McMorris, F. R.; Mulder, Henry Martyn; Ortega, Oscar Axiomatic characterization of the mean function on trees. (English) Zbl 1226.05087 Discrete Math. Algorithms Appl. 2, No. 3, 313-329 (2010). Summary: A mean of a sequence \(\pi= (x_1, x_2,\dots, x_k)\) of elements of a finite metric space \((X, d)\) is an element \(x\) for which \(\sum _{i=1}^k d^2(x,x_i)\) is minimum. The function Mean whose domain is the set of all finite sequences on \(X\) and is defined by \(\text{\textit{Mean}}(\pi ) = \{x | x\) is a mean of \(\pi\}\) is called the mean function on \(X\). In this note, the mean function on finite trees is characterized axiomatically. Cited in 14 Documents MSC: 05C05 Trees 05C90 Applications of graph theory 91B14 Social choice 91B72 Spatial models in economics Keywords:location function; mean function; median function; consensus function; tree PDFBibTeX XMLCite \textit{F. R. McMorris} et al., Discrete Math. Algorithms Appl. 2, No. 3, 313--329 (2010; Zbl 1226.05087) Full Text: DOI References: [1] Arrow K. J., Handbook of Social Choice and Welfare 1 (2002) · Zbl 1307.91009 [2] Arrow K. J., Handbook of Social Choice and Welfare 2 (2005) [3] DOI: 10.1137/0404028 · Zbl 0734.90008 [4] DOI: 10.1016/0165-4896(81)90041-X · Zbl 0486.62057 [5] DOI: 10.1137/1.9780898717501 · Zbl 1031.92001 [6] DOI: 10.1287/opre.46.3.347 · Zbl 0979.90118 [7] DOI: 10.1287/moor.15.3.553 · Zbl 0715.90070 [8] DOI: 10.1016/S0166-218X(02)00213-5 · Zbl 1026.06007 [9] DOI: 10.1016/S0166-218X(98)00003-1 · Zbl 0906.05023 [10] DOI: 10.1002/net.1027 · Zbl 0990.90063 [11] Mirchandani P. B., Discrete Location Theory (1990) · Zbl 0718.00021 [12] Mulder H. M., Australasian J. Combinatorics 41 pp 223– [13] DOI: 10.1016/0377-2217(94)00330-0 · Zbl 0914.90182 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.