Author: Anatol Rapoport
Publisher: Springer Science & Business Media
ISBN: 9401578400
Category : Business & Economics
Languages : en
Pages : 439
Book Description
This book presents the content of a year's course in decision processes for third and fourth year students given at the University of Toronto. A principal theme of the book is the relationship between normative and descriptive decision theory. The distinction between the two approaches is not clear to everyone, yet it is of great importance. Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Descriptive decision theory purports to describe how people actually make decisions in a variety of situations. Normative decision theory is much more formalized than descriptive theory. Especially in its advanced branches, normative theory makes use of mathematicallanguage, mode of discourse, and concepts. For this reason, the definitions of terms encountered in normative decision theory are precise, and its deductions are rigorous. Like the terms and assertions of other branches of mathematics, those of mathematically formalized decision theory need not refer to anything in the 'real', i. e. the observable, world. The terms and assertions can be interpreted in the context of models of real li fe situations, but the verisimilitude of the models is not important. They are meant to capture only the essentials of adecision situation, which in reallife may be obscured by complex details and ambiguities. It is these details and ambiguities, however, that may be crucial in determining the outcomes of the decisions.
Decision Theory and Decision Behaviour
Author: Anatol Rapoport
Publisher: Springer Science & Business Media
ISBN: 9401578400
Category : Business & Economics
Languages : en
Pages : 439
Book Description
This book presents the content of a year's course in decision processes for third and fourth year students given at the University of Toronto. A principal theme of the book is the relationship between normative and descriptive decision theory. The distinction between the two approaches is not clear to everyone, yet it is of great importance. Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Descriptive decision theory purports to describe how people actually make decisions in a variety of situations. Normative decision theory is much more formalized than descriptive theory. Especially in its advanced branches, normative theory makes use of mathematicallanguage, mode of discourse, and concepts. For this reason, the definitions of terms encountered in normative decision theory are precise, and its deductions are rigorous. Like the terms and assertions of other branches of mathematics, those of mathematically formalized decision theory need not refer to anything in the 'real', i. e. the observable, world. The terms and assertions can be interpreted in the context of models of real li fe situations, but the verisimilitude of the models is not important. They are meant to capture only the essentials of adecision situation, which in reallife may be obscured by complex details and ambiguities. It is these details and ambiguities, however, that may be crucial in determining the outcomes of the decisions.
Publisher: Springer Science & Business Media
ISBN: 9401578400
Category : Business & Economics
Languages : en
Pages : 439
Book Description
This book presents the content of a year's course in decision processes for third and fourth year students given at the University of Toronto. A principal theme of the book is the relationship between normative and descriptive decision theory. The distinction between the two approaches is not clear to everyone, yet it is of great importance. Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Descriptive decision theory purports to describe how people actually make decisions in a variety of situations. Normative decision theory is much more formalized than descriptive theory. Especially in its advanced branches, normative theory makes use of mathematicallanguage, mode of discourse, and concepts. For this reason, the definitions of terms encountered in normative decision theory are precise, and its deductions are rigorous. Like the terms and assertions of other branches of mathematics, those of mathematically formalized decision theory need not refer to anything in the 'real', i. e. the observable, world. The terms and assertions can be interpreted in the context of models of real li fe situations, but the verisimilitude of the models is not important. They are meant to capture only the essentials of adecision situation, which in reallife may be obscured by complex details and ambiguities. It is these details and ambiguities, however, that may be crucial in determining the outcomes of the decisions.
Non-Additive Measure and Integral
Author: D. Denneberg
Publisher: Springer Science & Business Media
ISBN: 9401724342
Category : Mathematics
Languages : en
Pages : 182
Book Description
Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory. In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.
Publisher: Springer Science & Business Media
ISBN: 9401724342
Category : Mathematics
Languages : en
Pages : 182
Book Description
Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory. In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.
Uncertainty and Quality in Science for Policy
Author: S.O. Funtowicz
Publisher: Springer Science & Business Media
ISBN: 9400906218
Category : Social Science
Languages : en
Pages : 254
Book Description
This book explains the notational system NUSAP (Numeral, Unit, Spread, Assessment, Pedigree) and applies it to several examples from the environmental sciences. The authors are now making further extensions of NUSAP, including an algorithm for the propagation of quality-grades through models used in risk and safety studies. They are also developing the concept of `Post-normal Science', in which quality assurance of information requires the participation of `extended peer-communities' lying outside the traditional expertise.
Publisher: Springer Science & Business Media
ISBN: 9400906218
Category : Social Science
Languages : en
Pages : 254
Book Description
This book explains the notational system NUSAP (Numeral, Unit, Spread, Assessment, Pedigree) and applies it to several examples from the environmental sciences. The authors are now making further extensions of NUSAP, including an algorithm for the propagation of quality-grades through models used in risk and safety studies. They are also developing the concept of `Post-normal Science', in which quality assurance of information requires the participation of `extended peer-communities' lying outside the traditional expertise.
Collective Decision-Making:
Author: Norman Schofield
Publisher: Springer Science & Business Media
ISBN: 9401587671
Category : Political Science
Languages : en
Pages : 430
Book Description
In the last decade the techniques of social choice theory, game theory and positive political theory have been combined in interesting ways so as to pro vide a common framework for analyzing the behavior of a developed political economy. Social choice theory itself grew out of the innovative attempts by Ken neth Arrow (1951) and Duncan Black (1948, 1958) to extend the range of economic theory in order to deal with collective decision-making over public goods. Later work, by William Baumol (1952), and James Buchanan and Gordon Tullock (1962), focussed on providing an "economic" interpretation of democratic institutions. In the same period Anthony Downs (1957) sought to model representative democracy and elections while William Riker (1962) made use of work in cooperative game theory (by John von Neumann and Oscar Morgenstern, 1944) to study coalition behavior. In my view, these "rational choice" analyses of collective decision-making have their antecedents in the arguments of Adam Smith (1759, 1776), James Madison (1787) and the Marquis de Condorcet (1785) about the "design" of political institutions. In the introductory chapter to this volume I briefly describe how some of the current normative and positive aspects of social choice date back to these earlier writers.
Publisher: Springer Science & Business Media
ISBN: 9401587671
Category : Political Science
Languages : en
Pages : 430
Book Description
In the last decade the techniques of social choice theory, game theory and positive political theory have been combined in interesting ways so as to pro vide a common framework for analyzing the behavior of a developed political economy. Social choice theory itself grew out of the innovative attempts by Ken neth Arrow (1951) and Duncan Black (1948, 1958) to extend the range of economic theory in order to deal with collective decision-making over public goods. Later work, by William Baumol (1952), and James Buchanan and Gordon Tullock (1962), focussed on providing an "economic" interpretation of democratic institutions. In the same period Anthony Downs (1957) sought to model representative democracy and elections while William Riker (1962) made use of work in cooperative game theory (by John von Neumann and Oscar Morgenstern, 1944) to study coalition behavior. In my view, these "rational choice" analyses of collective decision-making have their antecedents in the arguments of Adam Smith (1759, 1776), James Madison (1787) and the Marquis de Condorcet (1785) about the "design" of political institutions. In the introductory chapter to this volume I briefly describe how some of the current normative and positive aspects of social choice date back to these earlier writers.
Case-Based Approximate Reasoning
Author: Eyke Hüllermeier
Publisher: Springer Science & Business Media
ISBN: 1402056958
Category : Computers
Languages : en
Pages : 384
Book Description
Making use of different frameworks of approximate reasoning and reasoning under uncertainty, notably probabilistic and fuzzy set-based techniques, this book develops formal models of the above inference principle, which is fundamental to CBR. The case-based approximate reasoning methods thus obtained especially emphasize the heuristic nature of case-based inference and aspects of uncertainty in CBR.
Publisher: Springer Science & Business Media
ISBN: 1402056958
Category : Computers
Languages : en
Pages : 384
Book Description
Making use of different frameworks of approximate reasoning and reasoning under uncertainty, notably probabilistic and fuzzy set-based techniques, this book develops formal models of the above inference principle, which is fundamental to CBR. The case-based approximate reasoning methods thus obtained especially emphasize the heuristic nature of case-based inference and aspects of uncertainty in CBR.
Game Theoretical Applications to Economics and Operations Research
Author: T. Parthasarathy
Publisher: Springer Science & Business Media
ISBN: 1475726406
Category : Business & Economics
Languages : en
Pages : 304
Book Description
Game Theoretical Applications to Economics and Operations Research deals with various aspects of game theory and their applications to Economics and OR related problems. It brings together the contributions of a wide spectrum of disciplines such as Statistics, Mathematics, Mathematical Economics and OR. The contributions include decision theory, stochastic games, cooperative and noncooperative games. The papers in the volume are classified under five different sections. The first four sections are devoted to the theory of two-person games, linear complimentarity problems and game theory, cooperative and noncooperative games. The fifth section contains diverse applications of these various theories. Taken together they exhibit a rich versatility of these theories and lively interaction between the mathematical theory of games and significant economic problems.
Publisher: Springer Science & Business Media
ISBN: 1475726406
Category : Business & Economics
Languages : en
Pages : 304
Book Description
Game Theoretical Applications to Economics and Operations Research deals with various aspects of game theory and their applications to Economics and OR related problems. It brings together the contributions of a wide spectrum of disciplines such as Statistics, Mathematics, Mathematical Economics and OR. The contributions include decision theory, stochastic games, cooperative and noncooperative games. The papers in the volume are classified under five different sections. The first four sections are devoted to the theory of two-person games, linear complimentarity problems and game theory, cooperative and noncooperative games. The fifth section contains diverse applications of these various theories. Taken together they exhibit a rich versatility of these theories and lively interaction between the mathematical theory of games and significant economic problems.
Non-Bayesian Decision Theory
Author: Martin Peterson
Publisher: Springer Science & Business Media
ISBN: 1402086997
Category : Science
Languages : en
Pages : 176
Book Description
For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic com- nitytosuchanextentthatalternative,non-Bayesianpositionsareseldomextensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability fu- tions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern - cision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature.
Publisher: Springer Science & Business Media
ISBN: 1402086997
Category : Science
Languages : en
Pages : 176
Book Description
For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic com- nitytosuchanextentthatalternative,non-Bayesianpositionsareseldomextensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability fu- tions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern - cision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature.
Morality and Rational Choice
Author: J. Baron
Publisher: Springer Science & Business Media
ISBN: 9780792322764
Category : Education
Languages : en
Pages : 226
Book Description
This book develops and defends a version of utilitarianism, including expected-utility theory, as a normative model of decision making. The defense, based on the idea of utility as achievement of goals, considers the endorsement of a norm as a decision and asks what reasons we have to endorse norms for decision making. The reasons derive from our pre-existing goals, so any norm we endorse must not fly in the face of these goals, although it must not be selfishly biased, either. This approach is further clarified by drawing distinctions between decisions for the self, for a single other person, for several others, and for the self and others. The book discusses the implications of this argument for the psychological study of decision making, the act--omission distinction, moral education, decision analysis, risk analysis, and other questions of public policy. The final chapter sketches a prescriptive approach to group decision making.
Publisher: Springer Science & Business Media
ISBN: 9780792322764
Category : Education
Languages : en
Pages : 226
Book Description
This book develops and defends a version of utilitarianism, including expected-utility theory, as a normative model of decision making. The defense, based on the idea of utility as achievement of goals, considers the endorsement of a norm as a decision and asks what reasons we have to endorse norms for decision making. The reasons derive from our pre-existing goals, so any norm we endorse must not fly in the face of these goals, although it must not be selfishly biased, either. This approach is further clarified by drawing distinctions between decisions for the self, for a single other person, for several others, and for the self and others. The book discusses the implications of this argument for the psychological study of decision making, the act--omission distinction, moral education, decision analysis, risk analysis, and other questions of public policy. The final chapter sketches a prescriptive approach to group decision making.
The Foundations of Expected Utility
Author: P.C. Fishburn
Publisher: Springer Science & Business Media
ISBN: 9401733295
Category : Social Science
Languages : en
Pages : 181
Book Description
This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under uncertainty. Both parts are studies in the axiomatics of preferences for decision situations and in numerical representations for preferences. Proofs of the representation and uniqueness theorems appear at the ends of the chapters so as not to impede the flow of the discussion. A few warnings on notation are in order. The numbers for theorems cited within a chapter have no prefix if they appear in that chapter, but otherwise carry a chapter prefix (Theorem 3.2 is Theorem 2 in Chapter 3). All lower case Greek letters refer to numbers in the closed interval from o to 1. The same symbol in different chapters has essentially the same meaning with one major exception: x, y, ... mean quite different things in different chapters. I am indebted to many people for their help and encouragement.
Publisher: Springer Science & Business Media
ISBN: 9401733295
Category : Social Science
Languages : en
Pages : 181
Book Description
This book offers a unified treatment of my research in the foundations of expected utility theory from around 1965 to 1980. While parts are new, the presentation draws heavily on published articles and a few chapters in my 1970 monograph on utility theory. The diverse notations and styles of the sources have of course been reconciled here, and their topics arranged in a logical sequence. The two parts of the book take their respective cues from the von Neumann-Morgenstern axiomatization of preferences between risky options and from Savage's foundational treatment of decision making under uncertainty. Both parts are studies in the axiomatics of preferences for decision situations and in numerical representations for preferences. Proofs of the representation and uniqueness theorems appear at the ends of the chapters so as not to impede the flow of the discussion. A few warnings on notation are in order. The numbers for theorems cited within a chapter have no prefix if they appear in that chapter, but otherwise carry a chapter prefix (Theorem 3.2 is Theorem 2 in Chapter 3). All lower case Greek letters refer to numbers in the closed interval from o to 1. The same symbol in different chapters has essentially the same meaning with one major exception: x, y, ... mean quite different things in different chapters. I am indebted to many people for their help and encouragement.
Introduction to the Theory of Cooperative Games
Author: Bezalel Peleg
Publisher: Springer Science & Business Media
ISBN: 3540729453
Category : Business & Economics
Languages : en
Pages : 336
Book Description
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.
Publisher: Springer Science & Business Media
ISBN: 3540729453
Category : Business & Economics
Languages : en
Pages : 336
Book Description
This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.