  A general method is given for revising degrees of belief and arriving at
consistent decisions about a system of logically constrained issues. In
contrast to other works about belief revision, here the constraints are assumed
to be fixed. The method has two variants, dual of each other, whose revised
degrees of belief are respectively above and below the original ones. The upper
[resp. lower] revised degrees of belief are uniquely characterized as the
lowest [resp. highest] ones that are invariant by a certain max-min [resp.
min-max] operation determined by the logical constraints. In both variants,
making balance between the revised degree of belief of a proposition and that
of its negation leads to decisions that are ensured to be consistent with the
logical constraints. These decisions are ensured to agree with the majority
criterion as applied to the original degrees of belief whenever this gives a
consistent result. They are also also ensured to satisfy a property of respect
for unanimity about any particular issue, as well as a property of monotonicity
with respect to the original degrees of belief. The application of the method
to certain special domains comes down to well established or increasingly
accepted methods, such as the single-link method of cluster analysis and the
method of paths in preferential voting.
