Group Knowledge and Probability

Eleonora Cresto (Buenos Aires) gives a talk at the MCMP Colloquium (7 November, 2013) titled "Group Knowledge and Probability". Abstract: The talk addresses the concept of group knowledge and its role in probability aggregation. I start by acknowledging that we often feel compelled to credit group agents with epistemic attitudes that are not held by any of their members. Nonetheless, I argue that ideally responsible agents also �find a deflationary pressure to ground such attitudes in concrete individuals, for purely conceptual reasons - out of coherence. As a result of this, epistemically responsible groups are conceived of as dynamic entities; correspondingly, group knowledge gets defined in terms of a family of possible paths between distributed knowledge and common knowledge. Public Announcement logics can then be endowed with new tasks and goals - among them, the task of monitoring the satisfaction of normative requirements by epistemically responsible agents. Next, I argue that this conception of group knowledge provides a principled way to deal with group probabilities. I begin by considering sets of individual measures conditional on common and distributed knowledge, respectively. The proposal is further refined with the addition of a geometric pooling method on the conditional measures. The resulting aggregation procedure is shown to be in partial agreement with some proposals found in the recent literature. I contend, however, that a full-fledged understanding of group probabilities should focus on the distance between the two aggregated sets, and in the possible strategies to reduce it.