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Journal of Applied Mathematics
Volume 2017 (2017), Article ID 8025616, 5 pages
https://doi.org/10.1155/2017/8025616
Research Article

Axioms for Consensus Functions on the -Cube

1Departamento de Ciencias Básicas, Universidad Autóma Metropolitana Unidad Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, C.P. 02200 Ciudad de México, Mexico
2Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
3Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
4Department of Mathematics, Harold Washington College, Chicago, IL 60601, USA

Correspondence should be addressed to F. R. McMorris

Received 30 June 2016; Accepted 6 December 2016; Published 9 January 2017

Academic Editor: Dimitris Fotakis

Copyright © 2017 C. Garcia-Martinez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A value of a sequence of elements of a finite metric space is an element for which is minimum. The –function with domain the set of all finite sequences on and defined by is a value of is called the –function on . The and functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the –functions on the -cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.