The geometry of efficient fair division:
What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players g...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2005
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| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511546679 https://doi.org/10.1017/CBO9780511546679 https://doi.org/10.1017/CBO9780511546679 |
| Zusammenfassung: | What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 online resource (ix, 462 pages) |
| ISBN: | 9780511546679 |
| DOI: | 10.1017/CBO9780511546679 |
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| 245 | 1 | 0 | |a The geometry of efficient fair division |c Julius B. Barbanel ; with an introduction by Alan D. Taylor |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2005 | |
| 300 | |a 1 online resource (ix, 462 pages) | ||
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| 505 | 8 | 0 | |g Introduction |r Alan D. Taylor |g 1 |t Notation and preliminaries |g 2 |t Geometric object #1a : the individual pieces set (IPS) for two players |g 3 |t What the IPS tells us about fairness and efficiency in the two-player context |g 4 |t The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context |g 5 |t What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context |g 6 |t Characterizing Pareto optimality : introduction and preliminary ideas |g 7 |t Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures |g 8 |t Characterizing Pareto optimality II : partition ratios |g 9 |t Geometric object #2 : the Radon-Nikodym set (RNS) |g 10 |t Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association |g 11 |t The shape of the IPS |g 12 |t The relationship between the IPS and the RNS |g 13 |t Other issues involving Weller's construction, partition ratios, and Pareto optimality |g 14 |t Strong Pareto optimality |g 15 |t Characterizing Pareto optimality using hyperreal numbers |g 16 |t Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored |
| 520 | |a What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions | ||
| 650 | 4 | |a Partitions (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1818982576425009152 |
|---|---|
| any_adam_object | |
| author | Barbanel, Julius B. 1951- |
| author_additional | Alan D. Taylor |
| author_facet | Barbanel, Julius B. 1951- |
| author_role | aut |
| author_sort | Barbanel, Julius B. 1951- |
| author_variant | j b b jb jbb |
| building | Verbundindex |
| bvnumber | BV043945189 |
| classification_rvk | SK 150 |
| collection | ZDB-20-CBO |
| contents | Notation and preliminaries Geometric object #1a : the individual pieces set (IPS) for two players What the IPS tells us about fairness and efficiency in the two-player context The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context Characterizing Pareto optimality : introduction and preliminary ideas Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures Characterizing Pareto optimality II : partition ratios Geometric object #2 : the Radon-Nikodym set (RNS) Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association The shape of the IPS The relationship between the IPS and the RNS Other issues involving Weller's construction, partition ratios, and Pareto optimality Strong Pareto optimality Characterizing Pareto optimality using hyperreal numbers Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored |
| ctrlnum | (ZDB-20-CBO)CR9780511546679 (OCoLC)723681073 (DE-599)BVBBV043945189 |
| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/3 |
| dewey-search | 512.7/3 |
| dewey-sort | 3512.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546679 |
| format | Electronic eBook |
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| id | DE-604.BV043945189 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:25Z |
| institution | BVB |
| isbn | 9780511546679 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029354159 |
| oclc_num | 723681073 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (ix, 462 pages) |
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| publishDate | 2005 |
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| publisher | Cambridge University Press |
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| spelling | Barbanel, Julius B. 1951- Verfasser aut The geometry of efficient fair division Julius B. Barbanel ; with an introduction by Alan D. Taylor Cambridge Cambridge University Press 2005 1 online resource (ix, 462 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction Alan D. Taylor 1 Notation and preliminaries 2 Geometric object #1a : the individual pieces set (IPS) for two players 3 What the IPS tells us about fairness and efficiency in the two-player context 4 The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context 5 What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context 6 Characterizing Pareto optimality : introduction and preliminary ideas 7 Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures 8 Characterizing Pareto optimality II : partition ratios 9 Geometric object #2 : the Radon-Nikodym set (RNS) 10 Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association 11 The shape of the IPS 12 The relationship between the IPS and the RNS 13 Other issues involving Weller's construction, partition ratios, and Pareto optimality 14 Strong Pareto optimality 15 Characterizing Pareto optimality using hyperreal numbers 16 Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions Partitions (Mathematics) Partition Mengenlehre (DE-588)4707411-5 gnd rswk-swf Geometrische Methode (DE-588)4156715-8 gnd rswk-swf Geometrische Methode (DE-588)4156715-8 s 1\p DE-604 Partition Mengenlehre (DE-588)4707411-5 s 2\p DE-604 Taylor, Alan D. 1947- win Erscheint auch als Druckausgabe 978-0-521-84248-8 https://doi.org/10.1017/CBO9780511546679 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barbanel, Julius B. 1951- The geometry of efficient fair division Notation and preliminaries Geometric object #1a : the individual pieces set (IPS) for two players What the IPS tells us about fairness and efficiency in the two-player context The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context Characterizing Pareto optimality : introduction and preliminary ideas Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures Characterizing Pareto optimality II : partition ratios Geometric object #2 : the Radon-Nikodym set (RNS) Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association The shape of the IPS The relationship between the IPS and the RNS Other issues involving Weller's construction, partition ratios, and Pareto optimality Strong Pareto optimality Characterizing Pareto optimality using hyperreal numbers Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored Partitions (Mathematics) Partition Mengenlehre (DE-588)4707411-5 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| subject_GND | (DE-588)4707411-5 (DE-588)4156715-8 |
| title | The geometry of efficient fair division |
| title_alt | Notation and preliminaries Geometric object #1a : the individual pieces set (IPS) for two players What the IPS tells us about fairness and efficiency in the two-player context The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context Characterizing Pareto optimality : introduction and preliminary ideas Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures Characterizing Pareto optimality II : partition ratios Geometric object #2 : the Radon-Nikodym set (RNS) Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association The shape of the IPS The relationship between the IPS and the RNS Other issues involving Weller's construction, partition ratios, and Pareto optimality Strong Pareto optimality Characterizing Pareto optimality using hyperreal numbers Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored |
| title_auth | The geometry of efficient fair division |
| title_exact_search | The geometry of efficient fair division |
| title_full | The geometry of efficient fair division Julius B. Barbanel ; with an introduction by Alan D. Taylor |
| title_fullStr | The geometry of efficient fair division Julius B. Barbanel ; with an introduction by Alan D. Taylor |
| title_full_unstemmed | The geometry of efficient fair division Julius B. Barbanel ; with an introduction by Alan D. Taylor |
| title_short | The geometry of efficient fair division |
| title_sort | the geometry of efficient fair division |
| topic | Partitions (Mathematics) Partition Mengenlehre (DE-588)4707411-5 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| topic_facet | Partitions (Mathematics) Partition Mengenlehre Geometrische Methode |
| url | https://doi.org/10.1017/CBO9780511546679 |
| work_keys_str_mv | AT barbaneljuliusb thegeometryofefficientfairdivision AT tayloraland thegeometryofefficientfairdivision |