Preseparable Extensions of Multidimensional Preferences
Tóm tắt
Throughout much of the literature in economics and political science, the notion of separability provides a mechanism for characterizing interdependence within individual preferences over multiple dimensions. In this paper, we show how preseparable extensions can be used to construct certain classes of separable and non-separable preferences. We prove several associated combinatorial results, and we note a correspondence between separable preference orders, Boolean term orders, and comparative probability relations. We also mention several open questions pertaining to preseparable extensions and separable preferences.
Tài liệu tham khảo
Bradley, W.J., Hodge, J.K., Kilgour, D.M.: Separable discrete preferences. Math. Soc. Sci. 49, 335–353 (2005)
Fine, T., Gill, J.: The enumeration of comparative probability relations. Ann. Probab. 4(4), 667–673 (1976)
Gorman, W.M.: The structure of utility functions. Rev. Econ. Stud. 35, 367–390 (1968)
Hodge, J.K.: Separable Preference Orders. Ph.D. thesis, Western Michigan University (2002)
Hodge, J.K., Klima, R.E.: The Mathematics of Voting and Elections: A Hands on Approach. Mathematical World, vol. 22. American Mathematical Society, Providence (2005)
Hodge, J.K., Schwallier, P.: How does separability affect the desirability of referendum election outcomes? Theor. Decis. 61(3), 251–276 (2006)
Hodge, J.K., TerHaar, M.: Classifying interdependence in multidimensional binary preferences. Math. Soc. Sci. 55, 190–204 (2008)
Kilgour, D.M.: Separable and Non-separable Preferences in Multiple Referenda. Wilfrid Laurier University (1997)
Maclagan, D.: Boolean term orders and the root system B n . Order 15, 279–295 (1999)
Sloane, N.: The online encyclopedia of integer sequences. www.research.att.com/ njas/sequences/ (2008). Accessed 15 July 2008
Stanley, R.P.: Enumerative Combinatorics, vol. 2. Cambridge, New York (1999)
Yu, P.L.: Multiple Criteria Decision Making: Concepts, Techniques, and Extensions. Plenum, New York (1985)