In fair rent division, the problem is to assign rooms to roommates and fairly split the rent based on roommates' reported valuations for the rooms. Envy-free rent division is the most popular application on the fair division website Spliddit. The standard model assumes that agents can correctly report their valuations for each room. In practice, agents may be unsure about their valuations, for example because they have had only limited time to inspect the rooms. Our goal is to find a robust rent division that remains fair even if agent valuations are slightly different from the reported ones. We introduce the lexislack solution, which selects a rent division that remains envy-free for valuations within as large a radius as possible of the reported valuations. We also consider robustness notions for valuations that come from a probability distribution, and use results from learning theory to show how we can find rent divisions that (almost) maximize the probability of being envy-free, or that minimize the expected envy. We show that an almost optimal allocation can be identified based on polynomially many samples from the valuation distribution. Finding the best allocation given these samples is NP-hard, but in practice such an allocation can be found using integer linear programming.

Such an allocation is guaranteed to exist [Svensson, 1983].

Such an allocation is guaranteed to exist [ Svensson, 1983 ].

In fair rent division, the problem is to assign rooms to roommates and fairly split the rent based on roommates' reported valuations for the rooms. Envy-free rent division is the most popular application on the fair division website Spliddit. The standard model assumes that agents can correctly report their valuations for each room. In practice, agents may be unsure about their valuations, for example because they have had only limited time to inspect the rooms. Our goal is to find a robust rent division that remains fair even if agent valuations are slightly different from the reported ones.

In fair rent division, the problem is to assign rooms to roommates and fairly split the rent based on roommates' reported valuations for the rooms. Envy-free rent division is the most popular application on the fair division website Spliddit. The standard model assumes that agents can correctly report their valuations for each room. In practice, agents may be unsure about their valuations, for example because they have had only limited time to inspect the rooms. Our goal is to find a robust rent division that remains fair even if agent valuations are slightly different from the reported ones.

Designing and implementing explainable systems is seen as the next step towards increasing user trust in, acceptance of and reliance on Artificial Intelligence (AI) systems. While explaining choices made by black-box algorithms such as machine learning and deep learning has occupied most of the limelight, systems that attempt to explain decisions (even simple ones) in the context of social choice are steadily catching up. In this paper, we provide a comprehensive survey of explainability in mechanism design, a domain characterized by economically motivated agents and often having no single choice that maximizes all individual utility functions. We discuss the main properties and goals of explainability in mechanism design, distinguishing them from those of Explainable AI in general. This discussion is followed by a thorough review of the challenges one may face when working on Explainable Mechanism Design and propose a few solution concepts to those.

We achieve four objectives: (1) each agent is allowed to make a report that expresses her preference about violating her budget constraint, a feature not achieved by mechanisms that only elicit quasi-linear reports; (2) these reports are finite dimensional; (3) computation is feasible in polynomial time; and (4) incentive properties of envy-free mechanisms that elicit quasi-linear reports are preserved.

Algorithms are increasingly used to determine allocations of scarce, high-value resources. For example, spectrum auctions, which are used by governments to allocate radio spectrum, require algorithms to determine which combinations of bids can and should be accepted. Kidney exchanges allow patients that require a kidney transplant and have a willing but medically incompatible donor to trade their donors, and some of these exchanges now use algorithms to determine who matches with whom. These are very different application domains--for one, in the former, transfers of money play an essential role, but in the latter, they are illegal. Other applications have yet different features, so each application comes with its own requirements.