G. H. von Wright’s critique of Bayesian decision theory

4 August, 2014 at 12:33 | Posted in Theory of Science & Methodology | 4 Comments

Wright_kijoituskoneA farmer is offered a choice between, on the one hand, getting a horse if it is raining tomorrow and a cow if it is not raining and, on the other hand, a cow if it is raining and a horse if it is not. He prefers getting a horse to getting a cow; this is a ‘pure preference’. But which of the offered alternatives does he prefer? Assume that he professes to be indifferent as between them. How shall we then understand his attitude?

To this question there is an answer, first proposed by F. P. Ramsey, which has later come to play a great role in so-called Bayesian decision theory …

Ramsey thought that an attitude of indifference here means that the person rates the two events, ‘rain’ and ‘not rain’, as equally probable. Accepting this, one can then proceed as follows:

Assume that our farmer is next presented with this option: On the one hand a horse if it is raining and a sheep if it is not raining and, on the other hand, a cow if it is raining and a hog if it is not raining. Again he says he is indifferent. This, on Ramsey’s view, means that the value to him of a cow is as much less the value of the horse as the value of a sheep is less than that of a hog. With this the way is open to a metrization of value and the introduction of utility functions. This done, one can use attiyudes of indifference in other, more complex, conditional options for defining arbitrary degrees of (subjective) probability. The product of the value of a good an dthe probability of its materialization is called expected utility. Attitudes of preference in options aim at maximizing this quantity.

Ramsey’s method is elegant and ingenious. Nevertheless, it seems to rest on a mistake. It ignores the distinction between two senses of ‘indifference’.

The farmer who, when presented with the first of the above two options, professes an attitude of indifference can do so for one or two reasons. Either he ‘simply has no idea’ about the chances of rainfall for tomorrow and therefore cannot make up his mind about which alternative is more to his advantage.

This does not mean that he thinks rain and not-rain equally likely; he simply suspends judgement. Or, he considers them equally likely and therefore judges the two alternatives to be equally advantageous. He could, for example, support his attitude with the argument that if he repeatedly opted for one of the alternatives, no matter which one, on average half the number of times he would ‘probably’ get a horse, which is to his advantage, and half the number of times a cow, which is to his disadvantage. So, therefore, he is indifferent as between the alternatives. It is, in other words not his judgement of indifference which gives meaning to the probabilities for him; but it is his prior estimate of the probabilities which determines his attitude of indifference.

Georg Henrik von Wright

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4 Comments

  1. Most Bayesians I know would argue that rational people have transitive preferences.

    • Or is it that assumptions like completeness, transitivity, Independence of irrelevant alternative, define a meaning of “rationality” technically in a way that is at variance with other uses of rationality, e.g., in ordinary language and psychology?

      G. H. von Wright succeeded to the chair held by Wittgenstein at Cambridge and was an authority on LW’s later writing, some of which he edited. He was very kind when I was writing a dissertation on LW.

      Incidentally, Ramsey was also influential in the development of LW’s thinking, leading him to recognize issues in the Tractatus like specifying logical form, eventually resulting in the later work, for which he credited Sraffa also. People actually talked across disciplines in those days, at last at Cambridge.

      So it is not surprising to find von Wright calling out economists for appropriating commonly understood terminology like utility and rationality for special use, thereby creating ambiguity, often in the favor of an ideological position that may be questionable empirically if not untenable. At least von Mises was up front about his apriorism.

      As someone trained in analytical philosophy as Wittgenstein conceived of it, that is, as therapeutic — aimed at removing confusion resulting from misunderstanding of how language works, or worse, sophistry — it seems to me that a great deal of the controversy in economics could be rectified this way.

      When I look at now economists use assumptions and method, I am reminded more of speculative philosophy than the sciences. Of course, many heterodox economists, philosophers, and others in the sciences have done this already. It just hasn’t stuck owing to institutional factors concerning which conventional economists are in denial in elevating methodological individualism to a metaphysical first principle based on ontological individualism.

      • These issues go much broader than economics. The Bayesians I am thinking of are mostly aware of these sort of issues, but do not take them seriously. I am not clear why not, but many regard them as ‘beyond their pay grade’ or ‘good enough for politicians’. So I do not think that Lars’ quote would convince them.

        My view is that mathematics could also be used to ‘remove confusion’ but is more often used to obscure. However we do it, we should surely do better!

    • Pas moi. People’s choices are not always transitive. And choices are a natural operationalization of preferences. If human preferences are partially ordered, that would be consistent with the evidence. And it would provide a parsimonious explanation of that evidence.

      If all preferences are transitive, that does not fit the evidence. However, if we also assume that people with non-transitive choices are irrational, whatever that means, while people whose choices are transitive are rational, that also fits the evidence. But it seems kludgy to me. Why should transitivity be more rational than partial ordering?


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