Rationality and Operators

This unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality.

A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality conditions are introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by operators, which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality.

The author also applies his approach to welfare economics. The core problem of 'new welfare economics,' developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond 'new welfare economics.'

Develops a comprehensive approach to rationality of preference relation by employing operators on binary relations Provides mathematically useful results of operators on binary relations and synthesizes traditional concepts and approaches Proposes applications to traditional welfare economics to shed light on a new aspect of the relationship between social welfare and rationality Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction.- 1.1 The Aim of This Book.- 1.2 Rationality of Preference.- 1.3 An Operational Interpretation of Theorems of Welfare Economics.- 1.4 What Can the Operational Approach Achieve?.- 1.5 A Historical Perspective.- 1.6 The Structure of This Book.- 2 Preferences and Operators.- 2.1 Introduction.- 2.2 Binary Relations.- 2.3 Basic Results on Operators.- 2.4 Closure Operators.- 2.5 Concluding Remarks.- 3 Rationality and Operators.- 3.1 Introduction.- 3.2 Properties of Binary Relations.- 3.3 Choice Functions.- 3.4 Extensions.- 3.5 Concluding Remarks.- 4 Operations over the Set of Binary Relations.- 4.1 Introduction.- 4.2 Basic Results.- 4.3 Direct Operations over the Set of Binary Relations.- 4.4 Indirect Operations over the Set of Binary Relations.- 4.5 Concluding Remarks.- 5 Application to Welfare Economics.- 5.1 Introduction.- 5.2 Setting.- 5.3 Paretian Welfare Economics.- 5.4 The Kaldor-Hicks Compensation Principle.- 5.5 Bergsonian-Samuelson Approach of Welfare Economics.- 5.6Concluding Remarks.- 6 Conclusion: Beyond Ordinal Operators.- 6.1 More Applications.- 6.2 Operators for Ordinal Preferences.- 6.3 Operators for Cardinal Preferences.- 6.4 Final Remarks.- Index.