Home > The Economics Profession > Dutch books and money pumps (wonkish)

Dutch books and money pumps (wonkish)

from Lars Syll

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.

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  1. merijnknibbe
    December 26, 2012 at 2:46 pm | #1

    ´Dutch books´ are exactly what happened when people started to trust their money to hedge funds.

  2. Bruce E. Woych
    December 27, 2012 at 12:58 am | #2

    In real life (living…) this accurately describes the distinction between two corruptions; One linear and one circullar>>>
    …or placed in W.C. Field’s framework…the economy of “never give a sucker an even break.”

  3. Bruce E. Woych
    December 27, 2012 at 1:30 am | #3

    The prospect creates a mutually exclusive set of competitive contradictions; and rationalizes the outcome in “subject measures” that exclude the means justifying the ends and are entirely teleological frames…legitimating survival and justifying predatory success;…

    Placed still another way we might inquire as to whether “probability” can be measured lineally for any length of time without distortion (complexity) warping the grid being measured. What are the odds…if I didn’t do it someone else would have anyway…(probability as inevitability is a shadow line of inferences…).

    Can any “solution” to a problem go on over time in economics without opportunism taking over: incalculable chances for exploitation in every innovated direction but most easily corruption.

    Upper Class People More Likely to Behave Unethically
    Mar. 7, 2012 — A series of studies conducted by psychologists at the University of California, Berkeley and the University of Toronto in Canada reveal something the well off may not want to hear. Individuals who are relatively high in social class are more likely to engage in a variety of unethical behaviors. .

    “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.” from Lars Syll…(above)

    Well Bernie Madoff proves this conclusively; but when the roles are reversed and class institutions get ripped off…the rules are suddenly evoked.

    Institutional markets mislead and essentially do the same thing daily but with less obvious impact to people in power, and at scale rip offs that are just “business as usual” expectations (aka: blind probability) or asymmetrical information and knowledge.

  4. Bruce E. Woych
    December 27, 2012 at 1:55 am | #4

    An appeal to probability, also known as an appeal to possibility, is a logical fallacy in which it is assumed that because something could happen it inevitably will happen

    Interesting discussion of dualities & contradictions:

    As with “determinism” …probability becomes readily subject to abuse in “outcome based” worlds of competitive exclusion and public welfare…routinely so in real daily life when it selectively focuses upon private interest and agenda setting justifications.

    Academic pronounced Probability…is also (admit it or not…) subject to the worst kind of manipulation and abuse. As with markets, probability requires perfect information to be a working tool for discovery and foundations.

  5. Dave Raithel
    December 27, 2012 at 1:59 am | #5

    The dupe in the thought experiment has the wrong question. The right question is “Should I stay or should I go?” Near as the dupe knows he’s as likely to be without work as with work should he stay where he knows nothing much. Supposing he prefers work to not work, he goes back to Sweden – or to there if he’s from a third place not mentioned.

    My complaint is simply this: Not knowing rarely relieves us of the burden of choosing.

  6. Bruce E. Woych
    December 27, 2012 at 4:17 pm | #6

    “…this book makes an important contribution to understanding the infrastructure development process worldwide,…”
    “According to authors, the reason is that many of the participants in the process have incentives to underestimate costs, overestimate revenues, undervalue environmental impact, and overvalue economic development effects.[4] The central problems are lack of accountability and inappropriate risk sharing which can be improved by reforming the institutional arrangements of decision making and to institute accountability at the project development and evaluation stages.”

    Megaprojects and Risk: An Anatomy of Ambition [Paperback]
    Bent Flyvbjerg (Author), Nils Bruzelius (Author), Werner Rothengatter (Author)

  7. Bruce E. Woych
    December 27, 2012 at 4:22 pm | #7

    Probability and Finance: It’s Only a Game! [Hardcover]
    Glenn Shafer (Author), Vladimir Vovk (Author)

    • December 27, 2012 at 11:19 pm | #8

      Perhaps,maybe “probability” is misunderstood ?
      In reality a true projection of the “probability” of any future price or direction is subject to basic physical rules.
      The future will be either higher, lower, or the same.
      E.G., The stock market will be either higher, lower or the same.
      (You gotta love this one) A coin toss must land either on its head side, tail side, OR on its side.
      BUT what is the probability of that “side” landing?
      and would it be called a “black swan” event?
      Justaluckyfool (GOOGLE Account). “Anyone that attempts to predict future price is a fool.
      If by chance correctly then just a lucky fool, albeit still a fool.

  8. Bruce E. Woych

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