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.

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.

AN INSTANT NEW YORK TIMES BESTSELLER • A REESE'S BOOK CLUB PICK 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 domestic 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 4 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—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.

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.

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.

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).

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