QUALIFICATION PROBLEMS WITH AN UPPER BOUND

Abstract

We study qualification problem introduced by Kasher and Rubinstein (1997) and introduce an upper bound on the number of people who can be qualified. Following Abizada and Tapkı (2015), we analyze consistency requirement for this model. We introduce Priority Based Liberal rule, which is an extension of the Liberal rule, which has been analyzed widely in the literature. We characterize Priority Based Liberal Rule based on consistency and unanimity.  

Keywords

• Consistency,liberal rule,group identification,qualification problems,unanimity

References

1. Abizada, A. and Tapki, I. G. (2015), Two simple characterizations of the Liberal rule based on consistency requirement, mimeo.
2. Aumann, R. and Maschler, M. (1985), Game Theoretic Analysis of a Bankruptcy Problem from the Talmud, Journal of Economic Theory, Vol. 36, pp.195-213.
3. Çengelci, M. A. and Sanver, M. R. (2010), Simple collective identity functions, Theory and decision, Vol. 68, No. 4, pp. 417-443.
4. Ergin, H. (2000), Consistency in house allocation problems, Theory and Decision, Vol. 68, pp.77-97.
5. Hart, S. and Mas-Colell, A. (1989), Potential, Value and Consistency, Econometrica, Vol. 57, pp. 589-614.
6. Ju, B. (2013), On the characterization of liberalism by Samet and Schmeidler, Vol. 40, pp. 359-366.
7. Kasher, A. and Rubinstein, A. (1997), On the question ‘Who is J?’ A social approach, Logique Analyse, Vol.160, pp. 385-395.
8. Lensberg, T. (1988), Stability and the Nash solution, Journal of Economic Theory, Vol. 45, No. 2, pp. 330-341.

9. Moulin, H. (1985). The separability axiom and equal-sharing methods.Journal of Economic Theory, Vol. 36, No. 1, pp.120-148.
10. Peleg, B. (1986), On the reduced game property and its convers, International Journal of Game Theory, Vol. 15, pp.187-200.
11. Samet, D. and Schmeidler, D. (2003), Between Liberalism and Democracy, Journal of Economic Theory, Vol. 110, pp.203-233.
12. Sasaki, H., and Toda, M. (1992), Consistency and characterization of the core of two-sided matching problems, Journal of Economic Theory, Vol. 56, No. 1, pp. 218-227.
13. Sung, S. C., & Dimitrov, D. (2005), On the Axiomatic Characterization of Who is a J?, Logique et Analyse, Vol. 48, pp. 101-112.
14. Tadenuma, K. and Thomson, W. (1991), No-envy and consistency in economies with indivisible goods, Econometrica, Vol.59, pp.1755-1767.
15. Thomson, W. (1990), The Consistency Principle, in Game Theory and Applications, ed. By Ichiishi, T., Neyman, A., and Tauman, Y., New York: Academic Press: 187-215.
16. Thomson, W. (1994). Consistent solutions to the problem of fair division when preferences are single-peaked, Journal of Eonomic Theory, Vol. 63, 219-245.
17. Young, P. (1987), On dividing an amount according to individual claims or liabilities, Mathematics of Operations Research, Vol. 12, pp.398414.