On a preference analysis in a group decision making

Mazurek, Jiří (2015): On a preference analysis in a group decision making.

Abstract

The aim of the paper is to provide several quantitative measures concerning preference structure in a group decision making setting. These measures enable to assess group and individual discord, core preferences and outliers, or to find a consensus, where a consensus is defined as a preference with a minimum sum of distances to other preferences. Also, it is shown that a distance of a consensus to a median preference is upper bounded, which might reduce a search for a consensus significantly.

• Item Type: MPRA Paper
• Language: English
• Keywords: consensus; decision making; distance; discord; geometric median; group decision making; group discord; preference; preference structure.
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General

References

Arrow, K. J. (1951). Social Choice and Individual Values. New York: John Wiley & Sons, Inc.

Cook, W. D. (2006). Distance-Based and Ad Hoc Consensus Models in Ordinal Preference Ranking. European Journal of Operational Research, Nr. 172, 369-385.

Cook, W. D., Kress, M. (1985). Ordinal ranking with intensity of preference. Management Science, vol. 31, No. 1, 26-32.

Feldman, A. M., Serrano, R. (2006). Welfare Economics and Social Choice Theory, 2nd ed., New York: Springer.

Felsenthal, D. S. (2010). Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥2) must be elected. In: Assessing Alternative Voting Procedures, London School of Economics and Political Science, London, UK.

Fiedor, J. Mazurek, J. (2011). The Evaluation of the Entropy of Decision Makers’ Preferences in Ordinal Consensus Ranking Problem. In: Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011. Professional Publishing: Prague, 157-162.

Fishburn, P. C. (1973). The Theory of Social Choice. Princeton, N. J.: Princeton University Press.

Haldane, J. B. S. (1948). Note on the median of a multivariate distribution. Biometrika 35 (3–4), 414–417.

Herrera-Viedma, E., Alonso, S., Chiclana, F., Herrera, F. (2007). A consensus model for group decision making with incomplete fuzzy preference relations, Fuzzy Systems, IEEE Transactions 15 (5), 863-877.

Kameda, T., Tindale, R. S., & Davis, J. H. (2002). Cognitions, preferences, and social sharedness: Past, present, and future directions in group decision making. In S. L. Group Decision Making 51 Schneider & J. Shanteau (Eds.), Emerging perspectives on judgment and decision research. Cambridge, UK: Cambridge University Press.

Margolius, B. H. (2001). Permutations with Inversions. Journal of Integer Sequences, Vol. 4, 1-12.

Mazurek, J. (2011). The Fuzzy Permutation Model for the Ordinal Ranking Problem Solution. In: Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011 (Dlouhý, M., Skočdopolová, V., eds.). Professional Publishing, Prague, 462-467.

Myerson, R. B. (2013). Fundamentals of Social Choice Theory, Quarterly Journal of Political Science: Vol. 8: No. 3, 305-337.

Nurmi, H. (1999). Voting Paradoxes and How to Deal with Them. Berlin/Heidelberg/New York: Springer-Verlag.

Orlovsky, S. A. (1978). Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, Volume 1, Issue 3, 155–167.

Perny, P., Roubens, M. (1998). Fuzzy Preference Modeling. In R. Slowinski (ed.), Fuzzy Sets in Decision Analysis, Operations Research and Statistics. Boston/Dordrecht/London: Kluwer.

Saari, D. G. (2000). Mathematical Structure of Voting Paradoxes: I. Pairwise Votes, Economic Theory, Vol. 15, No. 1, 1-53.

Saaty, T. L. (2001). Fundamentals of Decision Making and Priority Theory. Pittsburgh, Pennsylvania: RWS Publications.

Sen, A. K. (1970). Collective Choice and Social Welfare. San Francisco, Calif.: Holden-Day.

Tavana, M., LoPinto, F., Smither, J. W. (2007). A Hybrid Distance-Based Ideal-Seeking Consensus Ranking Model. Journal of Applied Mathematics and Decision Sciences, 18 pages.

Taylor, A. D., Pacelli, A. M. (2009). Mathematics and Politics, Strategy, Voting, Power, and Proof, 2nd ed., Springer.

Vardi, Y., Zhang, Cun-Hui. (2000). The multivariate L1-median and associated data depth. Proceedings of the National Academy of Sciences of the United States of America 97 (4), 1423–1426

Voxman, W. (1998). Some remarks on distances between fuzzy numbers. Fuzzy Sets and Systems, 10(1-3), 353-365. Wulf, G. (2006). A primer in social choice theory. Oxford: Oxford University Press.

Zeshui Xu. (2013). Linguistic Decision Making: Theory and Methods, Springer Science & Business Media.

Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning - I, Information Sciences, vol. 8, no. 3, 199-249,