![]() Most often, the resulting credence is a weighted average of the individual expert opinions. The literature on probabilistic opinion pooling is replete with proposals for determining rational credences in such situations (see, e.g., Genest and Zidek 1986, Dietrich and List 2017). Note that cases in which an agent receives reports from multiple experts of differing competence are quite common. Indeed, to maintain otherwise-i.e., to maintain that one’s degree of belief in rain in Abergwyngregyn ought to be influenced at least as much by one’s prior degree of belief that Fred’s fibrosarcoma will recur as by the chance of rain in Abergwyngregyn-would clearly violate normal informal standards of what is reasonable. In the context of CBCP and Bayesian Conditionalisation, the Principal Principle implies that at time t, if one’s evidence includes the proposition that the current chance of A is x then one should believe A to degree x, as long as one’s other evidence E does not include anything that defeats this ascription of rational belief. P( A| X E) = x, where X says that the chance at time t of proposition A is x and E is any proposition that is compatible with X and admissible at time t. The Principal Principle, put forward by Lewis ( 1986), uses chances to constrain prior probabilities: Principal Principle. ![]() (The dynamic principle is usually known as Bayesian Conditionalisation.) The key question for the Bayesian is: what constraints must the prior function P satisfy? Changes to her degrees of belief can then be determined by reapplying CBCP to changes in evidence: e.g., on learning new evidence F, B E F( A) = P( A| E F). When the agent’s evidence consists just of E, B E( A) = P( A| E) is taken as expressing her current degree of belief in A. ![]() The dynamics of belief are captured as follows. Note that CBCP is a static principle: it governs conditional degrees of belief in the prior probability function, not changes to degree of belief. The agent’s unique probability function P is sometimes called her prior probability function. One key commitment of standard subjective Bayesianism is the claim that rationality requires that these conditional degrees of belief are conditional probabilities: CBCP.Ī rational belief function B is a conditional probability function, i.e., there is some probability function P such that for all A and E, B E( A) = P( A| E). Let the belief function B specify the degrees of belief of a particular agent: B E( A) is the degree to which she believes A, supposing only E, for all propositions A and E.
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