Decision Theory: a software implementation to educe the utility function

Texto

(1)UNIVERSIDADE FEDERAL DE PERNAMBUCO. PROGRAMA DE PÓS-GRADUAÇ

(2) O EM ENGENHARIA DE PRODUÇ

(3) O. DECISION THEORY: A SOFTWARE IMPLEMENTATION TO EDUCE THE UTILITY FUNCTION. CASSIANO HENRIQUE DE ALBUQUERQUE. Supervisor: Fernando Menezes Campello de Souza, PhD. RECIFE, FEBRUARY/2011.

(4) UNIVERSIDADE FEDERAL DE PERNAMBUCO. PROGRAMA DE PÓS-GRADUAÇ

(5) O EM ENGENHARIA DE PRODUÇ

(6) O. DECISION THEORY: A SOFTWARE IMPLEMENTATION TO EDUCE THE UTILITY FUNCTION. DISSERTACION SUBMITED AT UFPE TO OBTAIN THE MASTERS DEGREE BY. CASSIANO HENRIQUE DE ALBUQUERQUE. Supervisor: Fernando Menezes Campello de Souza, PhD.. RECIFE, FEBRUARY/2011.

(7) Catalogação na fonte Bibliotecária Rosineide Mesquita Gonçalves Luz / CRB4-1361 (BCTG). A345d Albuquerque, Cassiano Henrique de. Decision Theory: a software implementation to educe the utility function / Cassiano Henrique de Albuquerque. - Recife: O Autor, 2011. xv, 135f., il., figs., gráfs.; tabs. Orientador:Profº. Dr.Fernando Menezes Campello de Souza, PHD. Dissertação (Mestrado) – Universidade Federal de Pernambuco. CTG. Programa de Pós-Graduação em Engenharia de Produção, 2011. Inclui Referências Bibliográficas e Apêndices. 1. Engenharia de Produção. 2.Teoria da Decisão. 3.Edução de Preferências. 4.Teoria da Utilidade. 5.Engenharia de Software. 6.Desenvolvimento de Sistemas I. Campello de Souza, Fernando Menezes. II. Título.. 658.5 CDD (22.ed). UFPE/BCTG-078/2011.

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(9) If I have seen further, it is by standing on the shoulders of giants. Sir Isaa Newton's.

(10) I dedi ate this dissertation to my family and friends for all understanding and support.

(11) ACKNOWLEDGEMENTS I express my gratitude, rst of all, to Jehovah God, the Creator, for giving me permission to study a little more about his reations and for making me understand the ure of our ills is rst of all in our faith.. In parti ular, i thank my advisor, Professor. Fernando Menezes Campello de Souza, PhD, for the opportunity to have passed on to me a little of his vast knowledge on de ision theory, engineering and, of ourse, of life. The ommitment and patien e I found in all the di ult moments and pre ious hours blinded by night or day, and that gradually led me to omplete this study. I greatly appre iate my parents, Laudi éia Silva da Fonse a and Jose Antnio de Albuquerque, and other relatives, for all the support and en ouragement provided throughout my a ademi life, always ontributing positively to my upbringing and edu ation.. The my wife, Maiara. Albuquerque, who is invaluable to me, by helping me always to maintain my inner pea e and harmony always in order, with love, daily support, patien e and en ouraging me nd the best way. My sin ere thanks to Lu iano Demétrio for all his support during the development of this work, parti ulary during the di ult times that we spent. I would also like to thank everyone who parti ipated in the assessment spe ially Rafaella Azevedo for taking some time from her busy s hedule and also for bringing new ideas and elu idation about this resear h. To all my friends, espe ially Cristiano Melo, Elaine Cristina, Breno Miranda and Antonio Paulo by en ouragement and friendship during the entire master's degree. At PPGEP to olleagues for their help and the ex hange of ideas that allowed the onstru tion of this study.. At PPGEP o ials, for their kindness and help during. di ult times. I thank also prof. Roderi k Kay for tea hing me more about English, his friendliness and harisma in the CTG in our lasses on Thursdays. Finnaly I thank the CAPES - Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - for funding my post-graduate ourse.. Thanks a lot, Cassiano Henrique de Albuquerque.

(12) RESUMO A avaliação da função utilidade de um indivíduo (ou grupo de indivíduos) não é uma tarefa simples.. Aspe tos psi ológi os, teóri os e práti os intervêm neste pro esso e é. ne essário ter muito uidado na elaboração e implementação do proto olo.. A edução. (eli itação) da utilidade de a ordo om a teoria da de isão é uma tarefa que pode ser limitada devido a duas razões prin ipais: à mediação ognitiva e à falta de um suporte adequado a este m, de a ordo om a teoria de von Neumann e Morgenstern (1944). Realizou-se uma revisão das ferramentas omputa ionais existentes no ontexto de suporte a de isão. Identi ou-se os prin ipais problemas existentes para a avaliação da utilidade do de isor. Apresenta-se nesta dissertação o Sistema de Edução de Preferên ias (SEP), uma solução em termos de software que dá suporte a edução dos valores da utilidade usando apenas as hipóteses de von Neumann e Morgenstern.. No SEP foram desenvolvidos e. implementados vários algoritmos e interfa es para tornar mais fá il, rápida, agradável e onável a sistemáti a da edução da função utilidade. Eduz-se a utilidade via SEP para dinheiro e ompara-se os resultados om o método tradi ional em questionário de papel. Exempli a-se a edução multiatributo via software no ontexto de atástrofes naturais. Como onsequen ia o software minimiza os problemas inerentes ao pro esso de edução omo mostrado nos experimentos práti os ao longo desta dissertação. Palavras Chaves:. Edução de Preferên ias, Teoria da Utilidade, Teoria da De isão,. Engenharia de Software, Desenvolvimento de Sistemas..

(13) ABSTRACT The utility measurement of a person (or group of persons) is not a simple task. Ea h presents its own olle tion of psy hologi al, theoreti al and pra ti al problems and for this reason is ne essary to have very areful in formulating and implementing the proto ol. The edu tion (eli itation) of utility in de ision theory is a task that an be limited for two main reasons: ognitive mediation and the la k of adequate support to this task in a ordan e with the theory of von Neumann and Morgenstern (1944). A review of existing omputational tools is made in the de ision support ontext. The main problems for the utility evaluation of the de ision maker was identied.. In this thesis is presented the. System for Edu tion of Preferen es (SEP), a software solution that supports the edu tion of the utility values using only the hypotheses of von Neumann and Morgenstern.. In. the SEP were developed and implemented some algorithms and interfa es to make easy, enjoyable, fast and reliable the task of utility edu tion . Some experiment are made via SEP to edu e the Utility value for money and the results are ompares with the traditional method in the paper questionnaire.. Other experiment exemplies the multiattribute. utility edu tion by software in disasters ontext. As onsequen e the software minimizes the problems of edu tion pro ess as shown in pra ti al experiments in this dissertation.. Keywords:. Edu tion of Preferen es, Utility Theory, De ision Theory, Software En-. gineering, Computer Systems Development..

(14) List of Figures 2.1. Graphi al results (roulette)utility for money edu tion pro edure (DM-2). 31. 2.2. Graphi al results (roulette)utility for money edu tion pro edure (DM-7). 31. 2.3. Graphi al results (roulette)utility for money edu tion pro edure (DM-10). 32. 2.4. Graphi al results (roulette)utility for money edu tion pro edure (DM-69). 32. 2.5. Graphi al results (roulette)utility for money edu tion pro edure (DM-82). 33. 2.6. Graphi al results(roulette)-utility for money edu tion pro edure (DM-122). 33. 2.7. Graphi al results(roulette)-utility for money edu tion pro edure (DM-225). 34. 2.8. Graphi al results(roulette)-utility for money edu tion pro edure (DM-232). 34. 2.9. Results of utility for money edu tion pro edure for awless DM. . . . . . .. 35. 2.10 Results of utility for money edu tion pro edure- DM utilityalmostnoiseless.. 36. 3.1. Ve torial Payo an onsist of Variables, Attributes and/or Aspe ts . . . .. 46. 3.2. A Rational Agent and the Utility. . . . . . . . . . . . . . . . . . . . . . . .. 49. 3.3. Ways to show a lottery to the de ision maker . . . . . . . . . . . . . . . . .. 54. 3.4. Utility fun tion example for risk neutral de ision makers. . . . . . . . . . .. 58. 3.5. Utility fun tion example for risk prone de ision makers. . . . . . . . . . . .. 59. 3.6. A quadrati and a 4th degree utility fun tion (Con ave Shape).. . . . . . .. 60. 3.7. Utility fun tions for risk averse de ision makers. . . . . . . . . . . . . . . .. 61. 3.8. Utility fun tions for risk prone de ision makers.. . . . . . . . . . . . . . . .. 61. 4.1. The evolutionary-delivery model . . . . . . . . . . . . . . . . . . . . . . . .. 66. 4.2. The MVC pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68. 4.3. The division of payo set in overlap tra ks. 70. 4.4. The preferen es alibration on edu tion pro ess. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 72.

(15) 4.5. The input of indieren e value for the situations(λ) . . . . . . . . . . . . .. 73. 4.6. The ow hart of SEP a tivities. 76. 4.7. A De ision Maker Validation s reen on SEP. . . . . . . . . . . . . . . . . .. 77. 4.8. The main SEP s reen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77. 4.9. SEP The rst step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78. . . . . . . . . . . . . . . . . . . . . . . . .. 4.10 SEP The se ond step (part 1). . . . . . . . . . . . . . . . . . . . . . . .. 79. 4.11 SEP The se ond step (part 2). . . . . . . . . . . . . . . . . . . . . . . .. 80. . . . . . . . . . . . . . . . . . . . . . . . . . .. 81. 4.12 SEP - The nal step s reen. 4.13 SEP - The graph step s reen: utility values X payos. . . . . . . . . . . . .. 82. 4.14 SEP - Metri s of Development . . . . . . . . . . . . . . . . . . . . . . . . .. 83. 5.1. Graphi al results (paper)utility for money on edu tion pro edure (DM-1). 85. 5.2. Graphi al results (SEP)utility for money on edu tion pro edure (DM-1). 85. 5.3. Graphi al results (paper)utility for money on edu tion pro edure (DM-2). 86. 5.4. Graphi al results (SEP)utility for money on edu tion pro edure (DM-2). 86. 5.5. Graphi al results (paper)utility for money on edu tion pro edure (DM-3). 87. 5.6. Graphi al results (SEP)utility for money on edu tion pro edure (DM-3). 87. 5.7. Graphi al results (paper)utility for money on edu tion pro edure (DM-4). 88. 5.8. Graphi al results (SEP)utility for money on edu tion pro edure (DM-4). 88. 5.9. Graphi al results (paper)utility for money on edu tion pro edure (DM-5). 89. 5.10 Graphi al results (SEP)utility for money on edu tion pro edure (DM-5). 89. 5.11 Graphi al results (SEP)multi-attribute utility for desasters(DM-1) . . . .. 92. B.1. The main SEP s reen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130. B.2. SEP The rst step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131. B.3. SEP The se ond step (part 1). . . . . . . . . . . . . . . . . . . . . . . . 132. B.4. SEP The se ond step (part 2). . . . . . . . . . . . . . . . . . . . . . . . 132. B.5. The preferen es alibration on edu tion pro ess. B.6. The input of indieren e value for the situations(λ) . . . . . . . . . . . . . 134. B.7. SEP - The nal step s reen. B.8. SEP - The graph step s reen: utility values X payos. . . . . . . . . . . . . . . . 133. . . . . . . . . . . . . . . . . . . . . . . . . . . 135 . . . . . . . . . . . . 135.

(16) List of Tables 2.1. Serious onsequen es of de isions made without parameters.. . . . . . . . .. 23. 2.2. Questionnaire on utility edu tion for money. . . . . . . . . . . . . . . . . .. 29. 3.1. Standard-Gamble Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55. 5.1. Payo set. 91. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

(17) List of Abbreviations DSS. De ision Support System. SEP. System for Edu tion of Preferen es. DM. De ision Maker. PL/I. Programming Language One. SQL. Stru tured Query Language. JAVA. Programming Language. COBOL. Common Business-Oriented Language. MVC. Model View Controller. UML. Unied Modeling Language. MANECON. Program for De ision Analysis Mono Obje tive. MAUT. Multi Attribute Utility Theory. MUFCAP. Multiattribute Utility Fun tion Cal ulation and Assessment Program. GUI. Graphi al User Interfa e. ICOPSS. Intera tive Computer Program for Subje tive Systems. FORTRAN. Imperative Programming Language. MAP. Multiattribute Utility Analysis Program. MIDASS. Multi Intera tive De ision Analysis Support Systems. MOE. Multiattribute Out omes Evaluator. DFS. Depth rst sear h.

(18) Contents 1 INTRODUCTION. 16. 1.1. Justi ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17. 1.2. Obje tives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20. 1.2.1. General Obje tive . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20. 1.2.2. Spe i Obje tives. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20. 1.3. Basi Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20. 1.4. Work Organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21. 2 THE PROBLEMS. 22. 2.1. Problem 1 Cognitive Mediation . . . . . . . . . . . . . . . . . . . . . . .. 24. 2.2. Problem 2 The Quality of the Edu tion Pro edure . . . . . . . . . . . .. 26. 2.2.1. 27. Usual Approa hes . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 THEORETICAL BACKGROUND 3.1. 37. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38. 3.1.1. De ision Theory and Utility Theory . . . . . . . . . . . . . . . . . .. 38. 3.1.2. Software Implementations. . . . . . . . . . . . . . . . . . . . . . . .. 38. 3.1.3. DSS Approa hes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40. 3.2. Preferen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41. 3.3. De ision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43. 3.3.1. . . . . . . . . . . . . . . . . . . .. 44. Utility Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48. 3.4.1. The Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50. 3.4.2. Constru tion of Utility Fun tion . . . . . . . . . . . . . . . . . . . .. 52. 3.4. Stru ture of Set of Consequen es.

(19) 3.5. 3.6. Methods for Edu ing the Utility Fun tion. . . . . . . . . . . . . . . . . . .. 53. 3.5.1. Preferen es Relationship . . . . . . . . . . . . . . . . . . . . . . . .. 54. 3.5.2. Standard Gamble methods . . . . . . . . . . . . . . . . . . . . . . .. 54. Risk Attitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 3.6.1. Risk Averse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 3.6.2. Risk Neutral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 3.6.3. Risk Prone. 58. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 SEP A COMPUTATIONAL SOLUTION 4.1. 4.2. 4.3. 62. SEP Te hnologies and Tools. . . . . . . . . . . . . . . . . . . . . . . . .. 63. 4.1.1. Programming Language. . . . . . . . . . . . . . . . . . . . . . . . .. 64. 4.1.2. Software Development Pro ess . . . . . . . . . . . . . . . . . . . . .. 65. 4.1.3. Design Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67. SEP Elaborating the Algorithms . . . . . . . . . . . . . . . . . . . . . .. 68. 4.2.1. Sorting the Preferen es . . . . . . . . . . . . . . . . . . . . . . . . .. 69. 4.2.2. Generating the overlapping tra ks . . . . . . . . . . . . . . . . . . .. 70. 4.2.3. Edu ing the Utility . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71. Introdu ing the System for Edu ing Preferen es. . . . . . . . . . . . . . . .. 73. 4.3.1. Software Operation . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75. 4.3.2. Step 01 - Variables, Attributes or Aspe ts. . . . . . . . . . . . . . .. 78. 4.3.3. Step 02 - Items and Order . . . . . . . . . . . . . . . . . . . . . . .. 78. 4.3.4. Step 03 - Edu tion. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79. 4.3.5. Step 04 - Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81. 4.3.6. SEP - Metri s of Development . . . . . . . . . . . . . . . . . . . . .. 82. 5 EDUCING EXAMPLES 5.1. 5.2. Utility for Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84. 5.1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84. Multi-Attribute Utility for Disasters . . . . . . . . . . . . . . . . . . . . . .. 90. Experiment. 6 COMMENTS, CONCLUSIONS AND SUGGESTIONS 6.1. 84. Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93 94.

(20) 6.2. Con lusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96. 6.3. Suggestions for Future Studies . . . . . . . . . . . . . . . . . . . . . . . . .. 97. Referen es A Appendix A.1. 99 104. Edução da Função Utilidade para Dinheiro V. 9. B Appendix B.1. . . . . . . . . . . . . . 104. 128. A Tutorial Guide to Using SEP. . . . . . . . . . . . . . . . . . . . . . . . . 128. B.1.1. System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 128. B.1.2. Version/Li ense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128. B.1.3. For whom is this software? . . . . . . . . . . . . . . . . . . . . . . . 129. B.1.4. Exe uting and Removing SEP . . . . . . . . . . . . . . . . . . . . . 129. B.1.5. Using SEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129.

(21) INTRODUCTION. 1 INTRODUCTION A in erteza é a mar a indelével do universo. Fernando Menezes Campello de Souza All of us are de ision-makers. No matter if the de isions are simple or omplex, the reality is that we make de isions all the times and for dierent purposes, for example: what to eat, what to wear, where to spend the holidays, should we open a new bran h o e on site X, should I go to war with ountry Y; the questions are endless. The study of de ision making embra es normative, pres riptive and des riptive areas and has strong theoreti al links to the assumption of e onomi rationality and all its derivations (Seo et al. , 2007). Unfortunately, de ision makers almost never have a ess to the whole truth about their environment. They must, therefore, a t under un ertainty (Campello de Souza, 2007b). The presen e of un ertainty greatly hanges the way an agent makes de isions. A de ision maker is a logi al agent and typi ally has a goal and arries out any plan that is guaranteed to a hieve it. An a tion an be sele ted or reje ted on the basis of whether it a hieves the best onsequen e (goal, payo ) for him, regardless of what other a tions might a hieve (Almeida, 2002). To make su h hoi es, an agent must rst have preferen es between the dierent possible out omes of various plans.. A parti ular out ome is a ompletely spe ied state.. Typi ally, utility theory is used to represent and reason with preferen es.. 1. De ision anal-. ysis under un ertainty provides a framework of well dened rules to hoose an optimal strategy from among un ertain alternatives, where the variation in the risk attitude of the De ision Maker (DM), or the evaluator, should be taken into a ount. Utility Theory has been developed to ope with su h situations on an axiomati basis. Utility theory, however, pla es a burden on DM to assess with a onsisten y not only subje tive probabilities but also numeri al utility fun tions. In order to ondu t both evaluations deliberately, the de ision-maker should be supported with e ient tools. The measurement of the utility fun tion of an individual or group of individuals is not easy. It presents its own olle tion of psy hologi al, theoreti al and pra ti al problems 1 The. term utility is not used here in the sense of the quality of being useful. 16.

(22) INTRODUCTION and for this reason should not be undertaken lightly (Hull & H., 1973).. The edu tion. (eli itation) of utility in de ision theory is a limited task for two main reasons: ognitive mediation and the la k of an adequate support to this task in a ordan e with the theory of Von Neumann and Morgenstern (1944). The methods and softwares found in the literature to support the utility edu tion problem onsist of initially assessing a utility fun tion for ea h attribute and the aggregation of multiattribute (multiobje tive) utility onstru tion is done based on axioms of independen e among the attributes. Dierently from this, the solution developed in this dissertation (in software terms) rst edu es the utility values, using only the assumptions of Von Neumann and Morgenstern(1944), and thereafter, the values an be tted to generate the utility fun tion. The program developed in this resear h is not a ompetition between the existing software that implements the methods of multi riteria de ision, but the unpre edented onstru tion of an preferen es system edu ing based on the axiomati theory of von Neumann and Morgenstern(1944). The developed system supports any type of input dis rete data and its validation and has been - in terms of tests - were performed in the ontext mono obje tive (edu tion of the utility for money) and multiobje tive (edu ation of the utility for disasters). As result the software developed mitigates the main problems in edu ing utility fun tions namely: psy hologi al an horage, representativeness, la k of immediate feedba k to the de ision maker, la k of pre ision ontrol, distorted per eption of probabilities, and poor interfa e between the de ision maker and the analyst.. 1.1 Justi ation Making de isions is a omplex task. There is a need to think about how to assess preferen es. It is an abstra t (subje tive) and di ult task to onstru t and measure desires. The use of the utility fun tion in de ision-making is widely studied be ause of its relevan e (Russel & Norvig, 2010). To understand how de isions are made and what things inuen e the de ision making pro ess it is very important to have a me hanism to assist this pro ess. In pra ti e, this step onsists of interviews and ompiling questionnaires on 17.

(23) INTRODUCTION paper or ard, rst to obtain hara teristi s of the utility fun tion and, subsequently, to obtain the points ne essary for estimating the fun tion. In most ases the existing omputational support for this task omes down to spreadsheets. As a onsequen e, there is impre ision in the edu tion of utilities with a bias and intransigen e to wards the axioms of utility fun tion. The quality of de isions taken by de ision makers is often questioned be ause of the disastrous and ostly onsequen es that are generated in many ases. For example, we have ases in whi h ompanies pay for expensive re-work brought about by de isions being taken hastily by their managers (de ision makers in general). The study of the utility fun tion reveals two major lasses of problems namely: problems of ognitive mediation (Psy hologi al an horage, and problems of quality in the edu tion pro ess. The me ganisms of ognitive mediation are intrinsi to humans. Tversky and Daniel (1974). argued that the problems of mediating ognitively are based on three heuristi s. employed when judgments are made under un ertainty: (i) representativeness; (ii) availability of instan es or s enarios; and (iii) adjustment from an an hor. These heuristi s lead, to systemati and predi table errors. A better understanding of these heuristi s and of the biases to whi h they lead ould improve judgments and de isions in situations of un ertainty. It is lear what has happened in most ases when there is la k of support for de ision making in middle management, as it is very rare to nd a software program that assists in planning and organizing de ision-making and yet an edu e the real de ision-maker preferen es in question.. Real examples in Correa & Mano(2005) shown that wrong. de isions an lead ompanies to extensive losses, sin e the risk of making a de ision based solely on the limited per eption of an individual (or a group) is huge. However, in addition to nan ial risk, losses of strategi high magnitude losses may be in urred. Futhermore, it is ommon for de isions to be taken without taking into a ount the a tual preferen es organization, or that situations of Tradeos 2 situations. 2. (Keeney, 1976). A logi al. that involves losing one quality or aspe t of something in return for gaining another quality or aspe t. It implies a de ision to be made with full omprehension of both the upside and downside of a parti ular hoi e. 18.

(24) INTRODUCTION de ision must be supported by rational behavior, respe ting the axioms of rationality proposed by Von Neumann and Morgestern (1944).. Developing a tool that aids the. pro ess of edu ting preferen es and therefore an measure the utility fun tion of de ision makers is a ru ial task given the la k of tools in this regard. This tool should be easy to use and have a high redibility in terms of mathemati s and s ien e. However, the vast majority of existing tools in terms of software, make this task ad ho partly or totally disregarding the axioms of the theory (Almeida, 2010). This leads to loss of reliability, redibility and the s ienti basis. Problems regarding the quality of the pro ess of edu tion is another ategory that may be riti al in the task of edu ation of the utility fun tion. They involves questions like: Di ulty of elaborating the edu tion proto ol; Di ulty of answering the proto ol be ause be ause human beings are prone to failures of reasoning due to variables su h as fatigue and stress level; Cognitive Di ulty - Many resear hes illustrates this problem and indi ates that storage apa ity of a young adult is among 5 and 9 elements; Di ulty Feedba k - the traditional method (without the support of a spe i software) is slow and does not allow immediate feedba k of the behavior of the de ision makers (Tversky & Kahneman, 1974; Miller, 1956; Campello de Souza, 2007 ). Laudon(2004) said that a system ould assist the management de ision pro ess, ombining data, tools and sophisti ated analyti al models and user-friendly software in a single powerful system that an support semi-stru tured and unstru tured de ision making. In addition, a system provides users with a exible set of tools and apabilities to analyze data that are not present or in appli ations and tools. By using me hanisms of ontrol, a system an minimize the problem of having enough psy hologi al an hor for example and ontribute to de reasing the bias in the pro ess of edu tion of the de ision maker's preferen es.. A System for Edu tion of Preferen es(SEP) works with types of. de isions linked to many variables whi h are very often di ult to ontrol.. Its aim is. to provide support to solve unusual problems, marked by innovation and un ertainty (Mintzberg, 1976). Due to this, an implementation of a system for edu ing preferen es is proposed. The system for edu tion of preferen es is developed to provide an environment-friendly inter-. 19.

(25) INTRODUCTION fa e for edu ing user's preferen es towards risky alternatives using a variety of de ision theory methods (Moraes, 2003). By helping the de ision maker, the resulting utility measures an be found, and lead to this personal utility fun tion by using these data.. 1.2 Obje tives 1.2.1 General Obje tive To develop and implement a software to support the edu tion of preferen es due to intrinsi problems the task of preferen es edu tion in paper questionnaire su h as: psy hologi al an horage, representativeness, la k of immediate feedba k to the de ision maker, la k of pre ision ontrol, distorted per eption of probabilities, and poor interfa e between the de ision maker and the analyst;. 1.2.2 Spe i Obje tives 1. To apply omputer te hniques to fa ilitate and in rease the study of preferen es in the ontext of the Utility Theory put forward by von Neumann and Morgenstern be ause it is the only theory of mathemati al and axiomati basis for supporting this task;. 2. To develop and implement algorithms for sorting preferen es;. 3. To implement a algorithm for edu ing preferen es;. 4. To make experiments of preferen es edu tion via the software developed and ompares the results with the traditional method in paper questionnaires and/or spreadsheets;. 1.3 Basi Methodology There are an innite number of dierent things to onsider before de iding on systems and some of them are of major importan e in our lives.. 20. Spe ial attention is paid in.

(26) INTRODUCTION the resear h undertaken to reate a software to support the de ision-makers to assess this preferen es rationally. In the ase of the edu tion of utility fun tion, the algorithms shown in. Campello de Souza (2007b) was applied. This algorithm is alled overlapped traps. and works with adja ent values. This te hnique of Utility Theory is used to measure the de ision maker preferen es. Computational tools are used to implement a system to assess preferen es. The assessment of methods applied in this study require simulations with dierent s enarios that des ribe dierent agents, in dierent situations. More referen es will be presented throughout the text.. 1.4 Work Organization This hapter sets out the justi ation, the obje tives and the main a ademi approa h and in ludes a dis ussion of the methodology and a brief review of the literature. Chapter 2 presents the problems formally. Chapter 3 presents some on epts on erning the ba kground of De ision, Utility and Softwares that urrently exist. Chapter 4 presents the omputational solution proposed and developed with omputational tools and re ent te hnologies. Chapter 5 presents some edu ing examples via software. Chapter 6 presents on lusions and suggestions for future studies.. This dissertation uses the De ision Theory ontext. The book Rational De isions in Situations of Un ertainty,. Campello de Souza (2007b) is re ommended to absorb the. ontents proposed in this work more thoroughly. The next hapter des ribe the two main problems that o ur in the utility edu tion pro ess that prompted the omputational solution proposed in this dissertation.. 21.

(27) THE PROBLEMS. 2 THE PROBLEMS. Do you want to sell sugar water for the rest of your life, or do you want to ome with me and hange the world?. Steve Jobs (Apple CEO) to John S ulley from Pepsi-Cola ompany. A ording to Campello de Souza (2007b), the fundamental aspe t in the appli ation of de ision theory is the representation of the de ision maker's preferen es regarding the onsequen es of his a tions.. This mathemati al representation is a hieved by means. of a von Neumann-Morgentern utility fun tion.. In order to get to this mathemati al. representation it is ne essary to make an edu tion of the de ision maker' preferen es; it is ne essary to edu e his preferen es. This is done via an edu tion proto ol. But this task has two main problems: ognitive mediation and the quality of the edu tion pro edure.. The De ision Making Pro ess People are fa ed with de isions every day. This task an be quite di ult, spe ially if it involves many dierents paraments. It is extremely important that de isions ree t the personal preferen es of the de ision-maker in question, sin e this will ree t his well-being and satisfa tion. Table 2.1 exemplies de isions made empiri ally and/or hastily, without taking into a ount the real preferen es of de ision-maker, this an be atastrophi .. A brief dis-. ussion on the global business s enario brings us several examples of how the la k of parameters and a ting on impulse in de ision-making an be disruptive to a ompany. In this ontext the theory of utility fun tion rank the benets that are available to a person in making a de ision in a ordan e with the satisfa tion that it will bring. In a de ision, the out ome is un ertain, unknown. The de ision-maker should adopt a strategy to make his expe tation that of a hieving maximum benet possible. However, one an say that players have dierent proles. Some prefer to risk more than to avoid losing if this provides the possibility of high earnings. Others prefer to risk less than to losing even if this means less prot. The utility fun tion of a player expresses his aversion to risk (Campello de Souza, 2007b). 22.

(28) THE PROBLEMS Table 2.1:. Serious onsequen es of de isions made without parameters.. COMPANY Mer edesBenz. DECISION Installing a fa tory for the produ tion of a Class A ar in Juiz de Fora, MG, Brazil. General Mo- Signing an agreement tors with Ameri an autoworkers to ensure stable employment and health insuran e and oered private pensions that were too generous Mer k Selling the antiinammatory Vioxx knowing that it ould ause ardiovas ular disorders HP A quisition of rival Compaq. MISTAKE Wrongly sizing the market and brought a automobile that did not please Brazilians Not realize that longterm agreement limits the ompany and auses a high nan ial loss. COST $ 500 million (Estimated loss). Belittled the problem. Just pulled Vioxx o the shelves when there was no alternative after one year. The merger of the ompanies did not work. Sales have doubled but prots remained un hanged. Buying a Mi rosoft IBM did not foreoperating system to see they would be ome equip their personal hostage to Mi rosoft omputers. $ 28 billion (Fall in market value of Mer k between August 2004 and the end of 2005). ©. IBM. ©. Sour e: Revista Exame,2005.. $ 5.6 billion (Annual expenditures with health insuran e and pensions). $ 19 billion (Amount of pur hase) $ 75 billion (Loss of market value of IBM between the 80's and 90's). The study of the utility fun tion reveals two major lasses of problems namely: problems of ognitive mediation and problems of quality in the edu tion pro ess. This problems will be examined below.. 23.

(29) 2.1 Problem 1 Cognitive Mediation. THE PROBLEMS. As des ribed in Psy hology(2010) Cognitive mediation at its most basi is the o uren e of ognitive pro esses after the presentation of a stimulus su h that subsequent response behavior is altered. It indi ates su h fun tions or pro esses as per eption, introspe tion, memory, imagination, on eption, belief, reasoning, volition, and emotion. So ognitive pro esses are those involved in the a quiring, pro essing and using knowledge and information. De ision making is the ognitive pro ess leading to the sele tion of a ourse of a tion among alternatives. Every de ision making pro ess produ es a nal hoi e. It an be an a tion or an opinion. It begins when we need to do something but we do not know what. Therefore, de ision making is a reasoning pro ess whi h an be rational or irrational, and an be based on expli it assumptions or ta it assumptions. Common examples in lude de iding what to eat, what to wear, where to spend the holidays, should a new bran h o e be opened on site X, should i go to war with ountry Y. De ision making an be dened as a psy hologi al onstru t be ause the de ision to do annot be seen.. What the de ision shows is the observable behavior after that the. de ision has been made.. Therefore, it is on luded that a psy hologi al event alled. de ision making has o urred. From observable a tions, it is assumed that people have made a ommitment to bring the a tion about.. Stru tured rational de ision making is an important part of all s ien e-based professions, where spe ialists apply their knowledge in a given area to making informed de isions. For example, medi al de ision making often involves making a diagnosis and sele ting an appropriate treatment. Some resear h using naturalisti methods shows, however, that in situations with higher time pressure, higher stakes, or in reased ambiguities, experts use intuitive de ision making rather than stru tured approa hes, following a re ognition primed de ision approa h to t a set of indi ators into the expert's experien e and immediately arrive at a satisfa tory. 24.

(30) THE PROBLEMS ourse of a tion without weighing alternatives. Due to the large number of onsiderations involved in many de isions, omputerbased de ision support systems have been developed to assist de ision makers in onsidering the impli ations of various ourses of thinking. They an help redu e the risk of human errors.. De ision Making(2010) A heuristi is a strategy that an be applied to a variety of problems and that usually but not always yields a orre t solution. People often use heuristi s (or short uts) to redu e omplex problem solving to more simple judgmental operations. Three of the most popular heuristi s are dis ussed by Tversky and Kahnemann (1974):. . Heuristi of representativeness. What is the probability that person A (Steve,. a very shy and withdrawn man) belongs to group B (librarians) or C (exoti dan ers)? In answering su h questions, people typi ally evaluate the probabilities by the degree to whi h A is representative of B or C (Steve's shyness seems to be more representative for librarians than for exoti dan ers) and sometimes negle t base rates (there are far more exoti dan ers than librarians in a ertain sample).. . Heuristi of availability. This heuristi is used to evaluate the frequen y or. likelihood of an event on the basis of how qui kly instan es or asso iations ome to mind. When examples or asso iations are easily brought to mind, this fa t leads to an overestimation of the frequen y or likelihood of this event. Example: People overestimate the divor e rate if they an qui kly nd examples of divor ed friends.. . An horing and adjustment. People who have to make judgements under un-. ertainty use this heuristi by starting with a ertain referen e point (an hor) and then adjust it insu iently to rea h a nal on lusion.. Example: If you have to. judge another persons produ tivity, the an hor for your nal (adjusted) judgement may be your own level of produ tivity. Depending on your own level of produ tivity you might therefore underestimate or overestimate the produ tivity of this person.. 25.

(31) THE PROBLEMS One important point is that the de ision maker should have a lear per eption of what the payos are. They ought to have meaning for the de ision maker. If this is not so, there will be little sense in talking about his preferen es.. 2.2 Problem 2 The Quality of the Edu tion Pro edure In the very proof of the existen e of a utility fun tion, based on a set of axioms, von Neumann and Morgenstern dened what a utility fun tion is:. u(C) = Sup {λ ∈ (0, 1) | C ≻ λC + (1 − λ)C}.. (2.2.1). Dire tly from Denition 3.2.1 above emerges an edu tion proto ol. One asks the de ision maker to announ e what is the value of the distribution. C. λ. for whi h he is indierent between re eiving. for sure, or the game, the ompound lottery. announ ed will be, for the de ision maker, the utility of. C. λC + (1 − λ)C .. in the s ale. [C, C].. The value. More details. an be found in Campello de Souza (2007b). In the pra ti e of edu tion several problems may appear, as, for example:. . Psy hologi al an horage. . Representativeness. . Distorted per eption of probabilities. . Aspe t va illation. . Introspe tion noise. . Several ognitive mediation issues. No matter what proto ol is used, on e the utility values are edu ed, one should analyze the result in order to evaluate the quality of the pro edure. This is usually done using statisti al analysis. The more the proto ol mitigates the aforementioned problems, the better. 26.

(32) THE PROBLEMS The la k of an immediate feedba k to the de ision maker makes it di ult to make adjustments. It is hard for him to learn about his own preferen es. This is also a sour e of impre ision in the proto ols typi ally used.. 2.2.1 Usual Approa hes. Campello de Souza(2007a) showed that the two most important aspe ts in working with a traditional paper questionnaire for the edu tion of the utility fun tion are the dif ulty of produ ing the questionnaire and the di ulty of answering it. In this kind of questionnaire, there is a number of points whose utility will be inferred. The greater the number of questions, the better eviden e we have for the analyti al modeling of the utility fun tion of the individual. But onversely, the greater the number of questions, the greater the strain on wear of the de ider and in onsequen e may be undermining the pro ess of introspe tion in the de ision maker. In the resear h of Campello de Souza(2007a) a questionnaire with 42 questions was drawn up based on Standard Gamble with Overlapping Tra ks methods as des ribed in Chapter 02. It may be noted the di ulty existed for the de ision maker to de ide between the deterministi onsequen e or the lottery result, due to problems intrinsi to human ognitive mediation. In addition there is the issue of probability with whi h it feels indierent between the situations, that is fundamental to the value of utility. This point (even if using the methods of the adja ent values), depending on the stated problem an be quite omplex onsidering the di ulty of evaluating the alternatives in a range of probability ranging from 0 to 1.. The eort to redu e this bias is noted when examining the. questionnaire shown in Table 2.2, where the order of questions is made at random. For the pro edure of edu tion to be su essful, the respondents need to understand the questions and be made to spend some time on then and to make a areful examination of their own preferen es. They need to be able to assess the un ertainty present in ea h of the situations they are exposed to. Therefore, it is essential that de ision makers understand how the values of probabilities indi ate their attitude when dealing with un ertainty. Highlighted in this stage is the importan e of edu ation and training of the de ision 27.

(33) THE PROBLEMS maker for this task (Campello de Souza, 2007a). Besides the issues of the apa ity to understand, there is still the question of the available time and personal motivation needed from ea h de ision maker to answer several questions oherently. Many other resear hers who have used De ision Theory like Berenguer (2003), Oliveira (2010), Oliveira (2010b) worked with this kind of pro edures for edu tion personal interviews, questionnaires on paper or ard sto k. Several other methods for questionnaires have already been proposed and implemented su h as using of binary lotteries as an be seen in the Annex A to this dissertation. However, the problems are the same shown in this hapter.. Some Experiments Many utility fun tion edu tion pro edures have been arried out by the Systems Engineering Group, and students from the Program of Post-Graduation in Produ tion Engineering at Federal University of Pernambu o (dis ipline: Statisti al Inferen e). In one of those, 232 people had their utility fun tions for money edu ed. Two proto ols were used: one was based on paired omparisons (and linear programming, as explained in Campello de Souza (2007b)), and the other based on Standard Gamble with Overlapping Tra ks methods (equation 2.2.1). The proto ol is in the Appendix A. In order to improve the ognitive mediation, the probabilities involved were represented by ha hured roulettes. Also, the method of standard gamble with overlapping tra ks was used, in order to get better pre ision (Campello de Souza (2007b)). Six dierent s ales were used. The interviewers (graduate students) were very areful, and some explanations were written in the questionnaire for the respondents to be more aware of the issues involved. This would have diminished the ee t of auto orrelation of the responses, due to psy hologi al an horage. The questions should have been printed on ards, presented in random order to the respondents. The range of money values used was from to. −R$20, 000.00. +R$20, 000.00. What is expe ted is that the s atterplot of the utility values versus the money values. will reveal a ertain onsistent pattern. This means that there should be no:. 28.

(34) THE PROBLEMS Table 2.2:. Questionnaire on utility edu tion for money. MAIOR PRÊMIO (R$) MENOR PRÊMIO (R$) ( om probabilidade λ) ( om probabilidade 1 − λ) 0 -15000 10000 -5000 -5000 -20000 -5000 -20000 10000 -5000 20000 5000 0 -15000 -5000 -20000 5000 -10000 0 -15000 10000 -5000 0 -15000 20000 5000 -5000 -20000 0 -15000 10000 -5000 15000 0 0 -15000 15000 0 20000 5000 20000 5000 15000 0 5000 -10000 -5000 -20000 5000 -10000 10000 -5000 10000 -5000 -5000 -20000 15000 0 5000 -10000 15000 0 5000 -10000 20000 5000 5000 -10000 5000 -10000 10000 -5000 15000 0 20000 5000 -5000 -20000 0 -15000 20000 5000 15000 0 Sour e: (Campello de Souza, 2007a).. 29. λ. PRÊMIO FIXO (R$) (quantia erta; determinísti a) -12000 7000 -7000 -19000 -3000 6500 -10000 -13000 3000 -2000 -1000 -4000 13000 -9000 -5000 6000 10000 -11000 2500 15000 19000 5500 -9500 -15000 1000 5000 2000 -18000 12000 4000 11000 -6000 10500 -8000 0 9000 14000 16000 -16000 -14000 18000 8000.

(35) THE PROBLEMS . visible trends;. . outliers;. . auto orrelations;. . jumps or empty spa es; gaps. . deterministi patterns, as if the responses to the proto ol had been al ulated;. . hetero edasti ity;. . non-monotoni ity;. . weird patterns.. Natural and unavoidable impre ision should have the shape of a noise around some more stru tured shape.. This would be the unexplained variability.. An introspe tion. noise (Campello de Souza 2007, 2007b)), whi h typi ally should be Gaussian. Variability as a whole should be explained by some regression model, either linear (in the parameters) or nonlinear. In general, the shape of the utility fun tion for money is that of an elongated. S.. Many variations of that shape are shown in Campello de Souza (2007b), hapter 13. The Figures from 2.1 to 2.7 show some of the results of the experiment.. be noted that. u(−20, 000.00) = 0. and. u(+20, 000.00) = 1;. It should. this was the nal s ale for. the presentation of the result for all respondents. Similar problems o ur in the ase of multidimensional utility edu tion. The Utility for DM 2 in Figure. 2.1 shows the following problems : auto orrelation,. gaps and non-monotoni ity.. 30.

(36) THE PROBLEMS b b. 1.0 0.9 b. 0.8. Utility 2. b. 0.7 b b. 0.5 b. 0.4 b. b. b b. b b. b b. b. b b. b b. b b. b. 0.6. b. b. 0.3 0.2 0.1 b b. b b. b. b. b b. b b. b b b. b b. b b. b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. Money Values (R$ ×1000) Figure 2.1:. Graphi al results (roulette)utility for money edu tion pro edure (DM-2). The Utility for DM 7 (Figure 2.2) shows the following problems : auto orrelation and gaps.. 1.0 0.9 b. b. b. b b. b b. b b. Utility 7. b. b. b. b. 16. 18. b. b. b. 0.8 b b. 0.7. b. b b b. 0.6 b b. 0.5 b b. 0.4. b. b. b. b b. b. 0.3 0.2 b b. 0.1 b. b. b. b. b. b. b b. b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.2:. Graphi al results (roulette)utility for money edu tion pro edure (DM-7). 31.

(37) THE PROBLEMS The Utility for DM 10 (Figure. 2.3) shows the following problems : auto orrelation. and hetero edasti ity.. b. 1.0 0.9. Utility 10. 0.8 0.7 0.6 b. 0.5 b. 0.4. b b. 0.3 b b. 0.2 0.1 b b. b. b. b. b b. b. b. b b b b. b. b b. b. b. b. b b b. b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. b b. 0. b. 2. b b. b. b. 4. b. b. 6. b b. 8. b. 10. b. 12. 14. 16. 18. 20. Money Values (R$ ×1000) Figure 2.3:. Graphi al results (roulette)utility for money edu tion pro edure (DM-10). The Utility for DM 69 (Figure 2.4) shows the following problems : hetero edasti ity.. 1.0 b. b. 0.9. Utility 69. 0.8 b. 0.7 b. 0.6. b b. 0.5. b b. b. b. 0.4 b. 0.3 b. 0.2 b. 0.1 b. b. b. b b. b b. b. b b. b b. b. b. b. b. b. b. b b b. b b. b b. b. b. b b. b b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. Money Values (R$ ×1000) Figure 2.4:. Graphi al results (roulette)utility for money edu tion pro edure (DM-69). 32.

(38) THE PROBLEMS The Utility for DM 82 (Figure. 2.5) shows the following problems :. two outliers,. auto- orrelation and hetero edasti ity.. 1.0 b. 0.9 b b. b. b. b b b b b b. 4. 6. 8. b. b. b. b b b b. b. b. 16. 18. b b. b. b b. Utility 82. 0.8 b. 0.6. b b. b. 0.7. b. b. 0.5 b b. 0.4 0.3 0.2 b. 0.1. b b. b b. b b. b. b b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.5:. Graphi al results (roulette)utility for money edu tion pro edure (DM-82). The Utility for DM 122 (Figure 2.6) shows the following problems : outlier, auto orrelation, gap and hetero edasti ity.. 1.0 b b. 0.9. b. b. b. b b. b b. b b. b b. b b. b. b. b. b b. b. b. b b b b b. b. b. b b b. b b. b b. b. 16. 18. b. b. Utility 122. 0.8 0.7 0.6 0.5 0.4 b. 0.3 b. 0.2. b. b. 0.1 b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.6:. Graphi al results(roulette)-utility for money edu tion pro edure (DM-122). 33.

(39) THE PROBLEMS The Utility for DM 225 (Figure 2.7) shows the following problems : auto- orrelation and hetero edasti ity.. 1.0 b. 0.9. Utility 225. b. 0.7. b b. b b. b. 0.8. b. b b b b. b b b b. b. b. b b. b. b. 16. 18. b b. b. b. b b. b. b. 0.6 b. 0.5 0.4. b b. 0.3 0.2. b b. b. b. b b b. b. 0.1 b b b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.7:. Graphi al results(roulette)-utility for money edu tion pro edure (DM-225). The Utility for DM 232 (Figure 2.8) shows the following problems : auto- orrelation and linearity ( ould have been al ulated).. 1.0 b. 0.9 b. Utility 232. 0.8 b b. 0.7 b. 0.6 b. 0.5 b. 0.4 0.3 b b. 0.2 0.1 b. b. b. b b. b b. b. b b. b. b. b b. b. b. b. b. b. b. b. b. b. b b. b. b. 12. 14. b. b. 16. 18. b. b. b. b b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 20. Money Values (R$ ×1000) Figure 2.8:. Graphi al results(roulette)-utility for money edu tion pro edure (DM-232). A sort of awless result would be, for instan e, the one show in the s atterplot of 34.

(40) THE PROBLEMS Figure 2.9. Of ourse a through statisti al analysis would have to be ondu ted, but it this beyond the s ope of this dissertation.. 1.0. Utility awless. 0.9 0.8 b. 0.7. b b. b. b. b b. b. b b b b. b b. b b. b. b. 16. 18. b. b. b. b. 0.6 b. 0.5 b. 0.4 b. 0.3 b. 0.2 0.1 b b. b. b. b b. b. b. b. b. b b. b. b. b. b b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.9:. Results of utility for money edu tion pro edure for awless DM.. A very small amplitude noise would result in the s atterplot of Figure 2.10, whi h orresponds to the analyti al expression:. u(p) =. where. ε. is a random variable with. 0. 1 + ε, 1 + exp(−0.25p) mean and varian e equal to. 10−6 .. In pra ti e, it is. next to impossible to get a result like this. It should be remarked that the results of this experiment were not useless, but there was a lot of work on the statisti al analysis in order to take are of all the aws mentioned. The pre ision of the obtained (estimated) utility fun tions ould have been a lot better if the edu tion proto ol had been more elaborate. The next hapter introdu es a omputational solution for the problem of utility fun tion edu tion.. 35.

(41) Utility utilityalmostnoiseless. THE PROBLEMS. 1.0 0.9 0.8 b. 0.7 b. 0.6. b. b. b. b. b b. b. b. b b b. b. b. b. b. b. b. 16. 18. b. b. b. b b. 0.5 b. 0.4 b b. 0.3 0.2 0.1 b. b b. b b. b. b. b. b. b b b. b. b. b. b. b. −20 −18 −16 −14 −12 −10 −8 −6 −4 −2. 0. 2. 4. 6. 8. 10. 12. 14. 20. Money Values (R$ ×1000) Figure 2.10:. Results of utility for money edu tion pro edure- DM utilityalmostnoiseless.. 36.

(42) THEORETICAL BACKGROUND. 3 THEORETICAL BACKGROUND. In the aair of so mu h importan e to you, wherein you ask my advi e, I annot, for want of su ient premises, advise you what to determine, but if you please I will tell you how. When those di ult ases o ur, they are di ult, hiey be ause while we have them under onsideration, all the reasons pro and on are not present to the mind at the same time; but sometimes one set present themselves, and at other times another, the rst being out of sight. Hen e the various purposes or in linations that alternatively prevail, and the un ertainty that perplexes us. To get over this, my way is to divide half a sheet of paper by a line into two olumns; writing over the one Pro, and over the other Con. Then, during three or four days onsideration, I put down under the dierent heads short hints of the dierent motives, that at dierent times o ur to me, for or against the measure. When I have thus got them all together in one view, I endeavor to estimate their respe tive weights; and where I nd two, one on ea h side, that seem equal, I strike them both out. If I nd a reason pro equal to some two reasons on, I strike out the three. If I judge some two reasons on, equal to three reasons pro, I strike out the ve; and thus pro eeding I nd at length where the balan e lies; and if, after a day or two of further onsideration, nothing new that is of importan e o urs on either side, I ome to a determination a ordingly. And, though the weight of the reasons annot be taken with the pre ision of algebrai quantities, yet when ea h is thus onsidered, separately and omparatively, and the whole lies before me, I think I an judge better, and am less liable to make a rash step, and in fa t I have found great advantage from this kind of equation, and what might be alled moral or prudential algebra. Wishing sin erely that you may determine for the best, I am ever, my dear friend, yours most ae tionately.. B. Franklin The. Von Neumann and Morgenstern (1944) utility theory is the unique onstru t. embedded in a unique hypotheti al-dedu tive (s ienti ) set up alled de ision theory des ribed in Wald (1950) and Campello de Souza (2007b).. 37.

(43) THEORETICAL BACKGROUND. 3.1 State of the Art. 3.1.1 De ision Theory and Utility Theory The issue of utility under un ertainty has a long history, and has been shown mathemati ally sin e the time of Bernoulli (1760) by using the term Average Bonus.. In. parti ular, the notion of utility, already quite old, was extended to the ase of un ertainty by. Von Neumann and Morgestern (1944), who presented an axiomati theory. that had far-rea hing onsequen es. The idea was to use theory and pra ti e in various areas of knowledge, in luding e onomi s, engineering, administration, medi ine, psy hology, et .. Keeney and Raia (1976) give a thorough introdu tion to multiattribute utility. theory (MAUT). They des ribe early omputer implementations of methods for eli iting the ne essary parameters for a multiattribute utility fun tion with aggregation methods of mono-attribute utility through a onstants s ale and in lude several examples of there appli ations of this methods. Re ently, Campello de Souza (2007b) gives more explanations about de ision theory and utility theory and their appli ations to pra ti al ontexts.. 3.1.2 Software Implementations From the beginning, de ision analysis has been supported by the parallel development of omputer programs along with the preparation of Case Manuals, whi h has fa ilitated its empiri al appli ability and largely ontributed to its general a eptan e and a knowledgment in the s ienti and business worlds.. 1. Mono Obje tive Computer programs for de ision analysis were early developed by S hlaifer(1971) and other sta of the Graduate S hool of Business Administration in Harvard University (S hlaifer, 1971). This program was named the Mane on Colle tion (MANECON). MANECON has the eminent hara teristi s of introdu ing intera tive pro esses for logi al 1 Note. that all the programs shown are based on MAUT methods where rst tests and assumptions of independen e are performed, thus oming to a stru ture for the utility fun tion (whi h in most ases is additive or multipli ative).. 38.

(44) THEORETICAL BACKGROUND thinking while sear hing for onsistent evaluation by the de ision making under un ertainty. Although there were unavoidable te hni al limitations of omputer systems in the 1960's to the early 1970's, MANECON is onsidered a good pre edent in its true sense to intera tive omputer programs for de ision theory.. The MANECON programs were. stored in the mainframe of omputer systems and operated by man-ma hine intera tions. But MANECON was developed to work with mono obje tive problems only.. Multiobje tive Afterwards, de ision analysis made great progress in multiobje tive elds.. A om-. puter program for multiattribute utility analysis was presented by Keeney and Si herman (1975), whi h is named Multiattribute Utility Fun tion Cal ulation and Assessment Program (MUFCAP). MUFCAP was a large-s ale program originally written in a stru tured language PL /I, stored in a mainframe and operated by man-ma hine(Keeney, 1976). Sakawa and Seo (1980, 1982) revised MUFCAP as a new omputer program and named Intera tive Computer Program for Subje tive Systems (ICOPSS). ICOPSS supports graphi al representations in deriving and assessing values for s aling onstants. ICOPSS has also many other userfriendly apabilities for the input of data, to all upon them for further work and to write out on the s reen. ICOPSS is written in programming language FORTRAN in a partitioned form. Another software in the multiobje tive eld is Multiattribute Utility Analysis Program (MAP) whi h is written in the obje toriented C language and operated on workstation systems. The hierar hi al properties in assessing the multiattribute utility fun tions appropriate to using the obje t onguration of C through the inheritan e relationship.. The use of GUI devi es also greatly enhan es the user friendly properties in. operations(Sakawa & Seo, 1982). The above mentioned omputer programs were onstru ted in a true sense to support multiobje tive de ision analysis be ause the programs in lude the evaluation pro esses for the value tradeos among multiple obje tives. In these programs, however, the intera tive pro esses in the logi al thinking by DM it is not intended to support. They are intera tive only in the man-ma hine sense, the same as almost all the existing omputer. 39.

(45) THEORETICAL BACKGROUND programs for de ision support. In addition, the apability for the probability assessment in un ertain de ision environments is not in luded in these programs (Seo et al. , 2007).. Modern Approa hes IDASS (Intera tive De ision Analysis Support Systems) was developed as a visual extension of MUFCAP, but if one wants de ide on un ertainty with a friendly interfa e it is ne essary to use IDASS with the MAP due to its limitation of preferen es in un ertain environments with multiple obje tives (Seo & Nishizaki, 1997). MIDASS is a su essor of IDASS and presents a good graphi al interfa e and support to multiobje tive problems in a single tool (Seo et al. , 2007). Modern appli ations work with a database and graphi al interfa e and are developed for spe i ontexts su h as Multiattribute Out omes Evaluator (MOE) that works in a medi al ontext (Swan, 2004).. 3.1.3 DSS Approa hes Methods of Multi riteria De ision Support an be lassied a ording to dierent perspe tives. Many authors lassify them a ording to the main theory in whi h they are based. In this line, two major s hools of thought are highlighted: the Ameri an S hool, whi h is based on multi riteria aggregation te hniques with single riterion synthesis, and the Fren h S hool, whi h argues that there is no single riterion aggregation of synthesis; and is based on the on ept of relationship outranking. There are also intera tive methods, and hybrid alternative. The hybrid methods are traditionally asso iated with methods that use both the on epts of the Ameri an S hool and the Fren h S hool (Almeida, 2002; Almeida, 2010). There are many other software appli ations in the ontext of de ision support systems like the ExpertChoi e, HiView, V.I.S.A., Web-Hipre, Logi al De isions and Winpre (Xu & Simon, 2004). But there is no large systemati study that shows the relationship between the axiomati de ision theory of von Neumman Morgenstern and methods of multiobje tive or multi riteria de ision, so these theories have no onne tivity and the artifa ts generated for both areas of expertise are totally distin t.. 40.

(46) THEORETICAL BACKGROUND. Edu tion versus Eli itation The word. edu e. means, a ording to Campello de Souza (2007b), to out ondu t, or. to ondu t to the outside, or to draw out (from Latin ex-du ere, e-du ere), to get, to bring to light, to evoke. To edu e what? To edu e from the depths of the mind something that is already there in a latent state, or built-in. The word edu ere is a verb omposed of the prex ex (out) + du ere (to ondu t, to take), and means literally to drive out, to lead to the outside, to bring about. That is, to prepare the individual for the world. It is the origin of the word edu are (to edu ate); to evolve or develop, espe ially from a latent or potential state. One has to be areful not to use to edu e with to eli it. There are some subtle but important dieren es. To eli it means to make something to get out, to expel, to onjure, to exor ise, to ward o, to in ite, to provoke an automati response.. That is, given a. stimulus, one has a response. The eli ited is what has been extra ted, allured, attra ted, in ited, instigated, sedu ed.. To eli it has the sense of produ ing a for ed response; an. autoadaptative, Pavlovian response.. It is an expression frequently used in biology or. health studies. So, it is more appropriate, a ording to Campello de Souza (2007 ), to use the term edu tion, instead of eli itation.. 3.2 Preferen es Preferen es are basi ally the set of values and needs that hara terize individually ea h one of us, as a sort of ngerprint based on our individual vision of the world. When eli iting preferen es, the de ision maker is given the opportunity to rank the alternatives available. The result is mostly a table that assumes few a priori hara teristi s regarding preferen es so that they an be later translated into mathemati al language. As shown in Se tion 3.1.1, there are restri tions whi h are known as utility theory axioms or rationality axiom.. This means that entry to this set of preferen es is only. permitted to those preferen es that omply with the axioms of rationality. However, these assumptions are quite large and demo rati and do not restri t the. 41.

(47) THEORETICAL BACKGROUND entry of DM preferen es. As a result we obtain theoreti al models, whi h will help understand and predi t the reality of the hoi es of individual de ision makers. Also, this will simplify what we get in the real world for this model be omes feasible and translated into mathemati al language, one that allows us to predi t, understand, and work with reality. The main assumptions are (also shown mathemati ally in Se tion 3.1.1):. 1. The preferen es must be omplete, ie, the De ision Maker may rank any alternatives A and B submitted, ie, onsumers are always able to de ide between A and B. As shown in. Leite (2008), the fa t of not being allowed to have in omparability. between two possible onsequen es has been the target of mu h riti ism, espe ially from the Fren h s hool. This s hool argues that a de ision maker is often unable to express his preferen es primarily due to ambiguity, la k of information and oni t between attributes. Against these arguments, one should remember that this s hool prefers a tions. This disguises the random nature of the problem, introdu ing a false sense of ertainty. Thus, un ertainty and onsequen es of a tions are interpreted as ambiguity, la k of information, et . We are talking here about the onsequen es of preferen es. In this ase, the edu tion of a omplete ranking of the onsequen es, a essible to a de ision-maker, does not require mu h eort. It is more intuitive and real, ranking the onsequen es than ranking the a tion. 2. . In the ase of preferen e. for an attribute, the linearity is dire tly linked to the fa t that measurement s ales are naturally ordered, eg, if the attribute is money, more money is better than less money. In the ase of several attributes, the order may ome a priori in the proto ol as suggested here, or posteriori as is the ase of literature in general. That said, the linearity imposes no limitation on the de ision maker.. 2. The preferen es also have to be transitive, ie, the ordering of preferen es must be su h that if A is preferred to B and B is preferred to C, then A must also be preferred to C. If. (C1 ≻ C2 ). and. (C1 ≻ C3 ),. then. (C1 ≻ C3 ).. This assumption helps. to maintain the logi al onsisten y in preferen es a ording to the axioms of rationality (Von Neumann & Morgestern, 1944; Campello de Souza, 2007b). There is a entral prin iple in models of preferen e: the notion of ranking. 2 being. This is formal-. equivalent only to the unrealisti assumption that a tions lead to deterministi onsequen es 42.

(48) THEORETICAL BACKGROUND ized by transitivity and is the basis for the entire optimization. It is assumed that individuals have a ranking s ale that represents their preferen es.. 3. The third assumption is strong, be ause probably redu es the reality a little more than before: preferen es behave in su h a way that more is always preferred to less for elements that in rease our level of well being and vi e versa for onsequen es that diminish well-being, su h as pollution and diseases.. The idea behind this. assumption is to guarantee the monotoni ity of the utility fun tion that is built on our preferen es. Monotoni ity means that the fun tion is ontinuous in one dire tion (at least to the point of satiation) and this is what enables the maximization of this fun tion.. 3.3 De ision Theory De ision theory an be dened as a systemati approa h to de ision making in of un ertainty situations (Campolina & Ci onelli, 2006). shows this way may be done in three ways :. Resear hes into de ision theory. des riptive, normative and pres riptive.. (Chapman & Sonnenberg, 2000; Myers & M Cabe, 2005) De ision theory is des riptive or explanatory be ause its obje tives are to des ribe how de isions are a tually made but de ision theory does not explain or des ribe how and why de ision makers make hoi es. Moreover the de ision theory is normative or pres riptive, i.e., it is on erned with identifying the best de ision to take, assuming an ideal de ision maker who is fully informed, able to ompute with perfe t a ura y, and fully rational. De ision Theory (DT) oers an integrated stru ture to dene mathemati ally a preferen e and/or probability model. DT implementation was proposed by Von Neumann and Morgenstern(Von Neumann & Morgestern, 1944). These authors modeled the quantitative utility fun tion based on a set of axioms that des ribed a de ision-maker's behavior. The theory was unied with statisti s by Wald (1950). A ording to Campello de Souza(2007b) what de ision theory formalizes is the ommon sense idea that an individual should take the best a tion based upon what he or she wants, knows, and an do. De ision Theory involve some sets, probabilisti me hanisms,. 43.

(49) THEORETICAL BACKGROUND and de ision rules with basi parameters whi h are des ribed below:. 1. A set. A. of a tions (or alternatives).. An a tion. a. in. A. available to the de ision. maker able to a omplish a ertain task.. 2. A set. Θ of states. or states of nature. There is no ontrol over this element. It is not. known whi h state will be realized, it is under this un ertainty that one a tion is to be de ided on and the onsequen es a ept.. 3. A set of probability distributions. c. of a set. C.. distribution. If a tion. P(p|θ, a). a. P. on possible onsequen es (out omes or payos). and the state of nature is. θ,. then there is the probability. on the possible onsequen es.. The result is the a tion that maximizes the de ision maker's preferen es regarding the onsequen es of his de ision problem.. 3.3.1 Stru ture of Set of Consequen es Many hara teristi s are involved in the onstru tion of a Consequen e set su h as the basi elements alled Variables, Attributes or Aspe ts and the Measurement s ale.. S alar Consequen e and Ve torial Consequen e The onsequen es are measured a ording to their hara teristi s and an be s alar or ve torial. The dieren e between a s alar and a ve torial onsequen e is the amount of information needed to measure the payo in question a urately. The s alar stru ture needs only a numeri al value, or module, to be measured. A ve tor is a data stru ture formed by a set of data or other elements of the same type or a single stru ture. The ve tor may have one or more dimensions.. Variables, Attributes or Aspe ts There are three basi elements that form the set. C. : variables, attributes and aspe ts .. These elements are important in the de ision making pro ess be ause they permit better hara terization and enable better information to be olle ted. 44.

(50) THEORETICAL BACKGROUND A variable is a nonspe ied element of a set, that an assume any value in a value set. The variables that represent the onsequen es an be any ombination of attributes su h as ost, quality of life, happiness, number of failures and so forth, among others. There is no restri tion regarding the ontext that the de ision problem is found, whether in e onomi s, omputer s ien e or medi ine, et . . On the other hand, a ombination of these variables for the same individual is an attribute. An attribute is a ombination a ording to a rule or a formula. It is an indi ator, that is translated by a formula involving the variables. Any formula that makes sense is valid in the onstru tion of an attribute. The entral point is that attributes are represented in s ales of measures, ranging from ratios of relevan e to arithmeti operations(Campello de Souza, 2007b; Chankong & Haimes, 1983). But an attribute an be used as a variable, whi h will be useful in drawing up more onne ted onstru ts: aspe ts. These aspe ts are synthesis of attributes . A ve tor Payo or Consequen e an be formed by one or more variables, attributes or aspe ts as shown in Figure 3.1.. Measurement S ales A measurement s ale must have the following proprieties:. Completeness - it must. be able to represent all the fa ts possible (breadth) - and Uniqueness - every fa t has a unique representation ( oheren e). There are basi ally four s ales, proposed by Stevens (1946). in his seminal arti le . On the Theory of S ales of Measurement.:. . Nominal S ale The most elementary level of measurement.. Use numbers or. names for identi ation or lassi ation. Does not allow any arithmeti operation. Main fun tion is to make distin tions among the elements of the set;. . Ordinal S ale Beyond distinguishing between elements, this improved with an order relation between the elements of the set;. . Interval S ale Beyond order and distin tion, this is improved with the distan e between the elements of the set;. 45.

(51) THEORETICAL BACKGROUND. Figure 3.1:. . Ve torial Payo an onsist of Variables, Attributes and/or Aspe ts. Ratio S ale The most omplete S ale, is improved with the origin. All arithmeti operations are valid.. In most situations there is a need to measure various attributes of dierent types and due to this, dierent s ales of measurement may be needed. This multidimensional s ale ombines dierent attributes to form a single index of measurement. It is important to note the similarity between s ales and utilities. Therefore, a utility is a unique measuring s ale (sin e it represents only one individual) to measure the de ision maker's preferen es. Moreover, utility is represented by an interval s ale (Wanderley, 2008) Let. C1 , C2 , C3 , ..., Cn. (Payo ) set. C. A onsequen e. be the set of possible inputs of. n. attributes. The Consequen e. is dened by Cartesian produ t attributes, ie,. n∈C. is given by. orresponding elements of. = (c , c , c , ..., c ) 1. C1 , C2 , C3 , ..., Cn ,. 2. 3. n. C ≡ C1 × C2 × ... × Cn .. , where. c1 , c2 , c3 , ..., cn. respe tively(Wanderley, 2008).. 46. are the.

(52) THEORETICAL BACKGROUND If an attribute is represented on a nominal s ale, it must be ordered. It is onsidered in this dissertation that attributes are sorted naturally or were previously ranked. Given that the attributes element alled and. C. c1. Ci , i = 1, 2, 3..., n,. are nite and dis rete (limited), there is a best. and the worst element alled. i = 1, 2, 3..., n,.. cn i. for ea h attribute, where. The number of possible onsequen es is. c ∈ C,. ni =k Ci k,. ie, the ardinality of. is given by:. k C k=. n Q. k Ci k=. i=1. n Q. ni. i=1. Probability Sox et al. (2007) introdu e the following denitions for probability:. . Probability is a number between 0 and 1;. . Probability of an event ertainly o urring;. . Probability of an event not o urring for ertain is 0;. . Probability of an event o urring plus the probability of it not o urring is 1, when they are omplementary and mutually ex lusive.. The Kolmogorov axiomati treatment of probability des ribed in Campello de Souza (2009) is used in this dissertation.. There are two ways to estimate probabilities:. an. obje tive one and a subje tive one. The obje tive probability is that estimated by the relative frequen y of the event, usually obtained from re orded histori al data.. The. subje tive probability is estimated by one expert and ree ts the degree of belief that he has in an event o urring for ertain. The likelihood is that there is duality and the de ision maker needs to work impli itly with the two ways. Assigning probabilities in orre tly is a usual hara teristi of errors in human reasoning. There are three lassi s bias found in literature that indi ate errors in the use of ognitive heuristi s (the mental pro ess used to learn, remember and understand the knowledge)(Sox et al. , 2007).. 47.