03 Sep 2016

Three Oldies But Goodies on Utility Theory

David Friedman 10 Comments

Ah, my previous post on Mises vs. David Friedman has sparked controversy over cardinal vs. ordinal utility. Here are three things I wrote on this general topic: one, two, three.

However, I should admit that at some point, I am pretty sure I made a major concession to David Friedman (we were going back and forth on this stuff) that modern economists use a cardinal notion of utility in some applications. To be clear, I was NOT saying, “OK David you win, now I believe in cardinal utility,” but rather I said something like, “OK I will agree with you that there is no way to take what modern economists do in this setting and transform it into an equivalent (but more cumbersome) approach that is clearly based on ordinal preference rankings.”

However, I cannot right now say what that application was. I don’t think it can simply be the use of a “pure discount” on future utils, because in this paper Koopmans shows the assumptions one can make on ordinal preferences over streams of consumption in order to derive such a discount rate:

Koopmans, Tjalling C. (1960) “Stationary Ordinal Utility and Impatience,” Econometrica, Vol. 28, No. 2 (April), pp. 287-309.

But, presumably I remembered that paper when I made the concession to David, so I don’t know what to tell you kids right now except that some of my sweeping statements in the “one” and “two” essays above may be too much. In other words, even though Austrians are still right (in my mind) that utility theory should have an ordinal foundation, if David Friedman wants to argue that you can only do certain modern things with cardinal utility functions, he may be right (whereas in those essays I argued that he wasn’t).

10 Responses to “Three Oldies But Goodies on Utility Theory”

  1. Keshav Srinivasan says:

    Bob, I’m pretty sure it is just the pure discount rate. Here’s what you said in June of last year:

    “Ryan Murphy (basically) agrees with David R. Henderson and me on the ordinal/cardinal utility stuff. However, on Facebook I backed down somewhat in an argument with David Friedman, because when I was reading the climate change economics stuff (without thinking of this debate) I realized that the “pure discount rate” is clearly talking about the percentage comparison of a util today versus a util next year. Yes, there are ways you can relate this to ordinal rankings of flows of consumption over time, but economists in the trenches are clearly thinking of this as cardinal utility. (Indeed, that’s why in my dissertation I criticized Mises’ writings on the pure time preference theory–I said in certain passages Mises only makes sense if we think utility is cardinal, and surely he doesn’t want to go down that road.)”

    So you did say that pure discount rates can be related to ordinal preferences, it’s just that that’s not what economists have in mind when they discuss discount rates. So you may have made less of a concession than you remember.

    • Keshav Srinivasan says:

      By the way Bob, if it is possible to define a pure discount rate using ordinal preferences, then why doesn’t this blog post by Gene Callahan solve Sraffa’s multiple own-rates problem?


  2. scott says:

    I have not really followed this closely (& also probably don’t really grasp the distinction being drawn) but the objection(s) to a ‘hard ordinal’ view of things to my mind would be —

    — when people say things like ‘real’ wages, ‘real’ interest rates, etc., what can this mean if one isn’t talking about measures? Real what? What does that mean? As opposed to what? Does it make any sense to talk about actual as opposed to real? So we create this word ‘nominal’ to cover up that inconvenience and convert to … what? It seems to me what is meant is something ‘objective’, independent of context… in other words, a measure. So, either this activity is meaningful, or it is nonsense and people should stop. But if there is sense to it, and people are able to draw useful conclusions from the activity, then there is truth to the approach and the position of ‘hard ordinalism’ seems like it should be wrong.

    — when doing things like ‘correcting for inflation’, and creating price indexes, etc, what is the point of this if value is purely ordinal? Basically, this seems like nonsense behavior if you are a hard ordinalist because all value is contextual, therefore, comparisons across time (i.e., different contexts) are meaningless. Just as with the ‘interpersonal comparisons of utility’, or however that cliche goes. Even if the price of something is higher today than yesterday, you can’t say anything about the value. Essentially, ‘higher’ and ‘lower’ don’t mean anything from one ordinal ranking to another, so what’s the point to compare? It only makes sense if there is a sense of objective measurement going on in market processes. Kind of like the previous example.

    — using trivial, abstract situations to talk about valuation, like the pizzas vs paintings. Yes, it’s pretty easy to believe in the purely ordinal when you strip reality of pretty much everything except trivial considerations. How about talking about something a bit more real — like saving up to pay for a lifesaving operation for a child, or something like that? Is it a measure of your value of the kid of you work your tail off for years on end, or if you just blow it off and let him die? Or is it just ordinal preferences? I guess my point is that maybe sure, you can create reasonable constructions and use them to solve logic puzzles that you create and get the right answer, but does that really get at what’s going on?

    Basically, I see people doing things that don’t seem to make much sense if they really believed what they say they believe. Which makes me think that they actually believe in a measuring aspect but maybe don’t recognize it.

    I also really, really, really don’t like the non-theistic, anti-objective value insinuational aspect of it. Just because you can solve economics puzzles with an idea doesn’t make it true to the exclusion of the rest of reality. I wonder if people are trying for ‘rigorism’ at the expense of ‘realism.’ If I have to leave my ideas fuzzy, well, that’s what I’ll do.

    Just my two cents…

    • Andrew_FL says:

      Right, utility theory really does mean there is no such thing as a “correct” inflation adjustment or price index.

      • Tel says:

        Pick your favourite basket of goods.

        • Andrew_FL says:

          But it would be my favorite, not anyone else’s, yeah?

    • Chris says:

      I think this hits on a different (but still important) issue. Correcting for inflation is about trying to measure the market value of goods, not the subjective value. Prices for sure are objective and cardinal. It matters if something costs a dollar more or 100 dollars more (whereas with pure ordinal preferences we can’t say that for sure) Nominal is not a word to cover up anything, it literally just means the dollar (market) value of a good. Real is where things get tricky and there is definitely no bulletproof way to construct a perfect price index, but these are cardinal values so it does make sense to correct them for inflation.

      I don’t understand what you are saying in the last part. Usually I would think ordinal utility seems more realistic while cardinal is more convenient and arguably more rigorous (at least because it opens the door for more math).

      As Bob emphasized in the last post, it’s very important to differentiate between the market value of a good (it’s price) and the subjective value. The first is measurable, the second (in Bob’s opinion at least) is not.

  3. D, F. Linton says:

    Normally, you are very clear and I can follow you, but….

    Friedman claims there are neat things he wants to do that can only be done if values are cardinal. You agree with him. But if values are only ordinal, that’s hardly a concession at all since it only means David can’t do his cool things or if he does them anyway they are meaningless for describing human action.

    • Bob Murphy says:

      Hi DF Linton,

      Well you might not realize the broader argument. When people like Tyler Cowen were saying “a poor man gets more utility from $1 than a rich guy” David R. Henderson objected, saying that’s not how utility works in economics. Then people like D. Friedman jumped in, saying, “Yes since von Neumann Morgenstern we’ve used cardinal utility.” Again, that’s not right; you can do vNM utility without assuming cardinal utility makes sense. So initially I wasn’t doing an Austrian vs. mainstream, I was doing mainstream-who-knows-the-foundations-of-their-theory vs. people-who-are-misled-by-labels. So I’m saying I conceded to D. Friedman at some point that in the climate change debate, the cutting edge theorists were using cardinal utility as the foundation. (Even though I probably could show that it wasn’t totally necessary.)

      More context: When I was at NYU, I asked my game theory prof if vNM approach implied that utils were cardinal and he said, “Of course not!” like I was an idiot.

      • Andrew_FL says:

        I love it when professors respond like that.

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