Many different voting rules have been proposed in the literature and they can select very different alternatives. This naturally raises the question of whether this diversity in outcomes often occurs. Previous works have shown that the probability that voting rules agree on the same outcome is generally quite low under impartial culture. In this article, we use a similar probabilistic approach on single-peaked cultures, which are more structured and typically more realistic than impartial culture. We provide conditions for voting rules to agree under standard single-peaked cultures, and show that the probability of agreement between rather large families of voting rules is much higher under such cultures, with fast convergence of this probability with respect to the number of voters. We finally provide some insights on other structured preference distributions, observing that many exhibit similar convergence in agreement, including the Mallows’ distribution. Our study reveals a tendency of several well-known voting cultures to bias the outcome of voting rules, which is worth knowing before conducting experiments on synthetic data.

In fair division, local envy-freeness is a desirable property which has been thoroughly studied in recent years. In this paper, we study explanations which can be given to explain that no allocation of items can satisfy this criterion, in the house allocation setting where agents receive a single item. While Minimal Unsatisfiable Subsets (MUSes) are key concepts to extract explanations, they cannot be used as such: (i) they highly depend on the initial encoding of the problem; (ii) they are flat structures which fall short of capturing the dynamics of explanations; (iii) they typically come in large number and exhibit great diversity. In this paper we provide two SAT encodings of the problem which allow us to extract MUS when instances are unsatisfiable. We build a dynamic graph structure which allows to follow step-by-step the explanation. Finally, we propose several criteria to select MUSes, some of them being based on the MUS structure, while others rely on this original graphical explanation structure. We give theoretical bounds on these metrics, showing that they can vary significantly for some instances. Experimental results on synthetic data complement these results and illustrate the impact of the encodings and the relevance of our metrics to select among the many MUSes.

This article considers a house allocation setting–where exactly one object has to be assigned to each agent–in a repeated context, where the same allocation problem is decided a fixed given number of times, while taking previous decisions into account. Since fairness can be rarely achieved in a one-shot decision, we study whether fairness over time can be reached. In particular, we use several fairness criteria adapted to this particular repeated house allocation setting and investigate whether they can be satisfied. While we show that most related decision problems are computationally hard in general, we identify restricted positive cases.

We consider the problem of poll manipulation in political elections. In the context of strategic voting, we are interested in whether a polling institute can manipulate the information it communicates to voters in order to influence the outcome of the election. We start with a version of the problem where the polling institute is allowed to send any score to voters. Then, for realistic reasons, we investigate a restricted version in which the polling institute cannot announce scores which are too far from the truthful ones. While we show that both decision problems are computationally hard, we go beyond this worst-case complexity analysis by using probabilistic tools to address the possibility of successful and efficient manipulation in practice, w.r.t. several natural preference distributions.

We study whether Pareto-optimal stable matchings can be reached via pairwise swaps in one-to-one matching markets with initial assignments. We consider housing markets, marriage markets, and roommate markets as well as three different notions of swap rationality. Our main results are as follows. While it can be efficiently determined whether a Pareto-optimal stable matching can be reached when defining swaps via blocking pairs, checking whether this is the case for all such sequences is computationally intractable. When defining swaps such that all involved agents need to be better off, even deciding whether a Pareto-optimal stable matching can be reached via some sequence is intractable. This confirms and extends a conjecture made by Damamme, Beynier, Chevaleyre, and Maudet (2015) who have shown that convergence to a Pareto-optimal matching is guaranteed in housing markets with single-peaked preferences. We prove that in marriage and roommate markets, single-peakedness is not sufficient for this to hold, but the stronger restriction of one-dimensional Euclidean preferences is.

Rent division consists in simultaneously computing an allocation of rooms to agents and a payment, starting from an individual valuation of each room by each agent. When agents have budget limits, it is known that envy-free solutions do not necessarily exist. We propose two solutions to overcome this problem. In the first one, we relax envy-freeness to account for budget disparities. In the second one, we allow fractional allocations, in which agents may change rooms during the duration of the lease.

In the roommate problem, pairs of agents must be formed, based on ordinal preferences of the agents over each other. In this article, we examine fair roommate matchings by relaxing envy-freeness to account for justified envy based on the rank in the agents’ preferences. A rank-envy-free matching prevents that an agent prefers the partner of another agent whereas she has ranked it better. Although this requirement is pretty weak in house allocation [9], we show that it is more demanding in the roommate setting. We study parameterizations of rank-envy-freeness, as well as further natural relaxations of this concept. We also investigate the connections between the family of rank-based fairness criteria and known optimality or stability concepts.

We study a variant of hedonic games, called hedonic seat arrangements in the literature, where the goal is not to partition the agents into coalitions but to assign them to vertices of a given graph; their satisfaction is then based on the subset of agents in their neighborhood. We focus on ordinal hedonic seat arrangements where the preferences over neighborhoods are deduced from ordinal preferences over single agents and a given preference extension. In such games and for different types of preference restrictions and extensions, we investigate the existence of arrangements satisfying stability w.r.t. swaps of positions in the graph or the well-known optimality concept of popularity.

The formal study of coalition formation in multiagent systems is typically realized using so-called hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this paper, we study the convergence of simple dynamics leading to stable partitions in a variety of classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. We identify conditions for convergence, provide elaborate counterexamples of existence of individually stable partitions, and study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson (2002), Brandl, Brandt, and Strobel (2015), and Boehmer and Elkind (2020).

We consider the problem of the conjoint selection and allocation of projects to a population of agents, e.g. students are assigned papers and shall present them to their peers. The selection can be constrained either by quotas over subcategories of projects, or by the preferences of the agents themselves. We explore fairness and optimality issues and refine the analysis of the rank-maximality and popularity optimality concepts. We show that they are compatible with reasonable fairness requirements related to rank-based envy-freeness and can be adapted to select globally good projects according to the preferences of the agents.

This article deals with strategic voting under incomplete information. We propose a descriptive model, inspired by political elections, where the information about the vote intentions of the electorate comes from public opinion polls and a social network, modeled as a graph over the voters. The voters are assumed to be confident in the poll and they update the communicated results with the information they get from their relatives in the social network. We consider an iterative voting model based on this behavior and study the associated “poll-confident” dynamics. In this context, we ask the question of manipulation by the polling institute.

This article deals with object allocation where each agent receives a single item. Starting from an initial endowment, the agents can be better off by exchanging their objects. However, not all trades are likely because some participants are unable to communicate. By considering that the agents are embedded in a social network, we propose to study the allocations emerging from a sequence of simple swaps between pairs of neighbors in the network. This model raises natural questions regarding (i) the reachability of a given assignment, (ii) the ability of an agent to obtain a given object, and (iii) the search of Pareto-efficient allocations. We investigate the complexity of these problems by providing, according to the structure of the social network, polynomial and NP-complete cases.

In a voting system, voters may adopt a strategic behaviour in order to manipulate the outcome of the election. This naturally entails a game theoretic conception of voting. The specificity of our work is that we embed the voting game into a social context where agents and their relations are given by a graph, i.e. a social network. We aim at integrating the information provided by the graph in a refinement of the game-theotical analysis of an election. We consider coalitional equilibria immune to deviations performed by realistic coalitions based on the social network, namely the cliques of the graph. Agents are not fully selfish as they have consideration for their relatives. The corresponding notion of equilibrium was introduced by Hoefer et al. [12] and called considerate equilibrium. We propose to study its existence and the ability of the agents to converge to such an equilibrium in strategic voting games using well-known voting rules: Plurality, Antiplurality, Plurality with runoff, Borda, k-approval, STV, Maximin and Copeland.