Aggregation of individual opinions into a social decision is a problem widely observed in everyday life. For centuries people tried to invent the `best' aggregation rule. In 1951 young American scientist and future Nobel Prize winner Kenneth Arrow formulated the problem in an axiomatic way, i.e., he specified a set of axioms which every reasonable aggregation rule has to satisfy, and obtained that these axioms are inconsistent. This result, often called Arrow's Paradox or General Impossibility Theorem, had become a cornerstone of social choice theory. The main condition used by Arrow was his famous Independence of Irrelevant Alternatives. This very condition pre-defines the `local' treatment of the alternatives (or pairs of alternatives, or sets of alternatives, etc.) in aggregation procedures. Remaining within the framework of the axiomatic approach and based on the consideration of local rules, Arrovian Aggregation Models investigates three formulations of the aggregation problem according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. In other words, we study three aggregation models. What is common between them is that in all models some analogue of the Independence of Irrelevant Alternatives condition is used, which is why we call these models Arrovian aggregation models. Chapter 1 presents a general description of the problem of axiomatic synthesis of local rules, and introduces problem formulations for various versions of formalization of individual opinions and collective decision. Chapter 2 formalizes precisely the notion of `rationality' of individual opinions and social decision. Chapter 3 deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter 4 deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter 5 considers another model – Social Choice Correspondences when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function. Several new classes of rules are introduced and analyzed.
The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.
Over the last number of years there has been a growing interest in the analysis of complex networks which describe a wide range of real-world systems in nature and society. Identification of the central elements in such networks is one of the key research areas. Solutions to this problem are important for making strategic decisions and studying the behavior of dynamic processes, e.g. epidemic spread. The importance of nodes has been studied using various centrality measures. Generally, it should be considered that most real systems are not homogeneous: nodes may have individual attributes and influence each other in groups while connections between nodes may describe different types of relations. Thus, critical nodes detection is not a straightforward process. New Centrality Measures in Networks presents a class of new centrality measures which take into account individual attributes of nodes, the possibility of group influence and long-range interactions and discusses all their new features. The book provides a wide range of applications of network analysis in several fields – financial networks, international migration, global trade, global food network, arms transfers, networks of terrorist groups, and networks of international journals in economics. Real-world studies of networks indicate that the proposed centrality measures can identify important nodes in different applications. Starting from the basic ideas, the development of the indices and their advantages compared to existing centrality measures are presented. Features Built around real-world case studies in a variety of different areas (finance, migration, trade, etc.) Suitable for students and professional researchers with an interest in complex network analysis Paired with a software package for readers who wish to apply the proposed models of centrality (in Python) available at https://github.com/SergSHV/slric.
This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics.
The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.
This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics.
Over the last number of years there has been a growing interest in the analysis of complex networks which describe a wide range of real-world systems in nature and society. Identification of the central elements in such networks is one of the key research areas. Solutions to this problem are important for making strategic decisions and studying the behavior of dynamic processes, e.g. epidemic spread. The importance of nodes has been studied using various centrality measures. Generally, it should be considered that most real systems are not homogeneous: nodes may have individual attributes and influence each other in groups while connections between nodes may describe different types of relations. Thus, critical nodes detection is not a straightforward process. New Centrality Measures in Networks presents a class of new centrality measures which take into account individual attributes of nodes, the possibility of group influence and long-range interactions and discusses all their new features. The book provides a wide range of applications of network analysis in several fields – financial networks, international migration, global trade, global food network, arms transfers, networks of terrorist groups, and networks of international journals in economics. Real-world studies of networks indicate that the proposed centrality measures can identify important nodes in different applications. Starting from the basic ideas, the development of the indices and their advantages compared to existing centrality measures are presented. Features Built around real-world case studies in a variety of different areas (finance, migration, trade, etc.) Suitable for students and professional researchers with an interest in complex network analysis Paired with a software package for readers who wish to apply the proposed models of centrality (in Python) available at https://github.com/SergSHV/slric.
Aggregation of individual opinions into a social decision is a problem widely observed in everyday life. For centuries people tried to invent the `best' aggregation rule. In 1951 young American scientist and future Nobel Prize winner Kenneth Arrow formulated the problem in an axiomatic way, i.e., he specified a set of axioms which every reasonable aggregation rule has to satisfy, and obtained that these axioms are inconsistent. This result, often called Arrow's Paradox or General Impossibility Theorem, had become a cornerstone of social choice theory. The main condition used by Arrow was his famous Independence of Irrelevant Alternatives. This very condition pre-defines the `local' treatment of the alternatives (or pairs of alternatives, or sets of alternatives, etc.) in aggregation procedures. Remaining within the framework of the axiomatic approach and based on the consideration of local rules, Arrovian Aggregation Models investigates three formulations of the aggregation problem according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. In other words, we study three aggregation models. What is common between them is that in all models some analogue of the Independence of Irrelevant Alternatives condition is used, which is why we call these models Arrovian aggregation models. Chapter 1 presents a general description of the problem of axiomatic synthesis of local rules, and introduces problem formulations for various versions of formalization of individual opinions and collective decision. Chapter 2 formalizes precisely the notion of `rationality' of individual opinions and social decision. Chapter 3 deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter 4 deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter 5 considers another model – Social Choice Correspondences when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function. Several new classes of rules are introduced and analyzed.
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