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Documents authored by Brams, Steven J.

Document
DOI: 10.4230/DagSemProc.07261.1
07261 Abstracts Collection – Fair Division

Authors: Steven J. Brams and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division'' % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Steven J. Brams and Kirk Pruhs. 07261 Abstracts Collection – Fair Division. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.1,
  author =	{Brams, Steven J. and Pruhs, Kirk},
  title =	{{07261 Abstracts Collection – Fair Division}},
  booktitle =	{Fair Division},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.1},
  URN =		{urn:nbn:de:0030-drops-12444},
  doi =		{10.4230/DagSemProc.07261.1},
  annote =	{Keywords: Economics, Fairness, Allocation, Political Science}
}
Document
DOI: 10.4230/DagSemProc.07261.2
07261 Summary – Fair Division

Authors: Steven J. Brams and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
The problem of fair division – dividing goods or "bads" (e.g., costs) among entities in an impartial and equitable way – is one of the most important problems that society faces. A Google search on the phrase "fair allocation" returns over 100K links, referring to the division of sports tickets, health resources, computer networking resources, voting power, intellectual property licenses, costs of environmental improvements, etc.
Cite as

Steven J. Brams and Kirk Pruhs. 07261 Summary – Fair Division. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.2,
  author =	{Brams, Steven J. and Pruhs, Kirk},
  title =	{{07261 Summary  – Fair Division}},
  booktitle =	{Fair Division},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.2},
  URN =		{urn:nbn:de:0030-drops-12434},
  doi =		{10.4230/DagSemProc.07261.2},
  annote =	{Keywords: Economics, Fairness, Allocation, Political Science}
}
Document
DOI: 10.4230/DagSemProc.07261.5
Better Ways to Cut a Cake - Revisited

Authors: Steven J. Brams, Michael A. Jones, and Christian Klamler

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser's preferences, whereas the chooser can generally obtain more. By comparison, a new 2-person surplus procedure (SP'), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus - the part that remains after each player receives 50% - by giving each person a certain proportion of the surplus as he or she values it. For n geq 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP' and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.
Cite as

Steven J. Brams, Michael A. Jones, and Christian Klamler. Better Ways to Cut a Cake - Revisited. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.5,
  author =	{Brams, Steven J. and Jones, Michael A. and Klamler, Christian},
  title =	{{Better Ways to Cut a Cake - Revisited}},
  booktitle =	{Fair Division},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.5},
  URN =		{urn:nbn:de:0030-drops-12278},
  doi =		{10.4230/DagSemProc.07261.5},
  annote =	{Keywords: Fair division, cake-cutting, envy-freeness, strategy-proofness}
}
Document
DOI: 10.4230/DagSemProc.07261.6
Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure

Authors: Steven J. Brams, Michael A. Jones, and Christian Klamler

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
Properties of discrete cake-cutting procedures that use a minimal number of cuts (n-1 if there are n players) are analyzed. None is always envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ≥ 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, then halves of these halves, and so on. Among other properties, D&C (i) ensures players of more than 1/n shares if their marks are different and (ii) is strategyproof for risk-averse players. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed.
Cite as

Steven J. Brams, Michael A. Jones, and Christian Klamler. Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.6,
  author =	{Brams, Steven J. and Jones, Michael A. and Klamler, Christian},
  title =	{{Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure}},
  booktitle =	{Fair Division},
  pages =	{1--31},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.6},
  URN =		{urn:nbn:de:0030-drops-12211},
  doi =		{10.4230/DagSemProc.07261.6},
  annote =	{Keywords: Cake-cutting, proportionality, envy-freeness, efficiency, strategy-proofness}
}
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