In this case, all PCs will be considered, but some will be more preferred than others. Such concepts can be expressed in either a qualitative or a quantitative way. Preferences and constraints are closely related notions, since preferences can be seen as a form of "tolerant" constraints. For this reason, there are several constraint-based frameworks to model preferences. One of the most general frameworks, based on soft constraints (Meseguer, Rossi, and Schiex 2006), extends the classical constraint formalism to model preferences in a quantitative way, by expressing several degrees of satisfaction that can be either totally or partially ordered. When there are both levels of satisfaction and levels of rejection, preferences are bipolar and can be modeled by extending the soft constraint formalism (Bistarelli et al. 2006). Preferences can also be modeled in a qualitative way (also called ordinal), that is, by pairwise comparisons. In this case, soft constraints (or their extensions) are not suitable.

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In both individual and collective decision making, the space of alternatives from which the agent (or the group of agents) has to choose often has a combinatorial (or multi-attribute) structure. We give an introduction to preference handling in combinatorial domains in the context of collective decision making, and show that the considerable body of work on preference representation and elicitation that AI researchers have been working on for several years is particularly relevant. After giving an overview of languages for compact representation of preferences, we discuss problems in voting in combinatorial domains, and then focus on multiagent resource allocation and fair division. These issues belong to a larger field, known as computational social choice, that brings together ideas from AI and social choice theory, to investigate mechanisms for collective decision making from a computational point of view. We conclude by briefly describing some of the other research topics studied in computational social choice.

This article explains the benefits of preferences for AI systems and draws a picture of current AI research on preference handling. It thus provides an introduction to the topics covered by this special issue on preference handling.

The effective tailoring of decisions to the needs and desires of specific users requires automated mechanisms for preference assessment. We provide a brief overview of recent direct preference elicitation methods: these methods ask users to answer (ideally, a small number of) queries regarding their preferences and use this information to recommend a feasible decision that would be (approximately) optimal given those preferences. We argue for the importance of assessing numerical utilities rather than qualitative preferences, and survey several utility elicitation techniques from artificial intelligence, operations research, and conjoint analysis.

We give an overview of the multifaceted relationship between nonmonotonic logics and preferences. We discuss how the nonmonotonicity of reasoning itself is closely tied to preferences reasoners have on models of the world or, as we often say here, possible belief sets. Selecting extended logic programming with the answer-set semantics as a "generic" nonmonotonic logic, we show how that logic defines preferred belief sets and how preferred belief sets allow us to represent and interpret normative statements. Conflicts among program rules (more generally, defaults) give rise to alternative preferred belief sets. We discuss how such conflicts can be resolved based on implicit specificity or on explicit rankings of defaults. Finally, we comment on formalisms which explicitly represent preferences on properties of belief sets. Such formalisms either build preference information directly into rules and modify the semantics of the logic appropriately, or specify preferences on belief sets independently of the mechanism to define them.

Interactive artificial intelligence systems employ preferences in both their reasoning and their interaction with the user. This survey considers preference handling in applications such as recommender systems, personal assistant agents, and personalized user interfaces. We survey the major questions and approaches, present illustrative examples, and give an outlook on potential benefits and challenges.

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Moreover, the investor, the oncologist, and the airline manager are all in a situation where the number of available options or alternatives is very large or even infinite. There are infinitely many ways to invest money and infinitely many possible radiotherapy treatments, but the number of feasible crew schedules is finite, albeit astronomical in practice. The alternatives are therefore described by constraints, rather than explicitly known: the sums invested in every stock must equal the total invested; the radiotherapy treatment must meet physical and clinical constraints; crew schedules must ensure that each flight has exactly one crew assigned to operate it. Mathematically, the alternatives are described by vectors in variable or decision space; the set of all vectors satisfying the constraints is called the feasible set in decision space. The consequences or attributes of the alternatives are described as vectors in objective or outcome space, where outcome (objective) vectors are a function of the decision (variable) vectors.

We address user system interaction issues in product search and recommender systems: how to help users select the most preferential item from a large collection of alternatives. As such systems must crucially rely on an accurate and complete model of user preferences, the acquisition of this model becomes the central subject of our paper. Many tools used today do not satisfactorily assist users to establish this model because they do not adequately focus on fundamental decision objectives, help them reveal hidden preferences, revise conflicting preferences, or explicitly reason about tradeoffs. As a result, users fail to find the outcomes that best satisfy their needs and preferences. In this article, we provide some analyses of common areas of design pitfalls and derive a set of design guidelines that assist the user in avoiding these problems in three important areas: user preference elicitation, preference revision, and explanation interfaces. For each area, we describe the state-of-the-art of the developed techniques and discuss concrete scenarios where they have been applied and tested.