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22.07.2021 | Book Review

# William Thomson: “How to divide when there isn’t enough: from Aristotle, the Talmud and Maimonides to the axiomatics of resource allocation”

verfasst von: Juan D. Moreno-Ternero

Erschienen in: Social Choice and Welfare | Ausgabe 2/2021

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## Excerpt

A classic allocation problem is that in which one has to distribute a perfectly divisible and homogeneous good when there is not enough to cover all agents’ demands. It encompasses many different situations (such as the bankruptcy of a firm, the division of an estate to the creditors of a deceased, or the collection of a given amount of taxes, just to name a few) and it goes as far back as the history of economic thought. The following simple example comes from the Talmud (a great source of inspiration in this context). Two men disagree on the ownership of a garment, worth 200, say. The first man claims half of it, 100, and the other claims it all, 200. Assuming both claims to be made in good faith, how should the garment be distributed? …

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Fußnoten
1
In the above example, the point is the claims vector $$c=(100,200)$$ and the segment is the locus of the non-negative vectors $$(x_1,x_2)$$ dominated by the claims vector, such that their coordinates add up to the endowment $$E=100$$; that is, the portion of the line $$x_1+x_2=E$$, such that $$0\le x_i\le c_i$$, for each $$i=1,2$$.

2
As of today, O’Neill (1982) remains the most cited paper published in the history of Mathematical Social Sciences. Unfortunately, it can still be safely argued that not enough scholars have paid attention to it. Contrary to what happens with the general public, mainstream economic research does not devote enough attention to distributional questions.

3
I intentionally list consistency and solidarity separately, although Thomson argues that solidarity underpinnings can actually be provided for consistency.

4
These techniques can actually help to provide alternative proofs to many characterization results in the literature, such as that of the family of asymmetric rules mentioned above.

5
The two independence axioms can be interpreted as setting specific lower or upper bounds and applying the composition axioms afterwards. Alternative bounds would thus give rise to new composition operators, following the same route.

Literatur
O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371 CrossRef
Thomson W (2019) How to divide when there isn’t enough: from Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation, Econometric Society Monograph. Cambridge University Press, Cambridge CrossRef
Titel
William Thomson: “How to divide when there isn’t enough: from Aristotle, the Talmud and Maimonides to the axiomatics of resource allocation”
verfasst von
Juan D. Moreno-Ternero
Publikationsdatum
22.07.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Social Choice and Welfare / Ausgabe 2/2021
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-021-01355-6

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