Fair Division

Author : Steven J. Brams,Alan D. Taylor
Publisher : Cambridge University Press
Page : 292 pages
File Size : 51,9 Mb
Release : 1996-02-23
Category : Business & Economics
ISBN : 0521556449

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Fair Division by Steven J. Brams,Alan D. Taylor Pdf

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

Author : Herve Moulin
Publisher : MIT Press
Page : 302 pages
File Size : 55,8 Mb
Release : 2004-08-20
Category : Business & Economics
ISBN : 0262633116

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Fair Division and Collective Welfare by Herve Moulin Pdf

The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare. The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method. The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.

Author : Eve Rodsky
Publisher : Penguin
Page : 354 pages
File Size : 42,9 Mb
Release : 2019-10-01
Category : Social Science
ISBN : 9780525541950

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Fair Play by Eve Rodsky Pdf

A REESE'S BOOK CLUB PICK "A hands-on, real talk guide for navigating the hot-button issues that so many families struggle with."--Reese Witherspoon Tired, stressed, and in need of more help from your partner? Imagine running your household (and life!) in a new way... It started with the Sh*t I Do List. Tired of being the "shefault" parent responsible for all aspects of her busy household, Eve Rodsky counted up all the unpaid, invisible work she was doing for her family -- and then sent that list to her husband, asking for things to change. His response was... underwhelming. Rodsky realized that simply identifying the issue of unequal labor on the home front wasn't enough: She needed a solution to this universal problem. Her sanity, identity, career, and marriage depended on it. The result is Fair Play: a time- and anxiety-saving system that offers couples a completely new way to divvy up chores and responsibilities. Rodsky interviewed more than five hundred men and women from all walks of life to figure out what the invisible work in a family actually entails and how to get it all done efficiently. With four easy-to-follow rules, 100 household tasks, and a series of conversation starters for you and your partner, Fair Play helps you prioritize what's important to your family and who should take the lead on every chore from laundry to homework to dinner. "Winning" this game means rebalancing your home life, reigniting your relationship with your significant other, and reclaiming your Unicorn Space -- as in, the time to develop the skills and passions that keep you interested and interesting. Stop drowning in to-dos and lose some of that invisible workload that's pulling you down. Are you ready to try Fair Play? Let's deal you in.

Author : Julius B. Barbanel
Publisher : Cambridge University Press
Page : 480 pages
File Size : 48,7 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 : Jörg Rothe
Publisher : Springer
Page : 612 pages
File Size : 48,6 Mb
Release : 2015-08-18
Category : Business & Economics
ISBN : 9783662479049

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Economics and Computation by Jörg Rothe Pdf

This textbook connects three vibrant areas at the interface between economics and computer science: algorithmic game theory, computational social choice, and fair division. It thus offers an interdisciplinary treatment of collective decision making from an economic and computational perspective. Part I introduces to algorithmic game theory, focusing on both noncooperative and cooperative game theory. Part II introduces to computational social choice, focusing on both preference aggregation (voting) and judgment aggregation. Part III introduces to fair division, focusing on the division of both a single divisible resource ("cake-cutting") and multiple indivisible and unshareable resources ("multiagent resource allocation"). In all these parts, much weight is given to the algorithmic and complexity-theoretic aspects of problems arising in these areas, and the interconnections between the three parts are of central interest.

Author : Steven J. Brams
Publisher : Princeton University Press
Page : 390 pages
File Size : 52,6 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 : Jack Robertson,William Webb
Publisher : CRC Press
Page : 177 pages
File Size : 51,9 Mb
Release : 1998-07-15
Category : Mathematics
ISBN : 9781439863855

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Cake-Cutting Algorithms by Jack Robertson,William Webb Pdf

The challenge of dividing an asset fairly, from cakes to more important properties, is of great practical importance in many situations. Since the famous Polish school of mathematicians (Steinhaus, Banach, and Knaster) introduced and described algorithms for the fair division problem in the 1940s, the concept has been widely popularized. This book

Author : H. Peyton Young
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 47,7 Mb
Release : 1985-12-31
Category : Mathematics
ISBN : 0821867407

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Fair Allocation by H. Peyton Young Pdf

This collection of six papers provides a valuable source of material on the real-world problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic method, can be applied to give insight into complex social problems. Originally presented as an AMS Short Course, these papers could serve as a suitable text for courses touching on game theory, decision sciences, economics, or quantitative political science. Most of the material is accessible to the mathematically mature undergraduate with a background in advanced calculus and algebra. Each article surveys the recent literature and includes statements and sketches of proofs, as well as unsolved problems which should excite student curiosity. The articles analyze the question of fair allocation via six examples: the apportionment of political representation, the measurement of income inequality, the allocation of joint costs, the levying of taxes, the design of voting laws, and the framing of auction procedures. In each of these examples fairness has a somewhat different significance, but common axiomatic threads reveal broad underlying principles. Each of the topics is concerned with norms of comparative equity for evaluating allocations or with standards of procedures for effecting them; it is this focus on normative properties which suggests that a mathematical analysis is appropriate. Though game theory provides a useful tool in many of these allocation problems, the emphasis here is on standards rather than strategy and equity rather than rationality, an approach which more accurately mirrors real-world social problems.

Author : Felix Brandt,Vincent Conitzer,Ulle Endriss,Jérôme Lang,Ariel D. Procaccia
Publisher : Cambridge University Press
Page : 553 pages
File Size : 46,6 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 : Matthew D. Adler,Marc Fleurbaey
Publisher : Oxford University Press
Page : 848 pages
File Size : 40,7 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 : Kiese Laymon
Publisher : Simon and Schuster
Page : 304 pages
File Size : 55,9 Mb
Release : 2021-06-01
Category : Fiction
ISBN : 9781982174835

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Long Division by Kiese Laymon Pdf

Winner of the NAACP Image Award for Fiction From Kiese Laymon, author of the critically acclaimed memoir Heavy, comes a “funny, astute, searching” (The Wall Street Journal) debut novel about Black teenagers that is a satirical exploration of celebrity, authorship, violence, religion, and coming of age in post-Katrina Mississippi. Written in a voice that’s alternately humorous, lacerating, and wise, Long Division features two interwoven stories. In the first, it’s 2013: after an on-stage meltdown during a nationally televised quiz contest, fourteen-year-old Citoyen “City” Coldson becomes an overnight YouTube celebrity. The next day, he’s sent to stay with his grandmother in the small coastal community of Melahatchie, where a young girl named Baize Shephard has recently disappeared. Before leaving, City is given a strange book without an author called Long Division. He learns that one of the book’s main characters is also named City Coldson—but Long Division is set in 1985. This 1985-version of City, along with his friend and love interest, Shalaya Crump, discovers a way to travel into the future, and steals a laptop and cellphone from an orphaned teenage rapper called...Baize Shephard. They ultimately take these items with them all the way back to 1964, to help another time-traveler they meet to protect his family from the Ku Klux Klan. City’s two stories ultimately converge in the work shed behind his grandmother’s house, where he discovers the key to Baize’s disappearance. Brilliantly “skewering the disingenuous masquerade of institutional racism” (Publishers Weekly), this dreamlike “smart, funny, and sharp” (Jesmyn Ward), novel shows the work that young Black Americans must do, while living under the shadow of a history “that they only gropingly understand and must try to fill in for themselves” (The Wall Street Journal).

Author : Matthew McElligott
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 2020
Category : Division
ISBN : 1094258768

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Bean Thirteen by Matthew McElligott Pdf

Two bugs, Ralph and Flora, try to divide thirteen beans so that the unlucky thirteenth bean disappears, but they soon discover that the math is not so easy.

Author : Julius B. Barbanel
Publisher : Cambridge University Press
Page : 472 pages
File Size : 43,5 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 : David Lippman
Publisher : Unknown
Page : 0 pages
File Size : 42,9 Mb
Release : 2012-09-07
Category : Electronic books
ISBN : 1479276537

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Math in Society by David Lippman Pdf

Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

Author : Just Right Reader
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2021-08-31
Category : Electronic
ISBN : 1955903468

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Fred Sees... by Just Right Reader Pdf