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:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2005.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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: | 1 online resource (ix, 462 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 451-452) and index. |
| ISBN: | 0511109857 9780511109850 9780511546679 051154667X 9780521842488 0521842484 |
Internformat
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| 100 | 1 | |a Barbanel, Julius B., |d 1951- |1 https://id.oclc.org/worldcat/entity/E39PCjMkYt4x8cK47Mbp38tVG3 |0 http://id.loc.gov/authorities/names/n2004003180 | |
| 245 | 1 | 4 | |a The geometry of efficient fair division / |c Julius B. Barbanel ; with an introduction by Alan D. Taylor. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2005. | ||
| 300 | |a 1 online resource (ix, 462 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references (pages 451-452) and index. | ||
| 588 | 0 | |a Print version record. | |
| 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. | ||
| 505 | 0 | 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. |
| 650 | 0 | |a Partitions (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85098392 | |
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| adam_text | |
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| author | Barbanel, Julius B., 1951- |
| author_GND | http://id.loc.gov/authorities/names/n2004003180 |
| author_additional | Alan D. Taylor -- |
| author_facet | Barbanel, Julius B., 1951- |
| author_role | |
| author_sort | Barbanel, Julius B., 1951- |
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| 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 | (OCoLC)62325596 |
| 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 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocm62325596 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:48Z |
| institution | BVB |
| isbn | 0511109857 9780511109850 9780511546679 051154667X 9780521842488 0521842484 |
| language | English |
| oclc_num | 62325596 |
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| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Cambridge University Press, |
| record_format | marc |
| spelling | Barbanel, Julius B., 1951- https://id.oclc.org/worldcat/entity/E39PCjMkYt4x8cK47Mbp38tVG3 http://id.loc.gov/authorities/names/n2004003180 The geometry of efficient fair division / Julius B. Barbanel ; with an introduction by Alan D. Taylor. Cambridge, UK ; New York : Cambridge University Press, 2005. 1 online resource (ix, 462 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 451-452) and index. Print version record. 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. 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. Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) cct Partitions (Mathematics) fast has work: The geometry of efficient fair division (Text) https://id.oclc.org/worldcat/entity/E39PCFRY4hmfMm9jmjBpMpDtYX https://id.oclc.org/worldcat/ontology/hasWork Print version: Barbanel, Julius B., 1951- Geometry of efficient fair division. Cambridge, UK ; New York : Cambridge University Press, 2005 0521842484 (DLC) 2004045928 (OCoLC)54972740 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=132259 Volltext |
| 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) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) cct Partitions (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85098392 |
| 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 | geometry of efficient fair division |
| topic | Partitions (Mathematics) http://id.loc.gov/authorities/subjects/sh85098392 Partitions (Mathématiques) MATHEMATICS Number Theory. bisacsh Partitions (Mathematics) cct Partitions (Mathematics) fast |
| topic_facet | Partitions (Mathematics) Partitions (Mathématiques) MATHEMATICS Number Theory. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=132259 |
| work_keys_str_mv | AT barbaneljuliusb thegeometryofefficientfairdivision AT barbaneljuliusb geometryofefficientfairdivision |