Generalizing The Conjunction Rule for Aggregating Conflicting Expert Opinions

In multiagent expert systems, the conjunction rule is commonly used to combine expert information represented by imprecise probabilities. However, it is well known that this rule cannot be applied in the case of expert conflict. In this article, we propose to resolve expert conflict by means of a second-order imprecise probability model. The essential idea underlying the model is a notion of behavioral trust. We construct a simple linear programming algorithm for calculating the aggregate. This algorithm explains the proposed aggregation method as a generalized conjunction rule. It also provides an elegant operational interpretation of the imprecise second-order assessments, and thus overcomes the problems of interpretation that are so common in hierarchical uncertainty models

Imprecise Chance and the Best System Analysis

Much recent philosophical attention has been devoted to the prospects of the Best System Analysis (BSA) of chance for yielding high-level chances, including statistical mechanical and special science chances. But a foundational worry about the BSA lurks: there don’t appear to be uniquely correct measures of the degree to which a system exhibits theoretical virtues, such as simplicity, strength, and fit. Nor does there appear to be a uniquely correct exchange rate at which the theoretical virtues trade off against one another in the determination of an overall best system. I argue that there’s no robustly best system for our world – no system that comes out best under every reasonable measure of the theoretical virtues and exchange rate between them – but rather a set of ‘tied-for-best’ systems: a set of very good systems, none of which is robustly best. Among the tied-for-best systems are systems that entail differing high-level probabilities. I argue that the advocate of the BSA should conclude that the high-level chances for our world are imprecise