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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; ude.tii@sirromcm

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.

Linked References

  1. R. Holzman, “An axiomatic approach to location on networks,” Mathematics of Operations Research, vol. 15, no. 3, pp. 553–563, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Hansen and F. S. Roberts, “An impossibility result in axiomatic location theory,” Mathematics of Operations Research, vol. 21, no. 1, pp. 195–208, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. F. R. McMorris, H. M. Mulder, and R. V. Vohra, “Axiomatic characterization of location functions,” in Advances in Interdisciplinary Applied Discrete Mathematics, H. Kaul and H. M. Mulder, Eds., pp. 71–91, World Scientific, Singapore, 2011. View at Google Scholar
  4. P. B. Mirchandani and R. L. Francis, Eds., Discrete Location Theory, John Wiley & Sons, New York, NY, USA, 1990.
  5. W. H. E. Day and F. R. McMorris, Axiomatic consensus theory in group choice and biomathematics, vol. 29 of Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. J. Brams, D. M. Kilgour, and M. R. Sanver, “A minimax procedure for electing committees,” Public Choice, vol. 132, no. 3, pp. 401–420, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. D. M. Kilgour, S. J. Brams, and M. R. Sanver, “How to elect a representative committee using approval balloting,” in Mathematics and Democracy, B. Simeone and F. Pukelsheim, Eds., pp. 83–95, Springer, Berlin, Germany, 2006. View at Google Scholar
  8. O. Ortega and G. Kriston, “The median function on trees,” Discrete Mathematics, Algorithms and Applications, vol. 5, no. 4, Article ID 1350033, 14 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. F. R. McMorris, H. M. Mulder, and O. Ortega, “The p-function on trees,” Networks, vol. 60, no. 2, pp. 94–102, 2012. View at Google Scholar · View at MathSciNet
  10. H. M. Mulder and B. Novick, “An axiomatization of the median procedure on the n-cube,” Discrete Applied Mathematics, vol. 159, no. 9, pp. 939–944, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H. M. Mulder and B. Novick, “A tight axiomatization of the median procedure on median graphs,” Discrete Applied Mathematics, vol. 161, no. 6, pp. 838–846, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. F. R. McMorris, F. S. Roberts, and C. Wang, “The center function on trees,” Networks, vol. 38, no. 2, pp. 84–87, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. F. R. McMorris, H. M. Mulder, and O. Ortega, “Axiomatic characterization of the mean function on trees,” Discrete Mathematics, Algorithms and Applications, vol. 2, no. 3, pp. 313–329, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. M. Mulder, M. J. Pelsmajer, and K. B. Reid, “Axiomization of the center function on trees,” The Australasian Journal of Combinatorics, vol. 41, pp. 223–226, 2008. View at Google Scholar · View at MathSciNet
  15. A. Kezdy and R. C. Powers, The Center Function on Boolean Algebras, Department of Mathematics, University of Louisville, 2001.
  16. O. Ortega and C. Garcia-Martinez, “The median function on Boolean lattices,” Discrete Mathematics, Algorithms and Applications, vol. 6, no. 4, Article ID 1450056, 21 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. O. Ortega, C. Garcia-Martinez, and K. Adamski, “The p function on finite Boolean lattices,” Discrete Mathematics, Algorithms and Applications, vol. 8, Article ID 1650044, 15 pages, 2016. View at Google Scholar
  18. F. R. McMorris, H. M. Mulder, and F. S. Roberts, “The median procedure on median graphs,” Discrete Applied Mathematics, vol. 84, no. 1–3, pp. 165–181, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  19. K. Balakrishnan, M. Changat, H. M. Mulder, and A. R. Subhamathi, “Axiomatic characterization of the antimedian function on paths and hypercubes,” Discrete Mathematics, Algorithms and Applications, vol. 4, no. 4, 1250054, 20 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet