Utility Representation of an Incomplete Preference Relation

2002 ◽  
Vol 104 (2) ◽  
pp. 429-449 ◽  
Author(s):  
Efe A. Ok
Keyword(s):  
Preference Relation ◽  
Utility Representation ◽  
Incomplete Preference ◽  
Incomplete Preference Relation

scholarly journals SET-VALUED SHORTFALL AND DIVERGENCE RISK MEASURES

2017 ◽  
Vol 20 (05) ◽  
pp. 1750026 ◽  
Author(s):  
ÇAĞIN ARARAT ◽  
ANDREAS H. HAMEL ◽  
BIRGIT RUDLOFF
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Preference Relation ◽  
Market Risk ◽  
Dual Representation ◽  
Average Value ◽  
Multivariate Risk Measures ◽  
Average Value At Risk ◽  
Incomplete Preference Relation

Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate risk measures is constructed via a recent Lagrange duality for set optimization. In particular, it is shown that a shortfall risk measure can be written as an intersection over a family of divergence risk measures indexed by a scalarization parameter. Examples include set-valued versions of the entropic risk measure and the average value at risk. As a second step, the minimization of these risk measures subject to trading opportunities is studied in a general convex market in discrete time. The optimal value of the minimization problem, called the market risk measure, is also a set-valued risk measure. A dual representation for the market risk measure that decomposes the effects of the original risk measure and the frictions of the market is proved.

Coalitional Expected Multi‐Utility Theory

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 933-980 ◽  
Author(s):  
Kazuhiro Hara ◽  
Efe A. Ok ◽  
Gil Riella
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Preference Relation ◽  
Revealed Preference ◽  
Portfolio Diversification ◽  
Independence Axiom ◽  
Representation Theorems ◽  
Utility Representation ◽  
Reversal Phenomenon ◽  
Preference Reversal Phenomenon

This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision‐maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

scholarly journals Determination of Break-Even Point through Consumer Preference Relation

The Batuk ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 67-76
Author(s):  
Gopal Man Pradhan ◽  
Phanindra Kumar Katel
Keyword(s):  
Choice Theory ◽  
Preference Relation ◽  
Social Choice Theory ◽  
Individual Preference ◽  
Consumer Preference ◽  
Utility Representation ◽  
Goods And Services ◽  
Linear Utility ◽  
Break Even Point

Social choice theory beliefs about how the consumers function to chose their interested goods and services. Preference relation with affine indifference curves that has a concave representation has a linear utility representation. This study asks how individual preference relations might be combined to give a single ordering which captures the overall wishes of the group of individuals. There are certain properties that one would like such a utility rule, utility have thus become a more abstract concept that is not necessarily solely based on the satisfaction or pleasure received. Concept of cardinal utility is studied in three different situations Debreu (1958) gave quite different approach. This study maintains link between mathematical theory and financial concept to determine break-even point through the consumers’ preference relation.

Model and Method for Contributor’s Quality Assessment in Community Image Tagging Systems

2018 ◽  
pp. 45-51
Author(s):  
A. V. Ponomarev
Keyword(s):  
Large Scale ◽  
Wide Spectrum ◽  
Preference Relation ◽  
Pairwise Comparison ◽  
Ground Truth ◽  
Comparison Method ◽  
Characteristic Matrix ◽  
Image Tagging ◽  
Proposed Model

Introduction: Large-scale human-computer systems involving people of various skills and motivation into the information processing process are currently used in a wide spectrum of applications. An acute problem in such systems is assessing the expected quality of each contributor; for example, in order to penalize incompetent or inaccurate ones and to promote diligent ones.Purpose: To develop a method of assessing the expected contributor’s quality in community tagging systems. This method should only use generally unreliable and incomplete information provided by contributors (with ground truth tags unknown).Results:A mathematical model is proposed for community image tagging (including the model of a contributor), along with a method of assessing the expected contributor’s quality. The method is based on comparing tag sets provided by different contributors for the same images, being a modification of pairwise comparison method with preference relation replaced by a special domination characteristic. Expected contributors’ quality is evaluated as a positive eigenvector of a pairwise domination characteristic matrix. Community tagging simulation has confirmed that the proposed method allows you to adequately estimate the expected quality of community tagging system contributors (provided that the contributors' behavior fits the proposed model).Practical relevance: The obtained results can be used in the development of systems based on coordinated efforts of community (primarily, community tagging systems). 

scholarly journals ON THE REPRESENTATION OF THE NESTED LOGIT MODEL

2021 ◽  
pp. 1-11
Author(s):  
Alfred Galichon
Keyword(s):  
Closed Form ◽  
Logit Model ◽  
Random Variables ◽  
Nested Logit ◽  
Random Utility ◽  
Nested Logit Model ◽  
Utility Representation ◽  
Phd Thesis ◽  
Closed Form Formula

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

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