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Information and Preference in Partial Orders: A Bimatrix Representation

Published online by Cambridge University Press:  01 January 2025

Wade D. Cook ,
Moshe Kress  and
Lawrence M. Seiford
Wade D. Cook*
Affiliation:
Faculty of Administrative Studies, York University
Moshe Kress
Affiliation:
CEMA
Lawrence M. Seiford
Affiliation:
Department of General Business, University of Texas
*
Requests for reprints should be sent to Wade D. Cook, Room 340, Faculty of Administrative Studies, York University, Downsview, Ontario, M3J 2R6, CANADA.
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Abstract

This paper presents a bimatrix structure for examining ordinal partial rankings. A set of axioms is given similar to those of Kemeny and Snell (1962) and Bogart (1973), which uniquely determines the distance between any pair of such rankings. The l1 norm is shown to satisfy this set of axioms, and to be equivalent to the Kemeny and Snell distance on their subspace of weak orderings. Consensus formation is discussed.

Keywords

rankingpreferenceconsensusaxioms
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 2 , June 1986 , pp. 197 - 207
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

This research was supported by a NSERC grant A8966.

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