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The Benefits and Pitfalls of Using Imprecise Probabilities to Represent Uncertainty (talk recording available)
Dr,. James Joyce
Tuesday, November 10, 2009, 01:00pm - 02:00pm
University of Michigan, Department of Philosophy
In Bayesian Rationality (Oxford, 2007) M. Oaksford and N. Chater argue that rationality involves the ability to reason correctly about uncertainty, and that " cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems." (BBS 2009, p. 69) While I agree with the first point, and would like the second to be true, both ideas leave open the question of how probabilistic judgments and reasoning should be modeled. One issue, in particular, concerns whether to model beliefs, inferences, and information processing using "sharp" probabilities, thereby portraying agents as having a single subjective probability function, or whether to employ "imprecise" probabilistic models that use structured sets of probability functions to represent uncertainty? Many philosophers have championed imprecise probabilities as the right response to incomplete or ambiguous evidence, and some psychologists (e.g., N. Pfeifer and G. D. Kleiter) have suggested that imprecise models might serve better than sharp probabilities as "normative reference systems" that can be used to explain human cognition. I will sympathetically assess the normative prospects for one version of the theory of imprecise probabilities, arguing that it does a better job than "sharp" theories do at reflecting incomplete or ambiguous evidence. Moreover, since the imprecise view has the capacity to express far more types of attitudes and judgments than can be encoded in sharp probabilities, it allows us more freedom in representing mental states. This is both a benefit and a pitfall. Imprecise probabilities offer us more nuanced ways of representing beliefs, but also more nuanced ways of misrepresenting them. I will discuss cases of each type and draw some tentative morals.