By Irving John Good
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Extra resources for Good Thinking: The Foundations of Probability and Its Applications
To attempt to use a method other than the minimax method would lead to too large a probability of a large loss, especially in a game like poker. ) I am much indebted to the referee for his critical comments. CHAPTER 2 Twenty-seven Principles of Rationality (#679) In the body of my paper for this symposium I originally decided not to argue the case for the use of subjective probability since I have expressed my philosophy of probability, statistics, and (generally) rationality on so many occasions in the past.
Intuitive probability, (a) Subjective probabilities regarded as primary; (b) credibilities (logical probabilities) primary; (c) regarding it as mentally healthy to think of subjective probabilities as estimates of credibilities, without being sure that credibilities really exist; (d) credibilities in principle definable by an international body. . 9. Device of imaginary results, (a) Explicit use; (b) not. The device involves imaginary experimental results used for judging final or posterior probabilities from which are inferred discernments about the initial probabilities.
Another class of justifications, in which utilities are not mentioned, is exemplified by Bernstein (1921/22), Koopman (1940a, b), and R. T. Cox (1946, 1961). (See also pp. ) A less convincing, but simpler justification is that the product and addition axioms are forced (up to a monotonic transformation of probabilities) when considering ideal games of chance, and it would be surprising if the same axioms did not apply more generally. Even to deny this seems to me to show poor or biased judgment.
Good Thinking: The Foundations of Probability and Its Applications by Irving John Good