Axioms for Consensus Functions on the n‐Cube

C. Garcia-Martinez, F. R. McMorris, O. Ortega and R. C. Powers

Journal of Applied Mathematics, 2017, vol. 2017, issue 1

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.

Date: 2017
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https://doi.org/10.1155/2017/8025616

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2017:y:2017:i:1:n:8025616

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