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Pocedures for Random Division of a Set of Indivisible Googs

Marek Bożykowski

2016

( 26 )

DOI: 10.7206/DEC.1733-0092.78

https:/doi.org/10.7206/DEC.1733-0092.78

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.

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New International Version (Niv) Bible

Marek Bożykowski

2019

( 32 )

DOI: 10.7206/DEC.1733-0092.1360

https:/doi.org/10.7206/DEC.1733-0092.1360

Abstract

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Boska Komedia - Dante Alighieri. Komentarz

Marek Bożykowski

2017

( 28 )

DOI: 10.7206/DEC.1733-0092.100

https:/doi.org/10.7206/DEC.1733-0092.100

Abstract

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Fair division of a set of indivisible goods in a situation of unequal entitlements

Marek Bożykowski

2012

( 18 )

https:/doi.org/

Abstract

The paper presents modifi cation of four nonprobabilistic procedures of fair division of a set of indivisible goods with money: Original Knaster, Adjusted Knaster, Equal Shares and Second Prices. The purpose of modification is to adjust the aforementioned methods to the problem of division of a set of goods in a situation of unequal entitlements. Extended versions of six formal properties, namely: strong Pareto optimality, proportionality, envyfreeness, equitability, strategy-proofness and anonymity are also presented. Moreover,proofs of procedures having the same formal properties in a situation of unequal entitlements as in a situation of equal entitlements are shown.

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Procedures of fair division of a set of indivisible goods with money

Marek Bożykowski

2011

( 15 )

https:/doi.org/

Abstract

The paper presents and compares four nonprobabilistic procedures of fair division of a set of indivisible goods with money: Original Knaster, Adjusted Knaster, Equal Shares and Second Prices. The last two are presented for the first time in the article. The analysis concerns the formal properties of thosemethods, namely: strong Pareto optimality, proportionality, envy-freeness, fairness, strategy-proofness and anonymity. Moreover, classes of situations inwhich those procedures meet aforementioned properties will be compared.

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