied with many Austrians' very strong rejections of cardinal utility as a concept.
I think everyone would agree that there is no way to make interpersonal comparisons of utility, and that there is no way for an outside observer, or even for the actor himself, to put actual numbers on his utility.
Still, doesn't every decision need some sort of internal (mental) "unit of account" in order to compare the expected psychic benefit of two outcomes and decide which end to aim for? "Ah, but all you need to know is which of the two outcomes you prefer. That is ordinal utility." you might then respond. But let's view this from the perspective of the actor. If the actor is selling a bike and one buyer is willing to buy it for 8 carrots and 3 stuffed goats and another is willing to buy it for 5 stuffed goats and 4 carrots. In order to decide which person to sell the bike to, does he not need some way of comparing the utility of consuming carrots to the utility of whatever you can do with stuffed goats? Is it not required to somehow estimate (in your own head) to intensity of "utility" you will experience when eating one carrot, when eating two, three or ten carrots and compare it to the intensity of utility experienced when utilizing a stuffed goat, two stuffed goats, or five?
We need to be able to "lump together" the expected utility of different types of experiences in order to make choices for situations where the different possible outcomes each involve several independed ends, each yielding independent psychic benefits and/or psychic costs. And that includes virtually all decisions we ever make.
We may call this unit of account "intensity of good feelings" or whatever. It is true that no one can put a number on it, no one can measure it and no one can make interpersonal comparisons using it. But the acting individual nevertheless has to use a single scale to compare all different sources of utility, even if he does not understand how he comes to the conclusion that he prefers four stuffed goats and four carrots to a bike, but not three stuffed goats and five carrots.
It is this "unit of account" I think many neoclassical economists tries to symbolize with the letter U in their utility functions. You cannot use it to calculate anything. It is pointless to, as is commonly done in microeconomics and portfolio choice theory, estimate utility functions using numbers and figuring out the optimal amount of inputs to maximize utility. That is pure nonsense. And I agree with Mises that the use of mathematical functions is inappropriate to describe economic/praxeological relationships. Still, that does not necessarily mean that the concept as such is flawed. We could never find out how an individual evaluates the expected utilities of certain ends, but we do know that he does evaluate it and that he must have some sort of unit of account to compare the utilities of different ends.
With that in mind, is it really so unrealistic to use some mathematical equations, which Austrians often raise objections to, such as MU1/P1 = MU2/P2 which simply states (in an economy with only two goods) that an individual will purchase good 1 up until the point where the utility of the last unit of good 1 divided by its price equals to (or is less than, if you object to the psychological state of indifference) the utility of the last good purchased divided by its price?
This does not involve interpersonal comparisons of utility, but it does involve comparisons between the utilities of different ends using a single unit of account (U), namely a comparison between the utility of the consumption of good 1 and the consumption of good 2. If an individual had no single unit of account for utility, wouldn't his mind then be subject to Mises' economic calculation problem when making decisions?
These are just some thoughts I had. It is almost 2 am now so what I wrote may not make all that much sense, but I would still really appreciate it if someone could explain where my reasoning went wrong.
When deciding between choices, your value scale represents always represents them as a "consumption package". Your scenario can be explained just like any other "single" action, and it all boils down to whether or not the additional end of carrots ranks higher than the forgone end of stuffed goats. There is no "unit of account" utility needed to explain this. Take another example, you go to a resturant and order the rotisserie chicken. Then the waiter asks, "BBQ sauce or Honey Mustard?" Now the chicken is "the same", but now you need to consider BBQ and honey mustard. Well, just like considering between whether 4 additional carrots ranks higher than 2 stuffed goats, your ranking of BBQ sauce and honey mustard determines which "consumption package" (the two chickens) you buy.
If you would sell the bike for both options, and if the 4 additional carrots ranks higher than the 2 forgone stuffed goats, then you would choose Basket A. You only ever need ordinal rankings to make decisions, never utility "units of account".
Thanks for the reply.
Yes, I realize now that I used a bad example, as ultimately it boils down to a higher or lower preference for four carrots compared to two stuffed goats. Let's view another example instead. You are selling a bike and buyer A offers one stuffed goat and one carrot and buyer B offers one calculator and one vacuum cleaner. Suppose that your ordinal ranking is as follows:
1: stuffed goat, 2: vacuum cleaner, 3: calculator, 4: carrot (where 1 is the highest on your value scale)*
The choices you have are two bundles: Your highest preference plus your lowest preference (bundle I), or your second highest preference plus your second lowest preference (bundle II).
How do you know whether to trade for bundle I or bundle II? You know that you prefer a stuffed goat to both a vacuum cleaner and a calculator individually, and that you prefer both a vacuum cleaner and a calculator to a carrot. But if your value scale is purely ordinal, the question "by how much?" doesn't make any sense. You can't measure the distance between the utility derived from utilizing a stuffed goat and the utility derived from a vacuum cleaner or a calculator. And thus, you can't decide which bundle is preferable.
When you are writing 58008 on your calculator, the joy you feel is not a joy relative to the pleasure you would have felt consuming a carrot. It is a thing in itself, that would yield the same enjoyment regardless of how much you enjoy or dislike carrots. It is this intensity of a feeling that cardinal utility seeks to portray, an intensity that is not ordinal, because you would experience it even in the abscence of any other alternatives.
Now, returning to the value scale above and your choice between two bundles, you could argue that there is no need to compare the expected utility of one good to the expected utility of the other goods, because your choice is not between four goods, but between two bundles, and that you simply need to decide whichever bundle is higher on your ordinal value scale. That still leaves the issue of your subjective evaluation of the two bundles. How can you determine which bundle ranks higher on your value scale? The utility derived from vacuuming your house is distinctly different from the utility derived from eating a carrot, using your calculator. They yield different types of emotions and they fill different practical purposes. In order to know which bundle ranks higher on your ordinal value scale, you first need to compare the utility derived from all the different ends the various goods can be used to attain. And just as with factors of production in an "economy" without money, there is no way to evaluate and compare the services (psychic benefit/utility) that different types of consumer goods (or services) yield without a common unit of account, without at least some sort of internal calculation based on "cardinal utility" or whatever you wish to call it.
*It should be noted that preferences and ordinal rankings are never in terms of consumer goods, but rather in terms of the utility derived from the services they provide. Each consumer good generally yields many different kinds of services, each evaluated differently on one's value scale - making the need for a common unit of account even greater.
Again, remember that in any action you choose between "consumption packages", and that value scales change all the time depending on the choices an actor faces. When making the decision, your value scale isn't the above, but 1. Stuffed Goat/Carrot 2. Vaccum Cleaner/Calculator (or vice versa). Another example is You and a date need to decide what restaurant you go to. You can go to the Italian resturant, which has a nice ambient atmosphere and eat pasta. Or you can go to the Bar, which is a more rowdy atmosphere, and eat burgers and hot dogs. The goods you decide between are "Nice Italian Restaurant with Pasta" and "More laid back bar with less fancy food". And how you make that decision is ultimately up to you and can only be expressed as rankings. The value scale above would be applicable only when you have the option of selling your bike for all four separate goods. The subjectivity of the "goods" is crucial here.
The question you pose, "how" you decide between either of the two bundles, relates to how you rank your ends. If carrots are more servicable than calculators, (your hungry) then you would choose the carrot. A unit of account like you suggest would be equivalent to saying "The calculator is .76carrot satisfactions, so I'm going with the carrot." You don't need a unit of account to compare goods, you just need to know (and you express this through action) which one is more preferrable depending on which distinct satisfaction ranks higher on your value scale.
The situation under money is different. Money is a physical good that is a medium of exchange. Whichever one earns you the most profit (difference of money revenues minus costs) is the avenue you will take. The money can be used to buy (theoretically) any consumer good, which all rank differently on your value scale. You don't need a unit of account for utility measurements, since each satisfaction that the goods provide are distinctly different.
To which they never mention produce the same marginal rates of substition and hence results regardless of the functional transformation as a result of the chain rule. Ho hum.
"When the King is far the people are happy." Chinese proverb
For Alexander Zinoviev and the free market there is a shared delight:
"Where there are problems there is life."
Thanks for the reply, but it didn't exactly address the point I was trying to make. As I wrote in my previous post, you do choose between two different bundles of goods, but your evaluation of those bundles is the result of your evaluation of the utility you expect the different individual goods to yield. You buy a bundle of one stuffed goat and one carrot, but when you buy it you don't think to yourself "I can't wait to get home to consume this goat/carrot bundle". The two have nothing to do with eachother, there is no relation whatsoever between the utility derived from the stuffed goat and the utility derived from the carrot. The value of the bundle is the the value (your subjective evaluation) of the services they provide individually. The hunger reduction a carrot can provide is an entirely different thing from the joy of scaring children with stuffed goats, and they must therefore be evaluated independently. You do buy a bundle, but this bundle contains two different goods, and the value of the bundle is the summation of the value the different goods, assuming they aren't complements - which I don't think carrots and stuffed goats are.
The answer you gave to the question of how to decide which bundle was preferable was an answer to a different question. It was an answer to how to decide which you prefer of a carrot and a calculator. Here there are only two goods you choose from and there is thus no need for anything but ordinal ranking. But the example I used was one with two bundles, each containing two different goods. You choose between stuffed goat+carrot and vacuum cleaner+calculator. You do really like stuffed goats, so you prefer the goat to all the other goods. But at the same time, you aren't that hungry so you prefer both the vacuum cleaner and the calculator to the carrot. How do you decide which to choose? Your ordinal ranking is known, you know which goods you prefer to which. But how do you select the bundle without considering by how much you prefer the goat to the calculator and the vacuum cleaner, or by how much you prefer the vacuum cleaner and the calculator to the carrot? It can't be done if your evaluation is only ordinal. You can order the bundles ordinally, but that ranking is the result of your evaluation of the many different ends you can use the different goods to attain.
How can you evaluate bundle I relative to bundle II without estimating the expected utility derived from the different ends that can be satisfied by the different goods included in the bundles? With only an ordinal ranking like the one I wrote down in my previous post?
Thanks for the reply, but it didn't exactly address the point I was trying to make. As I wrote in my previous post, you do choose between two different bundles of goods, but your evaluation of those bundles is the result of your evaluation of the utility you expect the different individual goods to yield. You buy a bundle of one stuffed goat and one carrot, but when you buy it you don't think to yourself "I can't wait to get home to consume this goat/carrot bundle".
Again, it has to do with the classification of a “good”. You do not choose between 2 bundles each consisting of “two goods”, but really just two “goods”. Each group, the carrot/stuffed goat and vacuum cleaner/calculator are just two goods that satisfy distinct ends: 1. Enjoying carrot/stuffed goat and 2. Enjoying vacuum cleaner/calculator. Your quote “I can wait to consume this goat/carrot bundle” is awkward phrasing, because in reality know one ever thinks with the word “consuming” or “bundle” or even “Good A/B/C etc” all together, it’s just “I can’t wait to use my stuff when I get home”.
The two have nothing to do with each other, there is no relation whatsoever between the utility derived from the stuffed goat and the utility derived from the carrot. The value of the bundle is the value (your subjective evaluation) of the services they provide individually. The hunger reduction a carrot can provide is an entirely different thing from the joy of scaring children with stuffed goats, and they must therefore be evaluated independently. You do buy a bundle, but this bundle contains two different goods, and the value of the bundle is the summation of the value the different goods, assuming they aren't complements - which I don't think carrots and stuffed goats are.
The value of the bundle is the value (your subjective evaluation) of the services they provide individually. The hunger reduction a carrot can provide is an entirely different thing from the joy of scaring children with stuffed goats, and they must therefore be evaluated independently. You do buy a bundle, but this bundle contains two different goods, and the value of the bundle is the summation of the value the different goods, assuming they aren't complements - which I don't think carrots and stuffed goats are.
Technically speaking, this is all subjective. You can certainly use the two most unlikely objects together. But again, you’re missing the point. Ends are always distinctly different, and therefore depending on how an individual ranks his ends he will rank his distinctly different goods accordingly. In the act of choosing, actors always choose between distinctly different single goods depending on which good can be used for a higher ranked end, and virtually every good is a “consumption package”. If you won a contest and can choose gift bag one or two, each composed of a variety of different consumer products, each gift bag is its own good. And when deciding between the two bags, you will decide based on which variety of products serves higher ranked ends. You don’t start writing down a value scale of all the single “goods” and then do some arithmetic operations based on a utility unit of account. You simply decide, and that is only up to you, what good can satisfy your ends “Wants satisfied by Products in Gift Bag 1” or “Wants satisfied by Products in Gift Bag 2”.
That value scale posited above and the one you mention for the carrot/stuffed goat etc dilemma doesn’t factor into that act of choosing, that value scale comes about only when you have all the objects and if you want to use them independently, you need to decide which one to use, or if you are buying all of them individually. In that scenario the “bundles” spilt apart and they all become four separate distinct goods, and the same thing occurs for however many goods are in the gift bag. In the case of the restaurant example, you don’t say 1. Burgers 2. Italian Ambiance 3. Pasta 4. Rowdy Bar scene, when deciding between 1.Burgers/Bar 2.Ambiance/Pasta, only if you were to choose between all four individual goods. In the case of using your "stuff" as you drive home from the mall, when you are in your car then you can decide "Am I using my carrots and goat heads together?", "Eating Carrots first", or "Scaring kids first?".
Jrgen, I had similar thoughts and confusions a little while back. I believe BlackNumero was trying to bring home the essential point that choice is context dependent.
You point out unless they (carrot and goat) were compliments(or the opposite) there is little reason to believe it necessary to strictly express the decision so strictly as the comparison of 2 bundles; you may as well go and just "sum" the utilities(converting the ordinal rankings into monontonically increasing numbers). Hence with 4 goods A-D, with ordinal rankings:
1. A
2. B
3. C
4. D
Then since v(A)> v(B)>V(C)>V(D), V(A+B)>V(C+D), so A and B are valued to C and D right? Now this MAY be the case but as you implicitly acknowedge, this may not always be the case, since A and B may be compliments(or the opposite, they may not "go well" together). Furthermore I would add, value scales themselves must be entirely context dependent, and so this would also be the case given goods that are substitutes in the sense that they are capable of serving the same ends to different efficacies(Rothbard generalises the notion of substitutes to the sense that all goods are essentially substitutes for one another, but I won't go into that here). Hence if A and B were substitutes toward achieving the same end(for instance), then it would also not necessarily be the case that A and B would be preferred to C and D, since B might serve a much less valued end.
Hence we cannot impute the valuation of bundles of goods from individual goods and vice versa(as expressed cogently first by Menger). The tradeoffs in each situation of choice represents a tradeoffs of a different sort. Strictly, the avove value scale can only help us understand the tradeoff of one good, e.g. B for either A, C or D. We cannot use it to understand any other situation, since this would have to take into account how these can be combined to acheive an alternative set of ends in a situation of an entirely different context.
Hence value scales of the form shown above are defined strictly, only to help understand a given tradeoff and more generally to explain the consequences of the fact that men act and prefer one thing to another when constrained by scarcity. These value scales are simply a school of thought, and we cannot measure them, or conceive of them in any meaningful sense of existing "out there." As Rothbard noted in his essay on welfare economics, the only thing that can be observed from action is the demonstration of preference from a tradeoff, for the thing acquired over that given up. However valuation of ends, and how these meaningfully affect the valuation of goods we cannot know, and changes from one action to another, and as I have noted above, would occur even if valuations themselves did not change.
In conclusion, i would highly recommend a careful reading of Mises' section on marginal utility in Human Action. Do be wary however of one error he makes in his exposition however, which I pointed out here. Hope that helps.
abskebabs, I'm pretty sure that in the passage of Human Action you've quoted in the thread you linked to, Mises is using an hypothetical example rather than an illustration of what is logically necessary.
Aristippus is right, of course. And my post there spells it all out.
And BTW Bob Murphy wrote that the equivalent up to monotonic functions thing is 100% correct.
https://mises.org/journals/scholar/murphy.PDF
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It's easy to refute an argument if you first misrepresent it. William Keizer
This (put differently).
Aristippus is right, of course. And my post there spells it all out. And BTW Bob Murphy wrote that the equivalent up to monotonic functions thing is 100% correct. https://mises.org/journals/scholar/murphy.PDF I'm still curious as to how we can go from that to the MU/P=MU/P while retaining ordinality. Remember the conversation we had in a thread a while back? | Post Points: 20
I'm still curious as to how we can go from that to the MU/P=MU/P while retaining ordinality. Remember the conversation we had in a thread a while back?
Remember the conversation we had in a thread a while back?
Sure do. Bottom line was we both don't know how to derive that equation, despite Bob Murphy saying it can be done.
I wish a professional mathematician here would spell it all out. Meaning to show either that it is possible or that it is impossible to derive that thing using ordinals.
I have been writing an unfinished paper addressing this issue and other things which I'm currently on a hiatus with especially due to upcoming exams, but I highly recommend the following which I found an invaluable source:
https://mises.org/journals/scholar/Utility1.PDF
Remember the conversation we had in a thread a while back? Sure do. Bottom line was we both don't know how to derive that equation, despite Bob Murphy saying it can be done. I wish a professional mathematician here would spell it all out. Meaning to show either that it is possible or that it is impossible to derive that thing using ordinals.
My hunch is still that it can't be done, mainly because even if the numbers from an equation are purely ordinal, you still are dividing them by prices, not to mention equalizing them.
askebabs
Read the paper.
1. He doesnt give a counterexample, i.e. a case where human preferences say one thing and the corresponding utility function says another. All he's saying is that it might be wrong. I want more than that. Show me a concrete case where it's wrong.
2. Also, he appeals to arguments that IMHO miss the boat. They sound analogous to arguing that one cannot solve Diophantine equations using complex variables because there are no complex numbers in arithmatic.
Just to note; I don't agree with everything in that paper, but I do think he makes some rather good points. It's true he doesn't provide counter examples, and it is worth noting it is an unpublished working paper, but his point that equivalence has not been established stands; and I don't think we need to run in circles trying to prove a negative.
Yes, the key is whether equivalence has been established.
And that's why I think he is wrong. If you have an ordinal preference system [for one individual at one point in time], and a is more liked than b if and only if F(a)>F(b), then that's equivalence. I mean, what's missing?
Might the F function have all kinds of properties the human preference does not? Sure it will, like continuity. But so what? Any statement about F involving only inequalities will neccesarily be true in the corresponding statement about preferences.
I don't want to say much more on this for now, but a relation of representation =/= a relation of equivalence as it seems you think it does. Knowing that I value A more than B as Mahoney acknowledges could be represented as Mahoney notes without adding a whit of insight to our pre-existing knowledge by saying V(A)>V(B).
However, if I started saying V(A)>V(B) and then went on to say V(A)/V(B)=MRS from which I derive demand functions then we are entering the realm of the largely arbitrary and meaningless. What is V(A)/V(B)? 2/1, 3/2, 81/16? The subsequent theorems of Microeconomics that are then used to constrain the resulting indifference curves practically assume what they should be aiming to prove. Whether subsequent transformations of the utility function are montonically increasing or not is entirely irrelevant, given that the same MRS and demand functions will be produced regardless of the functional transformation as a result of the chain rule(the only necessary condition for the transformed functions is nonsingularity). The abritrariness lies in the original formulation of this utility function, not on subsequent transformations, which are a side issue entirely.
That's all for now, back to revision!
Keep up the good work! Nothing says die hard economists more than talking about cardinal utility and price theory on a Friday night
:)
No need to answer, or even read, this post right away. It stands in cyberspace, twiddling its thumbs patiently.
1. I indeed do not know what "equivalence" means the way you use it. The paper argues that results may be true about the function but false about the value system. I see that as a denial of logic and mathematics. That's why I ask for a counterexample.
2. It doesn't add to our insight by merely setting up the representation, but when we use the laws of math [which are distilled common sense] on the function we might very well learn something. For example Bob Murphy claims it gives a smooth easy way to deduce a true but otherwise difficult theorem. [Note that I am not saying I know he is right. But he might be. And if he is, it means the representation has added to our insight considerably]. And I see no apriori reason that there cannot possibly be things to be learned.
3. Asking what is V(a) / V(b) is like asking what is the square root of minus 1 [certainly not a whole number] when using complex variables to solve Diophantine equations. One does not have to be able to answer at every single step "what is this thingy in the real world of economics" to use math. What appears in the final result is the only thing that has to be understood; not the intermediate steps.
As a simple example, why does "-1 times -1 equals 1" make any sense whatsoever in the real world? No reason at all. Do you therefor reject all the results of physics [=everything] that use this principle in the intermediate steps?
4. I'm glad we agree that the key lies at the very start, in the original formulation of the utility function. And it seems to me that setting up "liking A more than B iff F[A] > F[B]" makes it not abitrary at all. That condition captures the essence of a human value system. Again. what's missing?
Closing remarks for the night (for me at least).
3. Asking what is V(a) / V(b) is like asking what is the square root of minus 1 [certainly not a whole number] when using complex variables to solve Diophantine equations. One does not have to be able to answer at every single step "what is this thingy in the real world of economics" to use math. What appears in the final result is the only thing that has to be understood; not the intermediate steps. As a simple example, why does "-1 times -1 equals 1" make any sense whatsoever in the real world? No reason at all. Do you therefor reject all the results of physics [=everything] that use this principle in the intermediate steps?
Now, although I'd say I have fairly good math skills relatively, your math skills/knowledge of terms is clearly superior to mine.
However, whatever the negative values of 1 may result in during the intermediate steps of solving real world equations, the same type of analysis is not applicable to human action, mainly because we using deduction to describe meaningful conscious plans of humans. If we know that humans act, and we want to explain the formation of a price, we can't make steps that are logically inconsistent, because that makes no sense when describing purposeful behavior. We say humans act...then marginal utility...then....rankings of two goods...then supply/demand curves for participants...then causal analysis of a plain state of rest=price (very basic proof obviously, but you get the point). All of this because it deals with human minds and deliberate actions, needs to be meaningful. On the other hand, physics and the natural sciences are not deductive and don't deal with conscious purposeful agents, so each step does not need to be meaningful.
Ala rothbard:
MES
Praxeology asserts the action axiom as true, and from this (together with a few empirical axioms—such as the existence of a variety of resources and individuals) are deduced, by the rules of logical inference, all the propositions of economics, each one of which is verbal and meaningful. If the logistic array of symbols were used, each proposition would not be meaningful. Logistics, therefore, is far more suited to the physical sciences, where, in contrast to the science of human action, the conclusions rather than the axioms are known. In the physical sciences, the premises are only hypothetical, and logical deductions are made from them. In these cases, there is no purpose in having meaningful propositions at each step of the way, and therefore symbolic and mathematical language is more useful.
Black Numero,
As you wake, you see my thank you for the compliment.
IMHO, Rothbard totally missed the boat both in what you quoted and in the paragraph after.
I ask you, what would Aristotle make of an argument like this:
1. In Physics, the conclusions are known, but not the axioms.
2. Therefore there is no purpose in having meaningful propositions each step of the way.
And I'll give you my answer: Non sequitor. [2. happens to be true, but does not follow from 1.]
Let's look at another one:
1a. The propositions of economics are verbal and meaningful.
2a. Therefore only verbal arguments should be used in econnomics.
Again, a non sequitor. In this case 2a is neither true, nor does it follow from 1a.
Also, he makes an assertion which has no proof, [because it is false], that there is some mystical gain in having each step of an argument "make sense". A chain of logical reasoning [=math] gains nothing by that. As long as each step follows from the previous ones, it is perfect and needs nothing more. Even Rothbard must admit this, as it follows from his misuse of Occam's razor.
In addition, statement 1. is false. After Newton, in a stroke of genius, discovered his laws of motion [which were stated verbally and meaningfully], they are treated as axioms. So the axioms are considered known by the scientific community. So that physics is now on the same footing as economics. Axioms are known, and stated verbally and meaningfully. Should physics therefor dispense with math?
The whole thing is akin to saying Newton was English, therefor physics should be studied in English, and Mises was Austrian, therefor Economics should be studied in Austrian.
And his next paragraph, that there is no advantage to using symbolic logic [logistics means something else], is also a big mistake. He writes, "Contrary to what might be believed, the use of verbal logic is not inferior to logistics." It certainly is. Granted that the rules of symbolic logic are derived from verbal logic, but symbolic logic has tremendous advantages that verbal argument lacks. For instance symbolic logic would have shown him the holes in his first specious paragraph.
Bottom line:
1. The intermediate steps never have to be "meaningful". They only have to follow from the previous steps of the argument. The conclusion of course has to be meaningful. Otherwise whats the point?
2. Which is the preferred language, English or german or symbolic logic, depends one thing. Which is most useful. For physics verbal language would be insuperably cumbersome. Austrian economics, at least in its current stage, is simple enough that on the contrary, it is symbolic logic that is a cumbersome distraction.
One last thing, just an aside. He appeals to Occam's razor, which has no application to the topic he discusses. It is also not a "fundamental scientific principle." Nor does it deal with multiplication of processes.
Bottom line: 1. The intermediate steps never have to be "meaningful". They only have to follow from the previous steps of the argument. The conclusion of course has to be meaningful. Otherwise whats the point? 2. Which is the preferred language, English or german or symbolic logic, depends one thing. Which is most useful. For physics verbal language would be insuperably cumbersome. Austrian economics, at least in its current stage, is simple enough that on the contrary, it is symbolic logic that is a cumbersome distraction. One last thing, just an aside. He appeals to Occam's razor, which has no application to the topic he discusses. It is also not a "fundamental scientific principle." Nor does it deal with multiplication of processes.
I don't think simply because we use deduction that it is per se meaningful, I think we use deduction because humans purposefully act, we know the action axiom (along with other typical complaints about positivism), and therefore each step of the way must be meaningful. As in my earlier example, when analyzing the formation of a price, we are dealing with conscious humans who freely make choices, and each step along the analysis must accurately describe human decision making and thought. Whereas in the physical world, the rules are different, and since particles are unmotivated we have greater freedom in doing what we need to get a hypothesized result. I guess in Mises's words, the telology versus causality/mechanism argument. This fits in with the Austrian principles why certain mathematics are inapplicable to forming laws about action. I think you disagree with them, but I believe that is where this argument gets its reasoning from.
Mathematics can certainly be a "useful" application towards human action. You can derive all the theorems you want using manipulation of equations, etc etc and then say these describe certain phenomeon about economics. But how many apply to the real world, let alone make sense and are meaningful and can explain purposeful action each step of the way? The tangency condition MU/P=MU/P is a prime example. In terms of human thinking, what does this mean? How can humans equalize marginal utility ordinal rankings and then divide them by a price? We find the optimal indifference basket according to which one hits the budget constraint via a calculus problem? Huh?
1. I meant meaningful in the sense Rothbard meant, that the intermediate step can be translated into English and assert something about the real world. [As opposed to, say, [-1][-1]=1]
With your understanding of meaningful [=of benefit to the human] symbolic logic is also meaningful every step of the way, which R. says it isnt.
2.
when analyzing the formation of a price, we are dealing with conscious humans who freely make choices, and each step along the analysis must accurately describe human decision making and thought.
I don't see why. The only thing of interest is the conclusion. Who cares if the middle steps, such as the use of -1 times -1 equals one, has meaning?
A good example of this is probability theory. Wondering if it is a good idea to bet that heads will land ten thousand times in a row [or another more complictaed question that needs adcnaced math], our human actor writes a string of uninterpretable equations and comes up with "the odds are a zillion to one of you winning." That's all he needs. He need not have an interpreatation of the process of integration from - infinity to plus infinity etc etc.
Here you have it. Analyzing the formation of a price [how much is alottery ticket with suc odds worth], dealing with a concious human being freely making a choice [to buy or not to buy, that is the question], and each step along the analysis cannot possibly describe human decision making and thought.
It is a very restrictive requirement imposed on the classical rules of reasoning, and I don't see where it comes from. Is it common sense? Not to me. Is it derivable from the law of the excluded middle or something? No. Is it derivable from the action axiom, or any set of axioms at all that seems obvious to the average intelligent person? No. It's mysticism.
It is like saying that if a sentient but powerless robot is programmed to think, that every program we feed into his machinery must make sense to him. But if we feed the exact same program to a non sentient robot, that's ok. What's the difference?
3. The only arguments Ive seen that are valid about why math is inapplicable to economics deal not with the process of mathematical reasoning after the initial assumptions are made, but with the initial assumptions themselves being a farce. But once you grant the initial assumptions implicit in an equation about economic life, you can't stop the ride anymore. The use of math will lead only to conclusions that indeed follow logically and impeccably from the intial equation.
4. Let's hold Rothbard to his own standard. He and I both agree that a verbal argument should conform to the accepted rules of Aristotelean logic, right? So please put together that paragraph of Rothbard's into a syllogism, so I wlll see clearly how it is not a non sequitor, contrary to what I have claimed. [of course this is a trick question, because it cannot be done].If it was high school geometry and Rothbard wrote that kind of reasoning on a test, he would flunk the course.
5. Time is short. That particualr equation will have to wait. Sadly it may wait for along time. Will give it my best shot Monday evening possibly. Busy till then.