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Five axioms for location functions on median graphs

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  • McMorris, F.R.
  • Mulder, H.M.
  • Novick, B.
  • Powers, R.C.

Abstract

__Abstract__ In previous work, two axiomatic characterizations were given for the median function on median graphs: one involving the three simple and natural axioms anonymity, betweenness and consistency; the other involving faithfulness, consistency and ½-Condorcet. To date, the independence of these axioms has not been a serious point of study. The aim of this paper is to provide the missing answers. The independent subsets of these five axioms are determined precisely and examples provided in each case on arbitrary median graphs. There are three cases that stand out. Here non-trivial examples and proofs are needed to give a full answer. Extensive use of the structure of median graphs is used throughout.

Suggested Citation

  • McMorris, F.R. & Mulder, H.M. & Novick, B. & Powers, R.C., 2014. "Five axioms for location functions on median graphs," Econometric Institute Research Papers EI 2014-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:51344
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    References listed on IDEAS

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    1. McMorris, F.R. & Novick, B. & Mulder, H.M. & Powers, R.C., 2015. "An ABC-Problem for Location and Consensus Functions on Graphs," Econometric Institute Research Papers EI 2015-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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