Page "Subjectivism" Paragraph 10

Many modern machine learning methods are based on objectivist Bayesian principles.

According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic.

In attempting to justify subjective probability, Bruno de Finetti created the notion of philosophical coherence.

According to his theory, a probability assertion is akin to a bet, and a bet is coherent only if it does not expose the wagerer to loss if their opponent chooses wisely.

To explain his meaning, de Finetti created a thought-experiment to illustrate the need for principles of coherency in making a probabilistic statement.

In his scenario, when someone states their degree-of-belief in something, one places a small bet for or against that belief and specifies the odds, with the understanding that the other party to the bet may then decide which side of the bet to take.

Thus, if Bob specifies 3-to-1 odds against a proposition A, his opponent Joe may then choose whether to require Bob to risk $ 1 in order to win $ 3 if proposition A is found to be true, or to require Bob to risk $ 3 in order to win $ 1 if the proposition A is not true.

In this case, it is possible for Joe to win over Bob.

According to de Finetti, then, this case is incoherent.