| Let D be the set of all (finite) discrete structures
of a particular type. (e.g., D could be a set of specialized
labeled graphs, unlabeled graphs, digraphs, partially ordered sets, acyclic
digraphs, hypergraphs, partitions, networks, etc.) For this talk
a consensus function on D is a map C:Dk ->
D. A major aspect of the consensus problem for D
is to find ``good" consensus functions that can capture the common agreement
of an input profile P=(D1,...Dk) of
members of D, i.e. C(P) should consist of the element
of D that best represents whatever similarity that all of the
Di's have amongst themselves. If possible, a good
function C should not only have this consensus aspect, but additionally
should satisfy mathematical properties that enable it to be understood
so that it can be effectively computed exactly or with approximating algorithms.
This talk will focus on the case where D is the set of all hypergraphs
that are structured into hierarchical classifications of a set S
of
objects. We are concerned with stable consensus functions in the
sense that if the profiles P and P' agree on a subset
X
of S, then so should C(P) and C(P'). Several versions
of this concept are given, each one being a generalization of the classical
independence
of irrelevant alternatives axiom of Arrow for weak orders.
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