Dutch books and money pumps (wonkish)

22 Dec, 2012 at 10:43 | Posted in Statistics & Econometrics | 4 Comments

Neoclassical economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules (preferably the ones axiomatized by Ramsey (1931), de Finetti (1937) or Savage (1954)) – that is, they maximize expected utility with respect to some subjective probability measure that is continually updated according to Bayes theorem. If not, they are supposed to be irrational, and ultimately – via some “Dutch book” or “money pump” argument – susceptible to being ruined by some clever “bookie”.
Bayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs, but – even granted this questionable reductionism – do rational agents really have to be Bayesian? As I have been arguing elsewhere (e. g. here and here) there is no strong warrant for believing so, but in this post I want to make a point on the informational requirement that the economic ilk of Bayesianism presupposes.

In many of the situations that are relevant to economics one could argue that there is simply not enough of adequate and relevant information to ground beliefs of a probabilistic kind, and that in those situations it is not really possible, in any relevant way, to represent an individual’s beliefs in a single probability measure.

Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10%. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.

That feels intuitively wrong though, and I guess most people would agree. Bayesianism cannot distinguish between symmetry-based probabilities from information and symmetry-based probabilities from an absence of information. In these kinds of situations most of us would rather say that it is simply irrational to be a Bayesian and better instead to admit that we “simply do not know” or that we feel ambiguous and undecided. Arbitrary an ungrounded probability claims are more irrational than being undecided in face of genuine uncertainty, so if there is not sufficient information to ground a probability distribution it is better to acknowledge that simpliciter, rather than pretending to possess a certitude that we simply do not possess.

I think this critique of Bayesianism is in accordance with the views of John Maynard Keynes’s A Treatise on Probability (1921) and General Theory (1937). According to Keynes we live in a world permeated by unmeasurable uncertainty – not quantifiable stochastic risk – which often forces us to make decisions based on anything but rational expectations. Sometimes we “simply do not know.” Keynes would not have accepted the view of Bayesian economists, according to whom expectations “tend to be distributed, for the same information set, about the prediction of the theory.” Keynes, rather, thinks that we base our expectations on the confidence or “weight” we put on different events and alternatives. To Keynes expectations are a question of weighing probabilities by “degrees of belief”, beliefs that have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents modeled by Bayesian economists.


  1. Entering the economic debate as a philosopher, what appears obvious to me is the erroneous presumption (hidden assumption) that this appraoch to rationality entails. The assumption that there is a representational (universal) rational agent further assumes that there is only one universe of discourse operative and that all share the same worldview (in Wittgenstein’s sense) that it describes and delimits through its norms. This worldview is a logical construct of “reality.”

    That is patently not the case as wide ideological disagreement shows. People, including economists who are supposedly “scientists,” disagree not only over norms but also what the facts may be, because “facts” don’t exist independently as “things” but rather are structured in terms of the manner of approach. Difference in worldview result in different ways of structuring facts in that the difference of worldviews are observable in terms of different rules and their application, for instance, criteria.

    Although I think this is the beginning of the matter, I don’t think that this is the end of the matter, in that there are a lot of other issues with “rationality,” too. But this is one that I seldom see even brought up, even though it should be obvious that economics can be viewed as a struggle among competing ideologies and the worldviews they entail. If this were not the case, then a “scientific” resolution would be possible and there would be a Kuhnian normal paradigm in economics. But that is not the case as far as I can see as an observer.

    Orthodox attempts to sustain the claim that it’s paradigm is normal and everything else is “heterodox,” but I don’t see that case being made successfully at all, especially when heterodox economists predicted the crisis and orthodox economists not only did not but claim that it is not possible, faling to add, in the “normal’ paradigm. That should call the “normal” paradigm into question, but they will not admit that. This is an indication of adherence to ideological norms over feedback for experience.

    • I can’t but agree, Tom. Neoclassical economics has been tremendously successful in usurping words like “rational” and “effective”, loaded them with very special meanings and relying on people not wanting to be considered as “irrational” or “inefifcient” thinking the economics-meaning of the terms are he same as the common sense meaning. Amartya Sen has done a tremendous job on this.

  2. Another criticism of the symmetry argument is this: In the absence of any information, Bayesianism argues that we should treat all possible outcomes as equally likely. This assumption corresponds to a uniform distribution across the possible outcomes. However, if I have no information at all, why should I believe the uniform distribution is appropriate. Surely, in the absence of any information, I should treat all possible *distributions* (not outcomes) as equally likely.

    Thus, I don’t see Bayesianism as being particularly a rational stance.

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