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Representations of Preferences Orderings 1st Edition by Douglas Bridges, Ghanshyam Mehta ISBN 3540588396 9783540588399

Name: Representations of Preferences Orderings 1st Edition by Douglas Bridges, Ghanshyam Mehta ISBN 3540588396 9783540588399
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Authors:Representations of Preferences Orderings-Springer-Verlag Berlin Heidelberg (1995) , Author sort:Heidelberg, Representations of Preferences Orderings-Springer-Verlag Berlin

SKU: EB-19402 Category: eBook DJVU Tags: Douglas Bridges, Ghanshyam Mehta, Preferences Orderings, Representations

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ISBN 10: 3540588396
ISBN 13: 9783540588399
Author: Douglas Bridges, Ghanshyam Mehta

A basic assumption made by pioneers of classical microeconomics such as Edgeworth and Pareto was that the ranking of a consumer’s preferences could always be measured numerically, by associating to each possible con sumption bundle a real number that measured its utility: the greater the utility, the more preferred was the bundle, and conversely. It took several decades before the naivety of this assumption was seriously challenged by economists, such as Wold, attempting to find conditions under which it could be justified mathematically. Wold’s work was the first in a long chain of results of that type, leading to the definitive theorems of Debreu and oth ers in the 1960s, and subsequently to the refinements and generalisations that have appeared in the last twenty-five years. Out of this historical background there has appeared a general mathe matical problem which, as well as having applications in economics, psy chology, and measurement theory, arises naturally in the study of sets bear ing order relations: Given some kind of ordenng t on a set 5, fina a real-valued mapping u on 5 such that for any elements x, y of 5, x t yif and only if u(x) 2: u(y). If also 5 has a topology (respective/y, differential structure), find conditions that ensure the continuity (respectively, differentiability) of the mapping u. A mapping ·u of this kind is called a representation of the ordering C:::.

Representations of Preferences Orderings 1st Edition Table of contents:

Part I: Foundations of Preference Theory

Introduction to Preferences and Orderings
- Defining Preferences and Preference Relations
- Types of Orderings: Total, Partial, and Linear
- The Role of Preferences in Decision Theory
- Historical Context and Evolution of Preference Models
Mathematical Structures of Preferences
- Ordered Sets and Lattices
- Properties of Preference Relations
- Reflexivity, Transitivity, and Completeness
- Equivalence Relations and Preference Classes
Preference Representation in Decision Theory
- Utility Functions and Their Representations
- Cardinal vs Ordinal Preferences
- Rationality and Consistency in Preference Orderings
- The Role of Independence and Compromise

Part II: Advanced Preference Representation Models

Continuous and Discrete Preferences
- Continuous Preference Structures and Topological Representation
- Discrete Preference Orders: Counting and Arrangement
- Stochastic Models for Preferences
- Application in Economics and Social Choice
Lexicographic and Multi-Criteria Preferences
- Lexicographic Ordering and Its Applications
- Multi-Objective Decision Making
- Representing Complex Preference Structures in Multi-Criteria Optimization
- Trade-offs and Preference Aggregation
Preference Orderings and Logical Representation
- Modal Logics of Preference and Choice
- Formal Systems for Expressing Preferences
- Preference Representation in Modal and Epistemic Logic
- Applications of Logic to Decision Theory and Ethics

Part III: Preference Orderings in Social Choice and Economics

Collective Preferences and Social Choice Theory
- Arrow’s Impossibility Theorem and Its Implications
- Preference Aggregation in Voting Systems
- Social Welfare Functions and Fairness
- Arrow’s Conditions and the Gibbard-Satterthwaite Theorem
Preference in Game Theory and Strategic Behavior
- Strategic Preference Modeling in Games
- Nash Equilibrium and Preference Structures
- Cooperative vs Non-Cooperative Preference Systems
- Applications to Auctions and Negotiation
Preference Representation in Welfare Economics
- Social Preferences and Resource Allocation
- Pareto Efficiency and Preference Relations
- The Role of Preferences in Public Policy and Economics
- The Ethics of Preference Representation in Welfare Economics

Part IV: Computational Approaches to Preference Representation

Algorithms for Representing and Comparing Preferences
- Algorithms for Sorting and Ranking Preferences
- Computational Complexity of Preference Aggregation
- Approximation Methods for Complex Preference Orders
- Heuristic Techniques for Multi-Objective Decision Making
Preference Modeling in Artificial Intelligence
- Preference-based Learning Algorithms
- Preference Representation in AI and Machine Learning
- Preference Inference and Personalization Techniques
- Applications in Recommender Systems and Decision Support Systems
Automated Preference Elicitation and Preference Learning
- Techniques for Eliciting Preferences from Agents
- Preference Learning in Uncertainty
- Bayesian Methods for Learning Preferences
- Case Studies in Automated Preference Systems

Part V: Applications and Implications of Preference Orderings

Preference Orderings in Economics and Market Design
- Modeling Consumer Preferences in Market Systems
- Auctions and Mechanism Design with Preference Orderings
- Predicting Market Outcomes Based on Preferences
- The Economics of Preference Modeling
Ethical Considerations in Preference Representation
- Ethical Dilemmas in Preference Elicitation
- Biases and Manipulation of Preferences
- Privacy Concerns in the Representation of Personal Preferences
- Fairness and Equity in Preference Modeling
Applications of Preference Orderings in Social Sciences
- Preference Modeling in Political Science and Public Opinion
- Psychological Aspects of Preference Formation
- Sociology of Preferences in Group Decision Making
- Ethical, Social, and Political Implications of Preference Systems

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Representations of Preferences Orderings 1st Edition by Douglas Bridges, Ghanshyam Mehta ISBN 3540588396 9783540588399

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