Abstract
A prametric is introduced for describing the consensus gap in group decision making problem and a consensus formation procedure is proposed. It is assumed that each individual’s ties-permitted ordinal ranking constitutes a partition of the alternative set, and that the alternatives in a tie are ranked together occupying consecutive positions. A preference sequence matrix is thus constructed with entries indicating the alternatives’ potential positions by the expert’s preferences. To elicit the group ranking, a certain prametric, namely, the consensus gap indicator is defined for measuring the consensus gap between two preference sequences with ties. Some properties are elaborated, among which an inequality is used to get the potential ties-permitted compromise ranking. An illustrative example is also included.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Armstrong RD, Cook WD, Seiford LM (1982) Priority ranking and consensus formation: the case of ties. Manag Sci 28(6):638–645
Arrow KJ (1951) Social choice and individual values. Wiley, New York
Cook WD (2006) Distance-based and ad hoc consensus models in ordinal preference ranking. Eur J Oper Res 172(2):369–385
Cook WD, Kress M, Seiford LM (1997) A general framework for distance-based consensus in ordinal ranking models. Eur J Oper Res 96(2):392–397
Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(16):1721–1732
Dyer JS, Sarin RK (1979) Group preference aggregation rules based on strength of preference. Manag Sci 25(9):822–832
Gavshin Y, Kruusmaa M (2008) Comparative experiments on the emergence of safe behaviours. In: TAROS, pp 65–71
Inuma M, Otsuka A, Imai H (2009) Theoretical framework for constructing matching algorithms in biometric authentication systems. In: Procedings of ICB09. Lecture notes in computer science, 5558, Alghero, Italy. Springer, Berlin, pp 806–815
Keeney RL (2013) Foundations for group decision analysis. Decis Anal 10(2):103–120
Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591
Kuhn HW (1955) The Hungarian method for the assignment problem. Nav Res Logist Q 2:83–97
Skala MA (2008) Aspects of metric spaces in computation. PhD thesis, University of Waterloo, Ontario, p 2
Slater P (1961) Inconsistencies in a schedule of paired comparisons. Biometrica 48:303–312
Typke R, Walczak-Typke A (2010) Indexing techniques for non-metric music dissimilarity measures. In: Rás ZW, Wieczorkowska AA (eds) Advances in music information retrieval. Springer, Berlin, pp 3–17
Xu Z (2013) Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decis Negot 22:463–482
Zeng S (2013) Some intuitionistic fuzzy weighted distance measures and their application to group decision making. Group Decis Negot 22:281–298
Zhou L, Chen H, Liu J (2013) Continuous ordered weighted distance measure and its application to multiple attribute group decision making. Group Decis Negot 22:739–758
Acknowledgments
The author would like to thank the Editor-in-Chief and the anonymous Referees for their helpful comments and suggestions that have led to an improved version of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hou, F. A Consensus Gap Indicator and Its Application to Group Decision Making. Group Decis Negot 24, 415–428 (2015). https://doi.org/10.1007/s10726-014-9396-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10726-014-9396-4