Stable matching problems have several practical applications. If preference lists are truncated and contain ties, finding a stable matching with maximal size is computationally difficult. We address this problem using a local search technique, based on Adaptive Search and present experimental evidence that this approach is much more efficient than state-of-the-art exact and approximate methods. Moreover, parallel versions (particularly versions with communication) improve performance so much that very large and hard instances can be solved quickly.

We consider a multi-agent scenario where a collection of agents needs to select a common decision from a large set of decisions over which they express their preferences. This decision set has a combinatorial structure, that is, each decision is an element of the Cartesian product of the domains of some variables. Agents express their preferences over the decisions via soft constraints. We consider both sequential preference aggregation methods (they aggregate the preferences over one variable at a time) and one-step methods and we study the computational complexity of influencing them through bribery. We prove that bribery is NPcomplete for the sequential aggregation methods (based on Plurality, Approval, and Borda) for most of the cost schemes we defined, while it is polynomial for one-step Plurality.

We consider multi-agent settings where a set of agents want to take a collective decision, based on their preferences over the possible candidate options. While agents have their initial inclination, they may interact and influence each other, and therefore modify their preferences, until hopefully they reach a stable state and declare their final inclination. At that point, a voting rule is used to aggregate the agents’ preferences and generate the collective decision. Recent work has modeled the influence phenomenon in the case of voting over a single issue. Here we generalize this model to account for preferences over combinatorially structured domains including several issues. We propose a way to model influence when agents express their preferences as CP-nets. We define two procedures for aggregating preferences in this scenario, by interleaving voting and influence convergence, and study their resistance to bribery.

This book provides a concise introduction to the main research lines in this field, covering aspects such as preference modelling, uncertainty reasoning, social choice, stable matching, and computational aspects of preference aggregation and manipulation. The book is centered around the notion of preference reasoning, both in the single-agent and the multi-agent settings. ISBN 9781608455867, 102 pages.

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with quantitative preferences: each man (resp., woman) provides a score for each woman (resp., man). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and/or optimal according to these notions. While expressivity greatly increases by adopting quantitative preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

We consider multi-agent systems where agents' preferences are aggregated via sequential majority voting: each decision is taken by performing a sequence of pairwise comparisons where each comparison is a weighted majority vote among the agents. Incompleteness in the agents' preferences is common in many real-life settings due to privacy issues or an ongoing elicitation process. In addition, there may be uncertainty about how the preferences are aggregated. For example, the agenda (a tree whose leaves are labelled with the decisions being compared) may not yet be known or fixed. We therefore study how to determine collectively optimal decisions (also called winners) when preferences may be incomplete, and when the agenda may be uncertain. We show that it is computationally easy to determine if a candidate decision always wins, or may win, whatever the agenda. On the other hand, it is computationally hard to know wheth er a candidate decision wins in at least one agenda for at least one completion of the agents' preferences. These results hold even if the agenda must be balanced so that each candidate decision faces the same number of majority votes. Such results are useful for reasoning about preference elicitation. They help understand the complexity of tasks such as determining if a decision can be taken collectively, as well as knowing if the winner can be manipulated by appropriately ordering the agenda.

Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework, based on both CP-nets and soft constraints, that handles both hard and soft constraints as well as conditional preferences efficiently and uniformly. We study the complexity of testing the consistency of preference statements, and show how soft constraints can faithfully approximate the semantics of conditional preference statements whilst improving the computational complexity

We review constraint-based approaches to handle preferences. We start by defining the main notions of constraint programming, then give various concepts of soft constraints and show how they can be used to model quantitative preferences. We then consider how soft constraints can be adapted to handle other forms of preferences, such as bipolar, qualitative, and temporal preferences. Finally, we describe how AI techniques such as abstraction, explanation generation, machine learning, and preference elicitation, can be useful in modelling and solving soft constraints.

We review constraint-based approaches to handle preferences. We start by defining the main notions of constraint programming, then give various concepts of soft constraints and show how they can be used to model quantitative preferences. We then consider how soft constraints can be adapted to handle other forms of preferences, such as bipolar, qualitative, and temporal preferences. Finally, we describe how AI techniques such as abstraction, explanation generation, machine learning, and preference elicitation, can be useful in modelling and solving soft constraints.

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning about multi-agent systems: strategic games, CP-nets, and soft constraints. To relate the notions of optimality in these formalisms we introduce a natural qualitative modification of the notion of a strategic game. We show then that the optimal outcomes of a CP-net are exactly the Nash equilibria of such games. This allows us to use the techniques of game theory to search for optimal outcomes of CP-nets and vice-versa, to use techniques developed for CP-nets to search for Nash equilibria of the considered games. Then, we relate the notion of optimality used in the area of soft constraints to that used in a generalization of strategic games, called graphical games. In particular we prove that for a natural class of soft constraints that includes weighted constraints every optimal solution is both a Nash equilibrium and Pareto efficient joint strategy. For a natural mapping in the other direction we show that Pareto efficient joint strategies coincide with the optimal solutions of soft constraints.