Subjective probability does not exist

from Asad Zaman

The title is an inversion of De-Finetti’s famous statement that “Probability does not exist” with which he opens his famous treatise on Probability. My paper, discussed below, shows that the arguments used to establish the existence of subjective probabilities, offered as a substitute for frequentist probabilities, are flawed.

The existence of subjective probability is established via arguments based on coherent choice over lotteries. Such arguments were made by Ramsey, De-Finetti, Savage and others, and rely on variants of the Dutch-Book, which show that incoherent choices are irrational – they lead to certain loss of money. So every rational person must make coherent choices over a certain set of especially constructed lotteries. Then the subjectivist argument shows that every coherent set of choices corresponds to a subjective probability on part of the decision maker. Thus we conclude that rational decision makers must have subjective probabilities. This paper shows that coherent choice over lotteries leads to weaker conclusion than the one desired by subjectivists. If a person is forced to make coherent choices for the sake of consistency in certain specially designed environment, that does not “reveal” his beliefs. The decision may arbitrarily chose a “belief”, which he may later renounce. To put this in very simple terms, suppose you are offered a choice between exotic fruits Ackee and Rambutan, neither of which you have tasted. Then the choice you make will not “reveal” your preference. But preferences are needed to ensure stability of this choice, which allows us to carry it over into other decision making environments.  read more