Article: Representing and Aggregating Conflicting Beliefs

JAIR is pleased to announce the publication of the following article:

Maynard-Zhang, P. and Lehmann, D. (2003)
  "Representing and Aggregating Conflicting Beliefs", 
   Volume 19, pages 155-203.

   For quick access via your WWW browser, use this URL:
     http://www.jair.org/abstracts/maynard03a.html

Abstract:
We consider the two-fold problem of representing collective beliefs
and aggregating these beliefs. We propose a novel representation for
collective beliefs that uses modular, transitive relations over
possible worlds. They allow us to represent conflicting opinions and
they have a clear semantics, thus improving upon the quasi-transitive
relations often used in social choice. We then describe a way to
construct the belief state of an agent informed by a set of sources of
varying degrees of reliability. This construction circumvents Arrow's
Impossibility Theorem in a satisfactory manner by accounting for the
explicitly encoded conflicts. We give a simple set-theory-based
operator for combining the information of multiple agents. We show
that this operator satisfies the desirable invariants of idempotence,
commutativity, and associativity, and, thus, is well-behaved when
iterated, and we describe a computationally effective way of computing
the resulting belief state. Finally, we extend our framework to
incorporate voting. 

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-- 
Steven Minton
JAIR Managing Editor