Bayesianism — a patently absurd approach to science

16 Mar, 2021 at 16:12 | Posted in Theory of Science & Methodology | 17 Comments

Mainstream economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules (preferably the ones axiomatised by Ramsey (1931), de Finetti (1937) or Savage (1954)) — that is, they maximise 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? However, there are no strong warrants for believing so.

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 the US 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 become unemployed and 90% to become 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.

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.’ There are no strong reasons why we should accept the Bayesian view of modern mainstream economists, according to whom expectations “tend to be distributed, for the same information set, about the prediction of the theory.” As argued by Keynes, we rather base our expectations on the confidence or “weight” we put on different events and alternatives. Expectations are a question of weighing probabilities by ‘degrees of belief,’ beliefs that standardly have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents modelled by mainstream economists.

Back in 1991, when yours truly earned his first PhD with a dissertation on decision making and rationality in social choice theory and game theory, I concluded that “repeatedly it seems as though mathematical tractability and elegance — rather than realism and relevance — have been the most applied guidelines for the behavioural assumptions being made. On a political and social level, it is doubtful if the methodological individualism, ahistoricity and formalism they are advocating are especially valid.”

This, of course, was like swearing in church. My mainstream colleagues were — to say the least — not exactly überjoyed.

One of my inspirations when working on that dissertation was Henry Kyburg, and I still think his critique is the ultimate take-down of Bayesian hubris:

From the point of view of the “logic of consistency”, no set of beliefs is more rational than any other, so long as they both satisfy the quantitative relationships expressed by the fundamental laws of probability. Thus I am free to assign the number 1/3 to the probability that the sun will rise tomorrow; or, more cheerfully, to take the probability to be 9/10 that I have a rich uncle in Australia who will send me a telegram tomorrow informing me that he has made me his sole heir. Neither Ramsey, nor Savage, nor de Finetti, to name three leading figures in the personalistic movement, can find it in his heart to detect any logical shortcomings in anyone, or to find anyone logically culpable, whose degrees of belief in various propositions satisfy the laws of the probability calculus, however odd those degrees of belief may otherwise be …

Now this seems patently absurd. It is to suppose that even the most simple statistical inferences have no logical weight where my beliefs are concerned. It is perfectly compatible with these laws that I should have a degree of belief equal to 1/4 that this coin will land heads when next I toss it; and that I should then perform a long series of tosses (say, 1000), of which 3/4 should result in heads; and then that on the 1001st toss, my belief in heads should be unchanged at 1/4 …

Henry E. Kyburg