Hedonic games provide a model of coalition formation in which a set of agents is partitioned into coalitions and the agents have preferences over which set they belong to. Recently, Aziz et. al. (2014) have initiated the study of hedonic games with dichotomous preferences, where each agent either approves or disapproves of a given coalition. In this work, we study the computational complexity of questions related to finding optimal and stable partitions in dichotomous hedonic games under various ways of restricting and representing the collection of approved coalitions. Encouragingly, many of these problems turn out to be polynomial-time solvable. In particular, we show that an individually stable outcome always exists and can be found in polynomial time. We also provide efficient algorithms for cases in which agents approve only few coalitions, in which they only approve intervals, and in which they only approve sets of size 2 (the roommates case). These algorithms are complemented by NP-hardness results, especially for representations that are very expressive, such as in the case when agents' goals are given by propositional formulas.

Understanding when and how computational complexity can be used to protect elections against different manipulative actions has been a highly active research area over the past two decades. A recent body of work, however, has shown that many of the NP-hardness shields, previously obtained, vanish when the electorate has single-peaked or nearly single-peaked preferences. In light of these results, we investigate whether it is possible to reimpose NP-hardness shields for such electorates by allowing the voters to specify partial preferences instead of insisting they cast complete ballots. In particular, we show that in single-peaked and nearly single-peaked electorates, if voters are allowed to submit top-truncated ballots, then the complexity of manipulation and bribery for many voting rules increases from being in P to being NP-complete.

Over the past two decades, water markets have been successfully fielded in countries such as Australia, the United states, Chile, China, etc. Water users, mainly irrigators, have benefited immensely from water markets. However, the current water market design also faces certain serious barriers. It has been pointed out that transaction costs, which exists in most markets, induce great welfare loss. For example, for water markets in western China discussed in this paper, the influence of transaction costs is significant. Another important barrier is the locality of trades due to geographical constraints. Based on the water market at Xiying Irrigation, one of the most successful water market in western China, we model the water market as a graph with minimum transaction thresholds on edges. Our goal is to maximize the transaction volume or welfare. We prove that the existence of transaction costs results in no polynomial time approximation scheme (PTAS) to maximize social welfare (MAX SNP-hard). The complexities on special graphs are also presented. From a practical point of view, however, optimal social welfare can be obtained via a well-designed mixed integer linear program and can be approximated near optimally at a large scale via a heuristic algorithm. Both algorithms are tested on data sets generated from real historical trading data. Our study also suggests the importance of reducing transaction costs, for example, institutional costs in water market design. Our work opens a potentially important avenue of market design within the agenda of computational sustainability.

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should fit. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a representative committee, where candidates are described by attributes such as sex, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a single committee that contains a certain number of young and old people, certain number of men and women, certain number of people with different professions, etc. With a single attribute the problem boils down to the apportionment problem for party-list proportional representation systems (in such case the value of the single attribute is the political affiliation of a candidate). We study some properties of the associated subset selection rules, and address their computation.

The fairness notion of maximin share (MMS) guarantee underlies a deployed algorithm for allocating indivisible goods under additive valuations. Our goal is to understand when we can expect to be able to give each player his MMS guarantee. Previous work has shown that such an MMS allocation may not exist, but the counterexample requires a number of goods that is exponential in the number of players; we give a new construction that uses only a linear number of goods. On the positive side, we formalize the intuition that these counterexamples are very delicate by designing an algorithm that provably finds an MMS allocation with high probability when valuations are drawn at random.

In this paper we expand the standard Hotelling-Downs model of spatial competition to a setting where clients do not necessarily choose their closest candidate (retail product or political). Specifically, we consider a setting where clients may disavow all candidates if there is no candidate that is sufficiently close to the client preferences. Moreover, if there are multiple candidates that are sufficiently close, the client may choose amongst them at random. We show the existence of Nash Equilibria for some such models, and study the price of anarchy and stability in such scenarios.

We introduce a new family of judgment aggregation rules, called the binomial rules, designed to account for hidden dependencies between some of the issues being judged. To place them within the landscape of judgment aggregation rules, we analyse both their axiomatic properties and their computational complexity, and we show that they contain both the well-known distance-based rule and the basic rule returning the most frequent overall judgment as special cases. To evaluate the performance of our rules empirically, we apply them to a dataset of crowdsourced judgments regarding the quality of hotels extracted from the travel website TripAdvisor. In our experiments we distinguish between the full dataset and a subset of highly polarised judgments, and we develop a new notion of polarisation for profiles of judgments for this purpose, which may also be of independent interest.

We study the societal tradeoffs problem, where a set of voters each submit their ideal tradeoff value between each pair of activities (e.g., "using a gallon of gasoline is as bad as creating 2 bags of landfill trash"), and these are then aggregated into the societal tradeoff vector using a rule. We introduce the family of distance-based rules and show that these can be justified as maximum likelihood estimators of the truth. Within this family, we single out the logarithmic distance-based rule as especially appealing based on a social-choice-theoretic axiomatization. We give an efficient algorithm for executing this rule as well as an approximate hill climbing algorithm, and evaluate these experimentally.

In a Fisher market game, a market equilibrium is computed in terms of the utility functions and money endowments that agents reported. As a consequence, an individual buyer may misreport his private information to obtain a utility gain. We investigate the extent to which an agent's utility can be increased by unilateral strategic plays and prove that the percentage of this improvement is at most 2 for markets with weak gross substitute utilities. Equivalently, we show that truthfully reporting is a 0.5-approximate Nash equilibrium in this game. To identify sufficient conditions for truthfully reporting being close to Nash equilibrium, we conduct a parameterized study on strategic behaviors and further show that the ratio of utility gain decreases linearly as buyer's initial endowment increases or his maximum share of an item decreases. Finally, we consider collusive behavior of a coalition and prove that the utility gain is bounded by 1/(1 - maximum share of the collusion). Our findings justify the truthful reporting assumption in Fisher markets by a quantitative study on participants incentive, and imply that under large market assumption, the utility gain of a buyer from manipulations diminishes to 0.

We introduce a roommate market model, in which 2n people need to be assigned to n rooms, with two people in each room. Each person has a valuation to each room, as well as a valuation to each of other people as a roommate. Each room has a rent shared by the two people living in the room, and we need to decide who live together in which room and how much each should pay. Various solution concepts on stability and envy-freeness are proposed, with their existence studied and the computational complexity of the corresponding search problems analyzed. In particular, we show that maximizing the social welfare is NP-hard, and we give a polynomial time algorithm that achieves at least 2/3 of the maximum social welfare. Finally, we demonstrate a pricing scheme that can achieve envy-freeness for each room.