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We consider the multiwinner election problem where the goal is to choose a committee of $k$ candidates given the voters' utility functions. We allow arbitrary additional constraints on the chosen committee, and the utilities of voters to belong to a very general class of set functions called $\beta$-self bounding. When $\beta=1$, this class includes XOS (and hence, submodular and additive) utilities. We define a novel generalization of core stability called restrained core to handle constraints and consider multiplicative approximations on the utility under this notion. Our main result is the following: If a smooth version of Nash Welfare is globally optimized over committees within the constraints, the resulting committee lies in the $e^{\beta}$-approximate restrained core for $\beta$-self bounding utilities and arbitrary constraints. As a result, we obtain the first constant approximation for stability with arbitrary additional constraints even for additive utilities (factor of $e$), and the first analysis of the stability of Nash Welfare with XOS functions even with no constraints. We complement this positive result by showing that the $c$-approximate restrained core can be empty for $c, Comment: accepted by the 24th ACM Conference on Economics and Computation (EC'23)

A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize welfare functions that reward more balanced surplus allocations. Our main result is the surprising existence of a novel signaling scheme that simultaneously $8$-approximates all welfare functions that are non-negative, monotonically increasing, symmetric, and concave, compared with any other signaling scheme. Classical examples of such welfare functions include the utilitarian social welfare, the Nash welfare, and the max-min welfare. Such a guarantee cannot be given by any consumer-surplus-maximizing scheme -- which are the ones typically studied in the literature. In addition, our scheme is socially efficient, and has the fairness property that buyers with higher values enjoy higher expected surplus, which is not always the case for existing schemes.

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an $\alpha$ factor. If no blocking committee exists under this definition, we call this an $\alpha$-core. Our main result is that an $\alpha$-core, for $\alpha < 67.37$, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to $\alpha < 9.27$ for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of $\alpha > 1.015$ for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities., Comment: Accepted by ACM-SIAM Symposium on Discrete Algorithms (SODA 2022)

In a multi-party machine learning system, different parties cooperate on optimizing towards better models by sharing data in a privacy-preserving way. A major challenge in learning is the incentive issue. For example, if there is competition among the parties, one may strategically hide his data to prevent other parties from getting better models. In this paper, we study the problem through the lens of mechanism design and incorporate the features of multi-party learning in our setting. First, each agent's valuation has externalities that depend on others' types and actions. Second, each agent can only misreport a type lower than his true type, but not the other way round. We call this setting interdependent value with type-dependent action spaces. We provide the optimal truthful mechanism in the quasi-monotone utility setting. We also provide necessary and sufficient conditions for truthful mechanisms in the most general case. Finally, we show the existence of such mechanisms is highly affected by the market growth rate and provide empirical analysis., Comment: 22 pages, 4 figures