25 research outputs found
Graph homomorphisms and components of quotient graphs
We study how the number of components of a graph can be expressed
through the number and properties of the components of a quotient graph
We partially rely on classic qualifications of graph homomorphisms
such as locally constrained homomorphisms and on the concept of equitable
partition and orbit partition. We introduce the new definitions of
pseudo-covering homomorphism and of component equitable partition, exhibiting
interesting inclusions among the various classes of considered homomorphisms.
As a consequence, we find a procedure for computing when the projection
on the quotient is pseudo-covering. That procedure becomes
particularly easy to handle when the partition corresponding to is an
orbit partition.Comment: arXiv admin note: text overlap with arXiv:1502.0296
Resolute refinements of social choice correspondences
Many classical social choice correspondences are resolute only in the case of
two alternatives and an odd number of individuals. Thus, in most cases, they
admit several resolute refinements, each of them naturally interpreted as a
tie-breaking rule, satisfying different properties. In this paper we look for
classes of social choice correspondences which admit resolute refinements
fulfilling suitable versions of anonymity and neutrality. In particular,
supposing that individuals and alternatives have been exogenously partitioned
into subcommittees and subclasses, we find out arithmetical conditions on the
sizes of subcommittees and subclasses that are necessary and sufficient for
making any social choice correspondence which is efficient, anonymous with
respect to subcommittees, neutral with respect to subclasses and possibly
immune to the reversal bias admit a resolute refinement sharing the same
properties.Comment: arXiv admin note: text overlap with arXiv:1503.0402