Review of Misak: beliefs are metaphorical bets

Thus far, I have presented Ramsey’s 1922 critique of Keynes’s objective theory of probability and recounted some memorable episodes from Ramsey’s personal life. I now want to move into the third and last part of Cheryl Misak’s beautiful biography of Frank Ramsey (“An Astonishing Half Decade”). During the last half decade of his short life, Ramsey made major contributions to a wide variety of fields, including economics, mathematics, and philosophy, but I shall focus here on his contributions to probability theory.

It was during this time that Ramsey developed his own full-fledged theory of “subjective” or psychological probability. He first painted a sketch of his approach to chance in a paper titled “Truth and Probability”, which he first presented at a meeting of the Moral Sciences Club in November of 1926. (See Misak, 2020, p. 263. Ramsey’s influential 1926 paper was eventually published posthumously in 1931.) We can summarize Ramsey’s revolutionary theory of probability in ten words: probabilities are beliefs and beliefs, in turn, are metaphorical bets, or in Ramsey’s words (quoted in Misak, p. 268), “Whenever we go to the station we are betting that a train will really run, and if we had not a sufficient degree of belief in this [outcome] we should decline this bet and stay at home.” (The image pictured below also provides a simple visualization of Ramsey’s approach.)

On this subjective view of probability, we can measure the strength of a person’s personal beliefs in betting terms, or again in Ramsey’s own words (p. 271), a “probability of 1/3 is clearly related to the kind of belief [that] would lead to a bet of 2 to 1.” In addition, Ramsey showed how one’s bets–i.e. one’s subjective or personal probabilities–should obey the formal axioms of probability theory. (As as aside, Misak includes a summary by Nils-Eric Sahlin of the technical details of Ramsey’s subjective or betting approach to probability. See Misak, pp. 272-273. See also this excellent entry in the Stanford Encyclopedia of Stanford.) It is hard to understate the importance of Ramsey’s subjective theory of probability. I will therefore discuss the deeper significance of Ramsey’s betting paradigm in my next post …

Image result for beliefs are bets

Source: Annie Duke, Thinking in Bets (2018)

About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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