Generalized target functions on trees

F. R. McMorris; H. M. Mulder; R. C. Powers

doi:10.47443/dml.2021.s106

Author(s)

F. R. McMorris Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, USA; Department of Mathematics, University of Louisville, Louisville, KY, USA

H. M. Mulder Econometrisch Instituut, Erasmus Universiteit, Rotterdam, Netherlands

R. C. Powers Department of Mathematics, University of Louisville, Louisville, KY, USA

Abstract

A location function on a finite connected graph G takes as input any k-tuple of vertices (a profile) and outputs a single vertex. If G is a fully-gated graph, then a target location function is defined by a predetermined vertex (the target) and outputs the unique vertex belonging to the convex closure of the profile which is closest to the target. If G is a tree, which is such a fully-gated graph, then any target function on G satisfies two conditions known in the literature as Weak Pareto Efficiency and Replacement Domination. In the continuous case, where edges can be seen as segments with interior points, these two conditions fully characterize the target functions. In previous work we proved that these two conditions do not suffice to characterize the target functions on finite trees, and that a third condition is needed. In this note we study the location functions on finite trees that are characterized by precisely these two conditions.

Publication Details

Page(s) 47-53

DOI 10.47443/dml.2021.s106

Published Journal: Discrete Mathematics Letters, Volume: 6, Issue: 0, Year: 2021

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Keywords

generalized target functions, Weak Pareto Efficiency, Replacement Domination, trees, axioms

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