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A tale of two mechanisms: Student placement.(English)Zbl 0916.90008

Summary: A new class of matching problems that models centralized college admissions via standardized tests is presented. The allocation mechanism that is used in real-life applications of this problem in Turkey is analyzed. It is shown that this mechanism, multi-category serial dictatorship, has a number of serious deficiencies, most notably inefficiency, vulnerability to manipulation, and the potential of penalizing students for improved test scores. Exploiting the relation between this class of problems and the celebrated college admissions model of Gale and Shapley (1962), an alternative mechanism is proposed that overcomes these deficiencies. This mechanism – the Gale-Shapley student optimal mechanism – is characterized as “best” in this context. \(\copyright\) Academic Press.

MSC:

91B14 Social choice

Cite

References:

[1]Abdulkadiroglu, A.; Sönmez, T., Random serial dictatorship and the core from random endowments in house allocation problems, Econometrica, 66, 689-701 (1998) ·Zbl 1019.91016
[2]Alcalde, J.; Barberà, S., Top dominance and the possibility of strategy-proof stable solutions to matching problems, Econ. Theory, 4, 417-435 (1994) ·Zbl 0830.90004
[3]Dubins, L. E.; Freedman, D. A., Machiavelli and the Gale-Shapley algorithm, Amer. Math. Monthly, 88, 485-494 (1981) ·Zbl 0449.92024
[4]Gale, D.; Shapley, L., College admissions and the stability of marriage, Amer. Math. Monthly, 69, 9-15 (1962) ·Zbl 0109.24403
[5]Hylland, A.; Zeckhauser, R., The efficient allocation of individuals to positions, J. Polit. Econ., 87, 293-314 (1979)
[6]McVitie, D. G.; Wilson, L. B., Stable marriage assignments for unequal sets, BIT, 10, 259-309 (1970) ·Zbl 0225.05002
[7]Postlewaite, A., Manipulation via endowments, Rev. Econ. Stud., 46, 255-262 (1979) ·Zbl 0409.90014
[8]Roth, A. E., The economics of matching: Stability and incentives, Math Oper. Res., 7, 617-628 (1982) ·Zbl 0496.90008
[9]Roth, A. E., The evolution of the labor market for medical interns and residents: A case study in game theory, J. Polit. Econ., 92, 991-1016 (1984)
[10]Roth, A. E., The college admissions problems is not equivalent to the marriage problem, J. Econ. Theory, 36, 277-288 (1985) ·Zbl 0594.90002
[11]Roth, A. E., A natural experiment in the organization of entry level labor markets: Regional markets for new physicians and surgeons in the U.K, Amer. Econ. Rev., 81, 415-440 (1991)
[12]Roth, A. E.; Peranson, E., The effects of a change in the NRMP matching algorithm, J. Amer. Medical Assoc., 278, 729-732 (1997)
[13]Roth, A. E.; Sotomayor, M., Two-Sided Matching: A Study in Game Theoretic Modeling and Analysis (1990), Cambridge Univ. Press: Cambridge Univ. Press London/New York ·Zbl 0726.90003
[14]Roth, A. E.; Xing, X., Jumping the Gun: Imperfections and institutions related to the timing of market transactions, Amer. Econ. Rev., 84, 992-1044 (1994)
[15]Sertel, M., Manipulating Lindahl equilibrium via endowments, Econ. Lett., 51, 167-171 (1994) ·Zbl 0815.90013
[16]Sönmez, T., Manipulation via capacities in two-sided matching markets, J. Econ. Theory, 77, 197-204 (1997) ·Zbl 0892.90011
[17]Svensson, L.-G., Queue allocation of indivisible goods, Soc. Choice Welfare, 11, 323-330 (1994) ·Zbl 0812.90034
[20]Zhou, L., On a conjecture by Gale about one-sided matching problems, J. Econ. Theory, 52, 123-135 (1990) ·Zbl 0725.90003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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