, Volume 118, Issue 3, pp 329–361

Minimal Belief Change and the Pareto Principle

  • Oliver Schulte

DOI: 10.1023/A:1005162303126

Cite this article as:
Schulte, O. Synthese (1999) 118: 329. doi:10.1023/A:1005162303126


This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the standard AGM postulates. The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. The Ramsey test is a well-known way of establishing connections between belief revision postulates and axioms for conditionals (“if p, then q”). Pareto-minimal theory change corresponds exactly to three characteristic axioms of counterfactual systems: a theory revision operator that satisfies the Ramsey test validates these axioms if and only if the revision operator is Pareto-minimal.

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Oliver Schulte
    • 1
  1. 1.Department of PhilosophyUniversity of AlbertaEdmontonCanada