Pocedures for Random Division of a Set of Indivisible Googs

Bożykowski, Marek

Abstract

In fair distribution of a set of indivisible goods it is problematic to provide basic equality if the goods differ in value. One of the most popular solutions to the problems are lotteries. The paper presents seven selected probabilistic procedures: random distribution, lexicographic procedure of equal chances of satisfaction, random serial dictatorship, core from random endowments, probabilistic serial, top trading cycles from equal division and
random priority with infi nite k factor. Some of these procedures always lead to the
same result as some other procedure, therefore these procedures are equivalent. The formal features of the procedures are also analysed in the paper: ordinal efficiency, ex post efficiency, and both strong and week version of: envy-freeness, proportionality, equitability, and individual strategy-proofness.

Keywords

fair distribution (1)indivisible goods (1)probabilistic procedures (1)random priority (1)probabilistic serial (1)

References

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Bogomolnaia, A., Moulin, H. (2001). A new solution to the random assignment problem. Journal of Economic Theory, 100, 295-328. [Google Scholar]
Bożykowski, M. (2011). Procedury podziału zbioru dóbr niepodzielnych z rekompensatami pieniężnymi. Decyzje, 15, 5-22. [Google Scholar]
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Kesten, O. (2009). Why Do Popular Mechanisms Lack Effi ciency in Random Environments? Journal of Economic Theory, 144, 2209-2226. [Google Scholar]
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APA style

Bożykowski, Marek (2016). Pocedures for Random Division of a Set of Indivisible Googs. (2016). Pocedures for Random Division of a Set of Indivisible Googs. Decyzje, (26), 59-107. https://doi.org/10.7206/DEC.1733-0092.78 (Original work published 06/2016AD)

MLA style

Bożykowski, Marek. “Pocedures For Random Division Of A Set Of Indivisible Googs”. 06/2016AD. Decyzje, no. 26, 2016, pp. 59-107.

Chicago style

Bożykowski, Marek. “Pocedures For Random Division Of A Set Of Indivisible Googs”. Decyzje, Decyzje, no. 26 (2016): 59-107. doi:10.7206/DEC.1733-0092.78.

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[1] Abdulkadiroğlu, A., Sönmez, T. (1998). Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica, 66, 689-701. [Google Scholar]

[2] Bogomolnaia, A., Moulin, H. (2001). A new solution to the random assignment problem. Journal of Economic Theory, 100, 295-328. [Google Scholar]

[3] Bożykowski, M. (2011). Procedury podziału zbioru dóbr niepodzielnych z rekompensatami pieniężnymi. Decyzje, 15, 5-22. [Google Scholar]

[4] Bożykowski, M. (2012). Problem podziału zbioru dóbr niepodzielnych w sytuacji nierównych uprawnień. Decyzje, 18, 25-47. [Google Scholar]

[5] Brams, S.J., Taylor, A.D. (1996). Fair Division: From cake-cutting to dispute resolution. Cambridge: Cambridge University Press. [Google Scholar]

[6] Foley, D.K. (1967). Resource allocation and the public sector. Yale Economic Essays, 7, 45-98. [Google Scholar]

[7] Katta, A.K., Sethurman, J. (2006). A solution to the random assignment problem on the full preference domain. Journal of Economic Theory, 131, 231-250. [Google Scholar]

[8] Kahneman, D. (2012). Pułapki myślenia. O myśleniu szybkim i wolnym. Media Rodzina. [Google Scholar]

[9] Kahneman, D., Tversky, A. (1984). Choices, Values, and Frames. American Psychologist, 39, 341-350. [Google Scholar]

[10] Kesten, O. (2006). Probabilistic Serial and Top Trading Cycles from Equal Division for the Random Assignment Problem. Carnegie Mellon University, artykuł niepublikowany. [Google Scholar]

[11] Kesten, O. (2009). Why Do Popular Mechanisms Lack Effi ciency in Random Environments? Journal of Economic Theory, 144, 2209-2226. [Google Scholar]

[12] Kuc, M. (2000). Analiza zasad sprawiedliwości Klemensa Szaniawskiego. Studia Socjologiczne, 1-2(156-157), 167-195. [Google Scholar]

[13] Kuhn, H.W. (1967). On games of fair division. W: Shubik M. (red.) Essays in Mathematical Economics: In Honor of Oskar Morgenstern (s. 29-37). Princeton: Princeton University Press. [Google Scholar]

[14] Lissowski, G. (1992). Probabilistyczny podział dóbr. Prakseologia, 3-4(116-117), 149-165. [Google Scholar]

[15] Lissowski, G. (2006). Probabilistyczne zasady równości Klemensa Szaniawskiego. Decyzje, 6, 5-32 [Google Scholar]

[16] Lissowski, G. (2008). Zasady sprawiedliwego podziału dóbr. Warszawa: Wydawnictwo Naukowe Scholar. [Google Scholar]

[17] Lissowski, G. (2013). Principles of Distributive Justice. Warszawa: Wydawnictwo Naukowe Scholar, Opladen, Berlin, Toronto: Barbara Budrich Publishers. [Google Scholar]

[18] Luce, R.D., Raiffa, H. (1964). Gry i decyzje. Warszawa: Państwowe Wydawnictwo Naukowe. [Google Scholar]

[19] Sandel, M.J. (2013). Czego nie można kupić za pieniądze. Kurhaus Publishing. [Google Scholar]

[20] Shapley, L.S., Scarf, H. (1974). On Cores and Indivisibility. Journal of Mathematical Economics, 1, 23-37. [Google Scholar]

[21] Szaniawski, K. (1966). O pojęciu podziału dóbr. Studia Filozofi czne, 2(45), 61-72. [Google Scholar]

[22] Szaniawski, K. (1975). Formal analysis of evaluative concepts. International Social Science Journal, 3(27), 446-457. [Google Scholar]

[23] Szaniawski, K. (1979). On formal aspects of distributive justice. W: Saarinen, E., Hilpinen, R., Provence Hintikka, M.B. (red.) Essays in Honour of Jaakko Hintikka on the Occasion of Fiftieth Birthday on January, 12, 1979 (s. 135-146). Dordecht: Reidel. [Google Scholar]

[24] von Neumann, J., Morgenstern O. (1947). Theory of Games and Economic Behavior. Princeton: Princeton University Press. [Google Scholar]

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