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We study the budget aggregation problem in which a set of strategic voters must split a finite divisible resource (such as money or time) among a set of competing projects. Our goal is twofold: We seek truthful mechanisms that provide fairness guarantees to the projects. For the first objective, we focus on the class of moving phantom mechanisms, which are -- to this day -- essentially the only known truthful mechanisms in this setting. For project fairness, we consider the mean division as a fair baseline, and bound the maximum difference between the funding received by any project and this baseline. We propose a novel and simple moving phantom mechanism that provides optimal project fairness guarantees. As a corollary of our results, we show that our new mechanism minimizes the L1 distance to the mean for three projects and gives the first non-trivial bounds on this quantity for more than three projects. 

We consider the problem of fairly dividing a collection of indivisible goods among a set of players. Much of the existing literature on fair division focuses on notions of individual fairness. For instance, envy-freeness requires that no player prefer the set of goods allocated to another player to her own allocation. We observe that an algorithm satisfying such individual fairness notions can still treat groups of players unfairly, with one group desiring the goods allocated to another. Our main contribution is a notion of group fairness, which implies most existing notions of individual fairness. Group fairness (like individual fairness) cannot be satisfied exactly with indivisible goods. Thus, we introduce two “up to one good” style relaxations. We show that, somewhat surprisingly, certain local optima of the Nash welfare function satisfy both relaxations and can be computed in pseudo-polynomial time by local search. Our experiments reveal faster computation and stronger fairness guarantees in practice. 

In fair division,equitabilitydictates that each partic-ipant receives the same level of utility. In this work,we study equitable allocations of indivisible goodsamong agents with additive valuations. While priorwork has studied (approximate) equitability in iso-lation, we consider equitability in conjunction withother well-studied notions of fairness and economicefficiency. We show that the Leximin algorithm pro-duces an allocation that satisfies equitability up toany good and Pareto optimality. We also give anovel algorithm that guarantees Pareto optimalityand equitability up to one good in pseudopolyno-mial time. Our experiments on real-world prefer-ence data reveal that approximate envy-freeness, ap-proximate equitability, and Pareto optimality canoften be achieved simultaneously.