Normal view MARC view

Decision theory: an introduction to the mathematics of rationality

Author: French, Simon Series: Mathematics and its applications Publisher: 1988Language: EnglishDescription: 448p. ; 24 cm.ISBN: 0470210915Type of document: BookBibliography/Index: Includes bibliographical references and index
Tags: No tags from this library for this title. Log in to add tags.
Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print T58.62 .F74 1988
(Browse shelf)
001266665
Checked out 20/05/2022 001266665
Total holds: 0

Includes bibliographical references and index

Digitized

Decision Theory An Introduction to the Mathematics of Rationality Table of Contents Preface ................................................................................................... 9 Chapter 1 DECISION PROBLEMS ........................................................... 13 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Preamble ....................................................................... The Allais paradox.......................................................... Minimax regret .............................................................. Independence of preferences .......................................... Preferences over time ..................................................... The St. Petersburg paradox............................................. The Borda count ............................................................ Real decision problems .................................................. Terminology and organisation of the book . .................... 13 14 16 18 18 22 23 24 27 1.10 General reading............................................................ 29 1.11 Problems ..................................................................... 30 Chapter 2 DECISIONS UNDER STRICT UNCERTAINTY. . 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Introduction .................................................................. Decision tables .............................................................. Four criteria .................................................................. Some reasonable properties............................................ Analysis of the criteria ................................................... References and further reading....................................... Problems ....................................................................... 32 32 33 36 39 46 56 57 Chapter 3 PREFERENCE ORDERS AND VALUE FUNCTIONS ........................................................................ 61 3.1 Introduction .................................................................. 61 3.2 Strict preference and indifference ................................... 62 3.3 Sets and relations ....................................................... 3.4 Weak preference.......................................................... 3.5 Indifference classes ..................................................... 3.6 Ordinal value theory ................................................... 3.7 Value difference measurement .................................... 3.8 Descriptive models of preference ................................. 3.9 References and further reading.................................... 3.10 Problems ................................................................... 66 69 73 74 82 92 96 96 Chapter 4 MULTI-ATTRIBUTE VALUE THEORY . . . ........................... 102 4.1 Introduction .............................................................. 4.2 Structuring of objectives and multi-attribute value functions ..................................................... 4.3 Preferential independence of two attributes . ............. 4.4 Additive value theory over two attributes . . ............... 4.5 Three or more attributes............................................ 4.6 Concavity and convexity............................................. 4.7 Allocation problems ................................................... 4.8 Linear value functions ............................................... 4.9 Discounting over time................................................ 4.10 Examination assessment ......................................... 4.11 Efficiency and Pareto optimality .............................. 4.12 References and further reading................................ 4.13 Problems 102 103 106 109 117 121 122 128 133 138 141 143 144 Chapter 5 UTILITY THEORY .............................................................. 149 5.1 Introduction .............................................................. 149 5.2 Preferences over lotteries............................................ 151 5.3 Decision tables, decision analysis and utility functions ................................................................ 163 5.4 Bayesian decision analysis I....................................... 168 5.5 Risk attitudes............................................................ 175 5.6 Multi-attribute utility theory ..................................... 182 5.7 Preferences over uncertain timestreams. . . ............... 191 5.8 Discussion................................................................. 196 5.9 References and further reading.................................. 202 5.10 Problems ................................................................. 204 Chapter 6 OBJECTIVE AND SUBJECTIVE PROBABILITY ................... 210 6.1 6.2 6.3 6.4 6.5 6.6 Introduction .............................................................. Random events and mathematical probability ........... The classical notion of probability ............................. The frequentist approach .......................................... Subjective probability................................................. A comparison of views ............................................... 210 211 217 220 222 232 6.7 Bayesian decision analysis II ..................................... 6.8 Bayes' theorem and the revision of belief . 6.9 Frequentist statistics or Bayesian statistics? . ............ 6.10 References and further reading................................. 6.11 Problems ................................................................. 237 244 247 253 255 Chapter 7 DECISION TREES AND MULTI-STAGE PROBLEMS ..................................................................... 259 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Introduction .............................................................. Decision trees ............................................................ Analysis of simple decision trees ................................ The synthesis and value of information. . . ................. Policies, decision trees and decision tables. . .............. References and further reading................................... Problems ................................................................... 259 260 264 267 274 276 277 280 Chapter 8 GROUP DECISIONS AND SOCIAL CHOICE . . 8.1 Introduction .............................................................. 280 8.2 Arrow's theorem ........................................................ 282 8.3 Group value functions and interpersonal comparisons ........................................................... 288 8.4 Pareto optimality and bargaining sets . . . . 298 8.5 Nash bargaining and arbitration ................................ 304 8.6 Game theory and conflict ........................................... 315 8.7 References and further reading................................... 319 8.8 Problems ................................................................... 320 Chapter 9 MEASUREMENT, MODELLING AND INTERPRETATION ..... 324 9.1 9.2 9.3 9.4 9.5 Introduction .............................................................. 324 Measurement theory and meaningfulness . . . 325 'Ordinal and cardinal utility' ...................................... 330 The need for a structured decision analysis . . 337 The guidance provided by a Bayesian decision analysis................................................................... 338 9.6 Descriptive and normative analyses ........................... 342 9.7 When a group is responsible for a decision . . 347 9.8 Some further remarks................................................ 350 Chapter 10 SOME NON-BAYESIAN APPROACHES . . . . 10.1 10.2 10.3 10.4 10.5 352 Introduction ............................................................ 352 Interactive multi-objective programming . . . 352 The analytic hierarchy process................................. 357 Fuzzy decision analysis ........................................... 361 Cost-benefit analysis ............................................... 370 Chapter 11 HINTS AND SOLUTIONS TO PROBLEMS . . ..................... 372 References ......................................................................................... 421 Symbol index ..................................................................................... 437 Author index ...................................................................................... 441 Subject index ..................................................................................... 445

There are no comments for this item.

Log in to your account to post a comment.
Koha 18.11 - INSEAD Catalogue
Home | Contact Us | What's Koha?