Preference relations

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Essential supremum and essential maximum with respect to random preference relations

Essential supremum and essential maximum with respect to random preference relations

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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Conjoint Measurement Models for Preference Relations

Conjoint Measurement Models for Preference Relations

relations % ∗∗ i at most five. Such preference relations can be fully characterized within model ( D10) [BOU 08, GRE 01a]. These examples show that models using traces on differences are well suited for describing and understanding outranking methods. We shall return to these models at the end of the follow- ing section where we shall show how relations obtained by comparing differences can generally be related to the description of the alternatives by levels on attributes. (We have assumed above that the X i are sets of real numbers endowed with their natural order which was supposed to be
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Learning preference relations over combinatorial domains

Learning preference relations over combinatorial domains

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

Learning conditionally lexicographic preference relations

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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Preference Modelling

Preference Modelling

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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Compact preference representation and combinatorial vote

Compact preference representation and combinatorial vote

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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Revealed preference theory: An algorithmic outlook

Revealed preference theory: An algorithmic outlook

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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Probabilistic Conditional Preference Networks

Probabilistic Conditional Preference Networks

Preference Relations We assume that individual preferences can be represented by an order (reflex- ive, antisymmetric and transitive) over the set of all outcomes V. A convenient way to specify such or- ders over outcomes in a multi-attribute domain is by means of local preference rules: each rule en- ables one to compare outcomes that have some spe- cific values for some attributes. Conditional preference networks [Boutilier et al., 2004] enable direct compar- isons between outcomes that differ in the value of one variable only (called swap pairs of outcomes). Such a rule has the form (X, u :>), with X ∈ V, u ∈ U for some U ⊆ V − {X}, and > a total order on X. According to (X, u :>), for every pair of outcomes o, o ′ such that
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Extending Variable Importance in Preference Networks

Extending Variable Importance in Preference Networks

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.

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Compact preference representation and Boolean games

Compact preference representation and Boolean games

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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Preference Modelling

Preference Modelling

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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Preference representation with 3-points intervals

Preference representation with 3-points intervals

Preference representation with 3-points intervals ¨ Ozt ¨urk Meltem and Tsouki`as Alexis 1 Abstract. In this article we are interested in the representation of qualitative preferences with the help of 3-points intervals (a vector of three increasingly ordered points). Preferences are crucial when an agent has to autonomously make a choice over several possible ac- tions. We provide first of all an axiomatization in order to character- ize our representation and then we construct a general framework for the comparison of 3-points intervals. Our study shows that from the fifteen possible different ways to compare 3-points intervals, seven different preference structures can be defined, allowing the represen- tation of sophisticated preferences. We show the usefulness of our results in two classical problematics: the comparison of alternatives and the numerical representation of preference structures. Concern- ing the former one, we propose procedures to construct non classical preference relations (intransitive preferences for example) over ob- jects being described by three ordered points. Concerning the latter one, assuming that preferences on the pairwise comparisons of ob- jects are known, we show how to associate a 3-points interval to every object, and how to define some comparison rules on these intervals in order to have a compact representation of preferences described with these pairwise comparisons.
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Preference Heterogeneity in Monetary Policy Committees

Preference Heterogeneity in Monetary Policy Committees

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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Binary Relations and Preference Modeling

Binary Relations and Preference Modeling

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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Essays on matching and preference aggregation

Essays on matching and preference aggregation

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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Rich preference-based argumentation frameworks

Rich preference-based argumentation frameworks

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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Possibilistic Conditional Preference Networks

Possibilistic Conditional Preference Networks

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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Qualitative Preference Modelling in Constraint Satisfaction

Qualitative Preference Modelling in Constraint Satisfaction

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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Approaching preference change by partial deliberation

Approaching preference change by partial deliberation

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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Patient Preference and Adherence Dovepress evaluating patient preference and satisfaction for human immunodeficiency virus therapy in France

Patient Preference and Adherence Dovepress evaluating patient preference and satisfaction for human immunodeficiency virus therapy in France

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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