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).