75775 Paris cedex 16, France. Email: emmanuel.lepinette@ceremade.dauphine.fr.
Abstract
In the first part of the paper we study concepts of supremum and maxi- mum as subsets of a topological space X endowed by **preference** **relations**. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility repre- sentations. In the second part of the paper we consider partial orders and **preference** **relations** ”lifted” from a metric separable space X endowed by a random **preference** relation to the space L 0 (X) of X-valued random variables. We provide an example of application of the notion of essential maximum to the problem of the minimal portfolio super-replicating an American-type contingent claim under transaction costs.

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Abstract. We address the problem of learning **preference** **relations** over multi- attribute (or combinatorial) domains. We do so by making hypotheses about the dependence structure between attributes that the **preference** relation enjoys. The first hypothesis we consider is the simplest one, namely, separability (no depen- dences between attributes: the **preference** over the values of each attribute is inde- pendent of the values of other attributes); then we consider the more general case where the dependence structure takes the form of an acyclic graph. In all cases, what we want to learn is a set of local **preference** **relations** (or equivalently, a CP- net) rather than a fully specified **preference** relation. We consider three forms of consistency between a CP-net and a set of examples, and for two of them we give an exact characterization in the case of separability, as well as complexity results.

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Learning conditionally lexicographic **preference** **relations** Richard Booth 1 , Yann Chevaleyre 2 , J´erˆome Lang 2 J´erˆome Mengin 3 and Chattrakul Sombattheera 4
Abstract. We consider the problem of learning a user’s ordinal pref- erences on a multiattribute domain, assuming that her preferences are lexicographic. We introduce a general graphical representation called LP-trees which captures various natural classes of such **preference** **relations**, depending on whether the importance order between at- tributes and/or the local preferences on the domain of each attribute is conditional on the values of other attributes. For each class we determine the Vapnik-Chernovenkis dimension, the communication complexity of **preference** elicitation, and the complexity of identify- ing a model in the class consistent with a set of user-provided exam- ples.

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A fundamental result ([72], [78]) shows that every partial order (resp. partial preorder) on a finite set can be obtained as an intersection of a finite number of total orders (resp. total preorders, see [25]).
A further analysis of the concept of incomparability can be found in [193] and [194]. In these papers it is shown that the number of **preference** **relations** that can be introduced in a **preference** structure, so that it can be represented through a characteristic binary relation, depends on the se- mantics of the language used for modelling. In other terms, when classical logic is used in order to model preferences, no more than three different **relations** can be established (if one characteristic relation is used). The introduction of a four-valued logic allows to extend the number of indepen- dently defined **relations** to 10, thus introducing different types of incomparability (and hesitation) due to the different combination of positive and negative reasons (see [191]). It is therefore possi- ble with such a language to consider an incomparability due to ignorance separately from one due to conflicting information.

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combinatorial vote J´erˆome Lang ∗
Abstract
In many real-world social choice problems, the set of alternatives is defined as the Cartesian product of (finite) domain values for each of a given set of variables, and these variables cannot be asusmed to be prefentially independent (to take an example, if X is the main dish of a dinner and Y the wine, preferences over Y depends on the value taken for X). Such combinatorial domains are much too large to allow for representing **preference** **relations** or utility functions explicitly (that is, by listing alternatives together with their rank or utility); for this reason, artificial intelligence researchers have been developing languages for specifying **preference** **relations** or utility functions as compactly as possible. This paper first gives a brief survey of compact representation languages, and then discusses its role for representing and solving social choice problems, especially from the point of view of computational complexity.

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1.3. Outline of the survey
We begin this survey by introducing key concepts in revealed **preference** theory, such as utility functions and **preference** **relations**, in Section 2. Next, in Section 3, we state the fundamental theorems that characterize rationaliz- ability in revealed **preference** theory. We explicitly connect rationalizability with properties of certain graphs, and we state the worst-case complexity of algorithms that establish whether a given dataset satisfies a particular “ax- iom” of revealed **preference**. In Section 4 we look at various kinds of utility functions that have been considered in the literature, and we provide cor- responding rationalizability theorems. Section 5 deals with goodness-of-fit and power measures, which respectively quantify the severity of violations and give a measure of how stringent the tests are. In Section 6 we explore collective settings, where the observed choices are the result of joint decisions by several individuals. Finally, in Section 7, we look at stochastic **preference** settings where the decision maker still attempts to maximize her utility, but her preferences are not necessarily constant over time. Instead, the decision maker has a number of different utility functions, and the function that she maximizes at any given time is probabilistically determined. We conclude in Section 8.

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In this paper we extend TCP-networks with vari- able importance statements that specify that a vari- able is more important than its ancestors in the net- work. These importance statements may induce **preference** **relations** on the set of outcomes that contain conflicting pairs. To handle such cases we propose a new semantics that aggregates **preference** and variable important information in such a way that preferences on more important variables over- ride preferences on less important variables.

lowing for incomplete knowledge states.
Yet another interesting issue for further research stems from the observation that is often unnatural to require players to express **preference** **relations** over strategy pro- files. Rather, they have natural preferences over a space of possible outcomes, and each strategy profile is then mapped to an outcome. Expressing preferences over outcomes rather than strategy profiles is not only more natural in many cases, but it may also make the description of players’ **preference** much more succinct, since there might generally be far less outcomes than strategy profiles. The point that de- serves then some attention is how the mapping from strategy profiles to outcomes can be described succinctly; this can be done for instance using a propositional language for concurrent actions, such as C [18].

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It should be noted that although **preference** **relations** have been natu- rally associated to ranking and choice problem statements, such a sepa- ration can be argued. For instance, there are sorting procedures (which can be seen as classification problems) that use **preference** **relations** in- stead of “nearness” ones [126, 136, 215]. The reason is the following: in order to establish that two objects belong to the same category we usu- ally either try to check whether the two objects are “near” or whether they are near a “typical” object of the category (see for instance [154]). If, however, a category is described, not through its typical objects, but through its boundaries, then, in order to establish if an object belongs to such a category it might make sense to check whether such an ob- ject performs “better” than the “minimum”, or “least” boundary of the category and that will introduce the use of a **preference** relation.

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1 Introduction
This short paper uses the individual voting records of the Monetary Policy Committee (MPC) of the Bank of England to study the extent and nature of **preference** heterogeneity among committee members. Understanding committees is important because many central banks use a committee structure to formulate policy. This is the case, for example, in 79 out of the 88 central banks in Fry et al. (2000). At the theoretical level, we use a simple generalization of the standard Neo Keynesian framework that allows members to di er in the relative weight they attach to output versus in ation stabilization and in their views regarding optimal in ation and natural output. Under the assumption of sincere voting, individual reaction functions are derived and estimated for each member and for the committee as a whole. The model implies that, given the economy parameters and private-sector expectations, committee members agree on their reaction to the expected output gap and demand shocks and disagree on their reaction to expected in ation and supply shocks. In addition, members will di er systematically in their preferred interest rate even if they share the same in ation target and estimate of the natural output rate.

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In all the structures introduced so far, the relation P was transitive and, hence, was acyclic. This seems a natural hypothesis. Abandoning it implies reconsidering the links existing between ‘**preference**’ and ‘choice’ as we already saw. Nevertheless, it is possible to obtain such preferences in experiments [MAY 54, TVE 69] when subjects are asked to compare objects evaluated on several dimensions. They are also common in social choice due to Condorcet’s paradox. Indeed, a famous result [MCG 53] shows that with a simple majority, any complete **preference** structure can be be obtained as the result of the aggregation of individual weak orders. With other aggregation methods, all **preference** structures may occur [BOU 96].

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In Chapter 3, we introduce a class of rules called augmented serial rules for combining individual preferences into a collective ordering. The aggrega- tion problem appears when faculty members want to devise a strategy for offering an open position without knowing whether any given applicant will ultimately accept an offer. It is a commonplace to order the applicants and make offers accordingly. Each of these augmented serial rules is parametrized by a list of agents (with possible repetition) and a committee voting rule. For a given **preference** profile, the collective ordering is determined as follows : The first agent’s most preferred alternative becomes the top-ranked alterna- tive in the collective ordering, the second agent’s most preferred alternative (among those remaining) becomes the second-ranked alternative and so on until two alternatives remain, which are ranked by the committee voting rule. The main result establishes that these rules are succinctly characterized by neutrality and strategy-proofness under the lexicographic extension. Additio- nal results show that these rules are strategy-proof under a variety of other reasonable **preference** extensions.

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8. Conclusion
This paper has presented a comprehensive study on the role that preferences can play in an argumentation framework. Two roles are distinguished. The first one consists of repairing the critical attacks. We have proposed a new approach for modeling this role and which overcomes the limitations of existing approaches. The basic idea is to invert the arrow of each critical attack instead of removing it. We have shown that such an approach is well-founded. The second role of preferences consists of refining the results of an argumentation framework. Indeed, we have shown that a refinement amounts to compare (using a **preference** relation, called a refinement relation) the extensions under a given semantics of an argumentation framework. It is clearly argued in the paper that the two roles are completely independent and should be modeled in different ways and at different steps of the evaluation process.

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u i )) = 1 where {¬a i } = D A i /{a i } with a i ∈ D A i ). Thus, we can always find an
optimal solution, starting from the root nodes where we choose each time the most or one of the most preferred value(s) (i.e. with possibility equal to 1). Then, depending on the parents instantiation, each time we again choose an alternative with a conditional possibility equal to 1. At the end of the procedure, we get one or several completely instantiated solutions having a possibility equal to 1. Consequently, partial **preference** orders with incomparable maximal elements can not be represented by a π-Pref net.

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4 Ceteris Paribus as structural **preference**
In order to be able to provide a final recommendation to a decision maker, we have to solve a **preference** aggregation problem. With this term we refer to the problem of establishing an overall **preference** relation (an order on the set of out- comes) taking into account all the criteria the decision maker considers relevant to his problem. Unfortunately there is no universal way to solve this problem (see [4] and [5]). Basically, what we know is that, under looser conditions on the type of preferences to aggregate and properties to satisfy by the final result, the resulting **preference** relation is not an order (neither completeness nor acyclicity can be guaranteed: see [3]). If the stake is to obtain rapidly a reasonable recom- mendation, we have to simplify both the possible types of **preference** statements that can be modelled and aggregated, and the aggregation procedure itself. For this purpose, in this paper we have chosen the use of the CP-nets formalism which guarantees an efficient computation of a final result, although it is less expressive than other frameworks.

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Related literature: There have been many attempts in economics, philosophy or soci- ology to understand the causes and consequences of **preference** changes. While a complete review of the literature on **preference** changes is behind the scope of this article, it is worth mentioning some previous works. In economics, Cyert and DeGroot [ 1979 ] have proposed a model of adaptive utility in which the DM is aware that her **preference** may change and adapts her behavior. Some authors have provided a representation in which the DM anticipates that she might change her **preference** [ Gul and Pesendorfer , 2005 , Kreps , 1979 ] and speculate over this potential change. Such approaches aim at clarifying how a rational DM should deal with these changes. They focus on the consequences of these changes for rational choice theory and do not explain how and why they occur. Only a few papers focused on how **preference** changes are triggered. Becker [ 1996 ]’s famous Accounting for taste intents to explain **preference** changes. But the causes he emphasizes are opaque and hardly shed light on the psychological process that yields **preference** formation. While he rhetorically invokes habit formation and argues that imagination plays a role in **preference** changes, his account of how these mental states induce these changes cannot be founded on an epistemic representation of the DM. 4 State dependent **preference** [ Hill , 2009 ] and

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A descriptive analysis of the demographic data was con- ducted. Statistical analysis of the data was carried out using a mixed logit regression model to evaluate patient prefer- ence for each treatment attribute. The strength of patient **preference** for each attribute is determined by the odds ratio (OR) and its 95% confidence interval (CI), which indicates the odds of preferring a level of an attribute compared to a reference level of the same attribute (all other things being equal). The reference levels chosen for each attribute are the “most preferred” levels. The significance of a specific attribute level refers to whether it has an association with patient **preference**. Thus, as the adjusted OR moves below 1, there is less chance of choosing a treatment with this level, compared to the reference level.

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