The Geometry Of Efficient Fair Division

Author : Julius B. Barbanel
Publisher : Cambridge University Press
Page : 480 pages
File Size : 52,5 Mb
Release : 2005-01-24
Category : Mathematics
ISBN : 1139444395

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The Geometry of Efficient Fair Division by Julius B. Barbanel Pdf

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.

Author : Julius B. Barbanel
Publisher : Cambridge University Press
Page : 472 pages
File Size : 49,7 Mb
Release : 2005-01-24
Category : Mathematics
ISBN : 0521842484

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The Geometry of Efficient Fair Division by Julius B. Barbanel Pdf

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.

Author : D. Marc Kilgour,Colin Eden
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 44,5 Mb
Release : 2010-08-02
Category : Mathematics
ISBN : 9789048190973

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Handbook of Group Decision and Negotiation by D. Marc Kilgour,Colin Eden Pdf

Publication of the Handbook of Group Decision and Negotiation marks a milestone in the evolution of the group decision and negotiation (GDN) eld. On this occasion, editors Colin Eden and Marc Kilgour asked me to write a brief history of the eld to provide background and context for the volume. They said that I am in a good position to do so: Actively involved in creating the GDN Section and serving as its chair; founding and leading the GDN journal, Group Decision and Negotiation as editor-in-chief, and the book series, “Advances in Group Decision and Negotiation” as editor; and serving as general chair of the GDN annual meetings. I accepted their invitation to write a brief history. In 1989 what is now the Institute for Operations Research and the Management Sciences (INFORMS) established its Section on Group Decision and Negotiation. The journal Group Decision and Negotiation was founded in 1992, published by Springer in cooperation with INFORMS and the GDN Section. In 2003, as an ext- sion of the journal, the Springer book series, “Advances in Group Decision and Negotiation” was inaugurated.

Author : Roger D. Congleton,Bernard N. Grofman,Stefan Voigt
Publisher : Oxford Handbooks
Page : 985 pages
File Size : 47,7 Mb
Release : 2019-01-08
Category : Business & Economics
ISBN : 9780190469733

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The Oxford Handbook of Public Choice by Roger D. Congleton,Bernard N. Grofman,Stefan Voigt Pdf

"This two-volume collection provides a comprehensive overview of the past seventy years of public choice research, written by experts in the fields surveyed. The individual chapters are more than simple surveys, but provide readers with both a sense of the progress made and puzzles that remain. Most are written with upper level undergraduate and graduate students in economics and political science in mind, but many are completely accessible to non-expert readers who are interested in Public Choice research. The two-volume set will be of broad interest to social scientists, policy analysts, and historians"--

Author : Anonim
Publisher : Springer
Page : 7493 pages
File Size : 45,6 Mb
Release : 2016-05-18
Category : Law
ISBN : 9781349588022

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The New Palgrave Dictionary of Economics by Anonim Pdf

The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product.

Author : Barry R. Weingast,Donald Wittman
Publisher : Oxford University Press
Page : 1112 pages
File Size : 54,5 Mb
Release : 2008-06-19
Category : Philosophy
ISBN : 9780199548477

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The Oxford Handbook of Political Economy by Barry R. Weingast,Donald Wittman Pdf

Over its lifetime, 'political economy' has had different meanings. This handbook views political economy as a synthesis of the various strands of social science, treating it as the methodology of economics applied to the analysis of political behaviour and institutions.

Author : Paul W. Goldberg,Mingyu Guo
Publisher : Springer
Page : 580 pages
File Size : 53,7 Mb
Release : 2012-12-05
Category : Computers
ISBN : 9783642353116

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Internet and Network Economics by Paul W. Goldberg,Mingyu Guo Pdf

This book constitutes the refereed proceedings of the 8th International Workshop on Internet and Network Economics, WINE 2012, held in Liverpool, UK, in December 2012. The 36 revised full papers and 13 revised short papers presented together with the abstracts of 3 papers about work in progress and 3 invited talks were carefully reviewed and selected from 112 submissions. The papers are organized in topical sections on algorithmic game theory; algorithmic mechanism design; auction algorithms and analysis; computational advertising; computational aspects of equilibria; computational social choice; convergence and learning in games; coalitions, coordination and collective action; economics aspects of security and privacy; economics aspects of distributed and network computing; information and attention economics; network games; price differentiation and price dynamics; social networks.

Author : Matthew D. Adler,Marc Fleurbaey
Publisher : Oxford University Press
Page : 848 pages
File Size : 45,9 Mb
Release : 2016-04-21
Category : Law
ISBN : 9780199325832

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The Oxford Handbook of Well-Being and Public Policy by Matthew D. Adler,Marc Fleurbaey Pdf

What are the methodologies for assessing and improving governmental policy in light of well-being? The Oxford Handbook of Well-Being and Public Policy provides a comprehensive, interdisciplinary treatment of this topic. The contributors draw from welfare economics, moral philosophy, and psychology and are leading scholars in these fields. The Handbook includes thirty chapters divided into four Parts. Part I covers the full range of methodologies for evaluating governmental policy and assessing societal condition-including both the leading approaches in current use by policymakers and academics (such as GDP, cost-benefit analysis, cost-effectiveness analysis, inequality and poverty metrics, and the concept of the "social welfare function"), and emerging techniques. Part II focuses on the nature of well-being. What, most fundamentally, determines whether an individual life is better or worse for the person living it? Her happiness? Her preference-satisfaction? Her attainment of various "objective goods"? Part III addresses the measurement of well-being and the thorny topic of interpersonal comparisons. How can we construct a meaningful scale of individual welfare, which allows for comparisons of well-being levels and differences, both within one individual's life, and across lives? Finally, Part IV reviews the major challenges to designing governmental policy around individual well-being.

Author : Isaac Elishakoff
Publisher : Springer Nature
Page : 292 pages
File Size : 48,7 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9783031404191

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Fair Share by Isaac Elishakoff Pdf

Author : Steven J. Brams
Publisher : Princeton University Press
Page : 390 pages
File Size : 54,5 Mb
Release : 2009-12-02
Category : Science
ISBN : 9781400835591

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Mathematics and Democracy by Steven J. Brams Pdf

Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

Author : Christoph Borgers
Publisher : SIAM
Page : 233 pages
File Size : 50,7 Mb
Release : 2010-01-01
Category : Political Science
ISBN : 9780898717624

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Mathematics of Social Choice by Christoph Borgers Pdf

Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

Author : Rongxing Guo
Publisher : Elsevier
Page : 570 pages
File Size : 44,9 Mb
Release : 2021-07-20
Category : Social Science
ISBN : 9780323915588

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Cross-Border Resource Management by Rongxing Guo Pdf

Approx.538 pages Approx.538 pages

Author : E. Arthur Robinson, Jr.,Daniel H. Ullman
Publisher : CRC Press
Page : 477 pages
File Size : 42,7 Mb
Release : 2010-12-09
Category : Business & Economics
ISBN : 9781439891179

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A Mathematical Look at Politics by E. Arthur Robinson, Jr.,Daniel H. Ullman Pdf

What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean’s method. How the US tried to use game theory to win the Cold War, and why it didn’t work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples. Tying the liberal arts classroom to real-world mathematical applications, this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.

Author : Felix Brandt,Vincent Conitzer,Ulle Endriss,Jérôme Lang,Ariel D. Procaccia
Publisher : Cambridge University Press
Page : 553 pages
File Size : 45,6 Mb
Release : 2016-04-25
Category : Business & Economics
ISBN : 9781107060432

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Handbook of Computational Social Choice by Felix Brandt,Vincent Conitzer,Ulle Endriss,Jérôme Lang,Ariel D. Procaccia Pdf

A comprehensive survey of computational aspects of collective decisions for graduate students, researchers, and professionals in computer science and economics.

Author : E. Arthur Robinson,Daniel H. Ullman
Publisher : CRC Press
Page : 440 pages
File Size : 52,7 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9781498798907

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The Mathematics of Politics, Second Edition by E. Arthur Robinson,Daniel H. Ullman Pdf

It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.