A DEFENSE OF IMPRECISE CREDENCES IN INFERENCE AND DECISION MAKING1

Abstract

Some Bayesians have suggested that beliefs based on ambiguous or incomplete evidence are best represented by families of probability functions. I spend the first half of this essay outlining one version of this imprecise model of belief , and spend the second half defending the model against recent objections, raised by Roger White and others, which concern the phenomenon of probabilistic dilation. Dilation occurs when learning some definite fact forces a person's beliefs about an event to shift from a sharp, pointvalued subjective probability to an imprecise spread of probabilities. Some commentators find dilation disturbing, both from an epistemic and a decisiontheoretic perspective, and place the blame on the use of sets of probabilities to model opinion. These reactions are based on an overly narrow conception of imprecise belief states which assumes that we know everything there is to know about a person's doxastic attitudes once we have identified the spreads of values for her imprecise credences. Once we recognize that the imprecise model has the resources to characterize a much richer family of doxastic attitudes than this, we will see that White's charges of epistemological and decision theoretic incoherence are unfounded. The Basic Ideas of Bayesian Epistemology Speaking broadly, the Bayesian approach to epistemology is based on four interconnected ideas: 1. Belief is not allornothing. Opinions come in varying gradations of strength which can range from full certainty of truth, through equal confidence in truth and falsehood, to complete certainty of falsehood. 2. Gradational beliefs are governed by the laws of probability, which codify minimum standards of inductive consistency (or " coherence ") to which rational opinions must conform.