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Axioms for centrality scoring with principal eigenvectors

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  • Mitri Kitti

    (University of Turku)

Abstract

Techniques based on using principal eigenvector decomposition of matrices representing binary relations of sets of alternatives are commonly used in social sciences, bibliometrics, and web search engines. By representing the binary relations as a directed graph the question of ranking or scoring the alternatives can be turned into the relevant question of how to score the nodes of the graph. This paper characterizes the principal eigenvector of a matrix as a scoring function with a set of axioms. Furthermore, a method of assessing individual and group centralities simultaneously is characterized by a set of axioms. A special case of this method is the hyperlink-induced topic search for ranking websites. In general, the method can be applied to aggregation of preferences or judgments to obtain a collective assessment of alternatives.

Suggested Citation

  • Mitri Kitti, 2016. "Axioms for centrality scoring with principal eigenvectors," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 639-653, March.
  • Handle: RePEc:spr:sochwe:v:46:y:2016:i:3:d:10.1007_s00355-015-0931-2
    DOI: 10.1007/s00355-015-0931-2
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    References listed on IDEAS

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    1. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    2. Giora Slutzki & Oscar Volij, 2005. "Ranking participants in generalized tournaments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 255-270, June.
    3. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    4. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    5. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    6. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    7. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 439-454, June.
    8. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 75-92, January.
    9. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
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    Cited by:

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