How to Expand Your Beliefs in an Uncertain World: A Probabilistic Model

In Gabriele Kern-Isberner, Thomas Lukasiewicz & Emil Weydert (eds.), Ki-2001 Workshop: Uncertainty in Artificial Intellligence. Informatik-Berichte (8/2001) (2001)
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Abstract

Suppose that we acquire various items of information from various sources and that our degree of confidence in the content of the information set is sufficiently high to believe the information. Now a new item of information is being presented by a new information source. Are we justified to add this new item of information to what we already believe? Consider the following parable: “I go to a lecture about wildlife in Greenland which was supposed to be delivered by an expert in the field. When I arrive I notice that the expert has excused himself and that the biology department has sent a newcomer to fill in for him. I have no beliefs about wildlife in Greenland, but I do have some beliefs about Greenland’s climate and about the kinds of climate conditions that various types of wildlife favor. Suppose that our newcomer proclaims that large colonies of elk roam in a particular valley on the southern tip of Greenland. Then I would certainly be willing to accept this item of information. But suppose that he proclaims that large colonies of armadillos roam in the same valley. Then I would not be willing to accept this item of information. Why do I accept the former but not the latter item of information? Let us suppose that neither item of information is logically inconsistent with what I already believe. Clearly, the former item of information is not inconsistent. But also the latter item is not: after all, there may be small pockets of Greenland with special climatological conditions and some Texan sailors may have set loose a pair of armadillos as a practical joke. But whereas the former item of information is quite plausible given my previous beliefs, the latter item of information is not. And this is what makes for the difference. Now suppose that our newcomer proclaims that large colonies of wild boars roam this valley in Greenland. I am not that sure anymore. Given everything I believe, I find wild boars in Greenland more plausible than armadillos in Greenland, but certainly less plausible than elk in Greenland. Had our expert presented the lecture and provided precisely the 2 same information, then I would have been willing to adopt the belief that there are wild boars in Greenland, but, with our newcomer delivering the lecture, I am not willing to do so. It is not that I would believe anything out of the expert’s mouth: also he could not have convinced me that there are armadillos in Greenland. But when it comes to wild boars, the difference between the expert’s and the newcomer’s credentials simply makes for the difference.” What we learn from this story is that the question of belief expansion has something to do with the reliability of the information source as well as with the plausibility of the new information, given what I already believe. The more reliable the information source is, the less plausible the new information needs to be given what I already believe, for me to be justified to add the belief to our belief set. The more plausible the new information is given what I already believe, the less reliable the information source needs to be given what I already believe, for me to be justified to add the belief to my belief set. The challenge is: can a precise account of this relationship be provided?

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Author Profiles

Stephan Hartmann
Ludwig Maximilians Universität, München
Luc Bovens
University of North Carolina, Chapel Hill

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