Wednesday, February 4, 2026

The good Bayesian lost at sea

 Humankind was slow to discover mathematical probability. The delay was

so striking that Hacking (1975) called it a “scandal of philosophy”

dating its emergence to 1654, when Blaise Pascal and Pierre Fermat exchanged

letters on gambling problems. Psychologists were equally slow. Since the

19th century, significant figures such as Wilhelm Wundt had debated the

relationship  between  intuition  and  logic,  but  overlooked  probability.  It

was not until the 1950s and 60s that psychologists began studying statis-

tical intuitions.

The first systematic investigation was conducted by Swiss psycholo-

gists Jean Piaget and Bärbel Inhelder in

The Origin of the Idea of Chance in  Children

 They  presented  children  of  various  ages  with

random devices and concluded that by age 12, children’s intuitions begin

to  align  with  the  laws  of  probability.  For  instance,  children  understand

the law of large numbers and, by age eight, the conjunction rule (Inhelder

and Piaget 1964). Around the same time, Egon Brunswik (1955) at the Uni-

versity of California, Berkeley, envisioned the perceptual system as an in-

tuitive statistician, one that calculates correlations and multiple regres-sions.

At the University of Michigan, Ward Edwards (1962, 1968), often re-

ferred to as the founder of behavioral decision theory, compared people’s

judgments  with  Bayes’  rule  and  found  that  people are  generally  good

Bayesians

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