Decision theory: an introduction to the mathematics of rationality
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Ellis Horwood limited
1986
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| Series: | Ellis Horwood series in mathematics and its applications
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 421-436 |
| Physical Description: | 448 Seiten Illustrationen |
| ISBN: | 0853126828 0470203080 |
Staff View
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Record in the Search Index
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| adam_text | Table of Contents Preface ............................................................................................... Chapter 1 DECISION PROBLEMS........................................... 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 9 13 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 . . General reading....................................................... Problems................................................................ 13 14 16 18 18 22 23 24 27 29 30 Chapter 2 DECISIONS UNDER STRICT UNCERTAINTY. . 32 Introduction........................................................... Decision tables....................................................... Four criteria........................................................... Some reasonable properties................................... Analysis of the criteria........................................ References and further reading.............................. Problems................................................................ 32 33 36 39 46 56 57 PREFERENCE ORDERS AND VALUE
FUNCTIONS............................................................... 61 3.1 3.2 61 62 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Chapter 3 Introduction.......................................................... Strict preference and indifference........................ 5
Contents 6 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Chapter 4 MULTI-ATTRIBUTE VALUE THEORY 102 Introduction............................................................ Structuring of objectives and multi-attribute value functions...................................................... Preferential independence of two attributes . . Additive value theory over twoattributes . . . Three or more attributes....................................... Concavity and convexity....................................... Allocation problems........................................... Linear value functions....................................... Discounting over time........................................... Examination assessment....................................... Efficiency and Pareto optimality........................ References and further reading............................. Problems............................................................... 102 UTILITY THEORY..................................................... 149 5.1 5.2 5.3 149 151 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Chapter 6 66 69 73 74 82 92 96 96 .... 4.1 4.2 Chapters Sets and relations.................................................. Weak preference....................................................... Indifference classes.................................................. Ordinal value theory............................................. Value difference measurement............................... Descriptive models of preference.......................... References and further reading...............................
Problems................................................................ 103 106 109 117 121 122 128 133 138 141 143 144 Introduction.......................................................... Preferences over lotteries....................................... Decision tables, decision analysis and utility functions............................................................... 5.4 Bayesian decision analysis 1.................................. 5.5 Risk attitudes.......................................................... 5.6 Multi-attribute utility theory............................. 5.7 Preferences over uncertain timestreams. . . . 5.8 Discussion............................................................... 5.9 References and further reading............................. 5.10 Problems............................................................... 163 168 175 182 191 196 202 204 OBJECTIVE AND SUBJECTIVE PROBABILITY . 210 Introduction.......................................................... Random events and mathematical probability . The classical notion of probability................... The frequentisi approach................................. Subjective probability........................................... A comparison of views...................................... 210 211 217 220 222 232 6.1 6.2 6.3 6.4 6.5 6.6
7 Contents Bayesian decision analysis II............................ Bayes’ theorem and the revisionof belief . . . Frequentisi statistics or Bayesianstatistics? . . References and further reading............................ Problems.............................................................. 237 244 247 253 255 DECISION TREES AND MULTI-STAGE PROBLEMS.............................................. 259 6.7 6.8 6.9 6.10 6.11 Chapter 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Chapters GROUP DECISIONS AND SOCIAL CHOICE . 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Chapter 9 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 . 280 282 Introduction.................................................... Arrow’s theorem.......................................... Group value functions and interpersonal comparisons................................................... Pareto optimality and bargaining sets .... Nash bargaining and arbitration.................. Game theory and conflict........................... References and further reading....................... Problems........................................................ 288 298 304 315 319 320 MEASUREMENT, MODELLING AND INTERPRETATION................................ 9.1 9.2 9.3 9.4 9.5 9.6
9.7 9.8 324 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 Descriptive and normative analyses........... 342 When a group is responsible for a decision . . 347 Some further remarks................................... 350 Chapter 10 SOME NON-BAYESIAN APPROACHES .... 10.1 10.2 10.3 10.4 10.5 Introduction................................................. Interactive multi-objective programming . . The analytic hierarchy process..................... Fuzzy decision analysis............................... Cost-benefit analysis................................... 352 352 352 . 357 361 370
8 Contents Chapter 11 HINTS AND SOLUTIONS TO PROBLEMS . . 372 References............................................................................................ 421 Symbol index................................................................... 437 Author index....................................................................................... 441 Subject index....................................................................................... 445 .
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Allgemeines Mathematik Philosophie Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:40Z |
| institution | BVB |
| isbn | 0853126828 0470203080 |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM DE-12 DE-384 DE-355 DE-BY-UBR DE-824 DE-29 DE-83 DE-188 DE-706 DE-739 |
| physical | 448 Seiten Illustrationen |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Ellis Horwood limited |
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| series2 | Ellis Horwood series in mathematics and its applications |
| spelling | French, Simon 1950- Verfasser (DE-588)170688240 aut Decision theory an introduction to the mathematics of rationality Simon French Chichester Ellis Horwood limited 1986 448 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Ellis Horwood series in mathematics and its applications Literaturverzeichnis Seite 421-436 Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 s DE-604 Statistische Entscheidungstheorie (DE-588)4077850-2 s Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304799&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | French, Simon 1950- Decision theory an introduction to the mathematics of rationality Entscheidungstheorie (DE-588)4138606-1 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| subject_GND | (DE-588)4138606-1 (DE-588)4077850-2 |
| title | Decision theory an introduction to the mathematics of rationality |
| title_auth | Decision theory an introduction to the mathematics of rationality |
| title_exact_search | Decision theory an introduction to the mathematics of rationality |
| title_full | Decision theory an introduction to the mathematics of rationality Simon French |
| title_fullStr | Decision theory an introduction to the mathematics of rationality Simon French |
| title_full_unstemmed | Decision theory an introduction to the mathematics of rationality Simon French |
| title_short | Decision theory |
| title_sort | decision theory an introduction to the mathematics of rationality |
| title_sub | an introduction to the mathematics of rationality |
| topic | Entscheidungstheorie (DE-588)4138606-1 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| topic_facet | Entscheidungstheorie Statistische Entscheidungstheorie |
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