Information gain and approaching true belief

QS 2012
Recent years has seen a renewed interest in the philosophical study of information. In this paper a two-part analysis of information gain – objective and subjective – in the context of doxastic change is presented and discussed. Objective information gain is analyzed in terms of doxastic movement towards true belief, while subjective information gain is analyzed as an agent’s expectation value of her objective information gain for a given doxastic change. The resulting expression for subjective information gain turns out to be a familiar one with well-known formal properties: the Kullback-Leibler divergence. The suggested measure of subjective information gain is then compared with the view that information gain equals uncertainty reduction. Three counterexamples to the latter view are suggested and it is also argued that the numerical results given by the suggested measure of subjective information gain in those three cases are considerably more intuitive.

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