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Axioms for Consensus Functions on the n‐Cube

Author

Listed:
  • C. Garcia-Martinez
  • F. R. McMorris
  • O. Ortega
  • R. C. Powers

Abstract

A p value of a sequence π = (x1, x2, …, xk) of elements of a finite metric space (X, d) is an element x for which ∑i=1kdp(x,xi) is minimum. The lp–function with domain the set of all finite sequences on X and defined by lp(π)={x: x is a p value of π} is called the lp–function on (X, d). The l1 and l2 functions are the well‐studied median and mean functions, respectively. In this note, simple characterizations of the lp–functions on the n‐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.

Suggested Citation

  • C. Garcia-Martinez & F. R. McMorris & O. Ortega & R. C. Powers, 2017. "Axioms for Consensus Functions on the n‐Cube," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnljam:v:2017:y:2017:i:1:n:8025616
    DOI: 10.1155/2017/8025616
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    References listed on IDEAS

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