Main The Little Blue Reasoning Book: 50 Powerful Principles for Clear and Effective Thinking
The Little Blue Reasoning Book: 50 Powerful Principles for Clear and Effective ThinkingBrandon Royal
For Reasoning Aficionados From All Walks of Life!THE LITTLE BLUE REASONING BOOK is based on a simple but powerful observation: Individuals who develop outstanding reasoning and thinking skills do so primarily by mastering a limited number of the most important reasoning principles and concepts, which they use over and over again. What are these recurring principles and concepts? The answer to this question is the basis of this book. Interwoven within the book's five chapters — Perception & Mindset, Creative Thinking, Decision Making, Analyzing Arguments, and Mastering Logic — are 50 reasoning tips that summarize the common themes behind classic reasoning problems and situations. Appendixes contain summaries of fallacious reasoning, analogies, trade-offs, and a review of critical reading skills.
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THE LITTLE BLUE Reasoning Book 50 POWERFUL PRINCIPLES FOR CLEAR AND EFFECTIVE THINKING Brandon Royal Published by Maven Publishing © 2010 by Brandon Royal All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanicalâ†œ—â†œincluding photocopying, recording, or any information storage and retrieval systemâ†œ—â†œwithout permission in writing from the author or publisher. Reviewers, however, may quote brief passages in a review, and individuals wanting to reference material from this book for academic or non-commercial purposes may do so provided the book, with title and author’s name, is cited as a source. Published by: Maven Publishing 4520 Manilla Road Calgary, Alberta, Canadaâ•‡ T2G 4B7 www.mavenpublishing.com Library and Archives Canada Cataloguing in Publication: Royal, Brandon The little blue reasoning book : 50 powerful principles of clear and effective thinking / by Brandon Royal. ISBN 978-1-897393-60-4 Library of Congress Control Number: 2009909356 In addition to the paperback edition, this book is available as an eBook and in the Adobe PDF file format. Technical Credits: Cover Design: George Foster, Fairfield, Iowa, USA Editing: Jonathan K. Cohen, Irvine, California, USA Illustrations: Ashley Vercekaites, Calgary, Canada This book’s cover text was set in Minion. The interior text was set in Scala and Scala Sans. Contents Preface 7 Introduction 9 Quiz Chapter 1: Chapter 2: 11 Perception & Mindset Selective Perception 15 The Magic of Coincidence 16 The Four Classic Mindsets 19 Creative Thinking Overview 27 Lateral Thinking 27 Divergent vs. Convergent Thinking 33 Mind Maps 38 Devil’s Advocate Technique 39 Idea Killers and Idea Growers 42 Brainstorming 49 Reframing Problems 54 Selling Creative Ideas 55 Chapter 3: Chapter 4: Decision Making Overview 59 Pros-and-Cons Analysis 60 Matrixes 66 Decision-Event Trees 76 Probability Trees 81 Weighted Ranking 81 Utility Analysis 88 Sunk Costs 91 Hypothesis Testing 93 Prisoner’s Dilemma 98 Analyzing Arguments Overview 105 The ABCs of Argument Structure 106 Evaluating Arguments 107 The Five Common Reasoning Flaws 114 Testing Critical Reasoning 127 Putting It All Together 145 Chapter 5: Mastering Logic Overview 149 “Ifâ•›…â•›Then” Statements 150 “No-Some-Most-All” Statements 153 Mutual Inclusivity and Exclusively 155 Statements of Logical Equivalency 157 Testing Logic-based Reasoning 159 Appendix I – Summary of Reasoning Tips 1 to 50 171 Appendix II – Fallacious Reasoning 177 Appendix III – Avoiding Improper Inferences 188 Appendix IV – Analogies 190 Appendix V – The Ten Classic Trade-offs 196 Appendix VI – Critical Reading and Comprehension 205 Appendix VII – Tips for Taking Reading Tests 209 Answers and Explanations 225 Quiz – Answers 281 Selected Bibliography 283 Index 285 About the Author Preface Henry Humidor purchased a box of very rare, very expensive cigars and insured them, among other things, against fire. Within a month, having smoked his entire stockpile of cigars, he filed a claim against the insurance company. In his claim, Henry stated the cigars were lost “in a series of small fires.” The insurance company refused to pay, citing the obvious reason: he had consumed the cigars in the normal fashion. Henry sued and won! In delivering the ruling, the judge agreed that the claim was frivolous. He stated that the man nevertheless held a policy from the company in which it had warranted that the cigars were insurable and also guaranteed that it would insure against fire, without adequately defining what is considered to be an “unacceptable fire,” and was obligated to pay the claim. Rather than endure a lengthy and costly appeals process, the insurance company accepted the ruling and paid Henry $15,000 for the rare cigars he lost in the “fires.” Butâ•›… After Henry cashed the check, the insurance company had him arrested on twenty-four counts of arson! With his own insurance claim and testimony from the previous case used against him, Henry Humidor was convicted of intentionally setting fire to his insured property and was sentenced to twenty-four months in jail and a $24,000 fine. Welcome to the wonderful world of reasoning. 7 Introduction Some 2,500 years ago, Socrates gave birth to the art and science of what we now call critical reasoning. Through a system of inquiry, known as the “Socratic method,” Socrates used a series of probing questions to obtain answers and then critique those answers. In this manner, he sought to reveal the key issues behind perplexing problems, to uncover the merit and flaws in commonly held ideas, and to expose those contradictory beliefs that often hide behind smooth-sounding but empty rhetoric. It is indeed humorous to reflect on Socrates’ observation that one cannot necessarily rely on the “sound” judgment of those individuals occupying positions of authority; they may be prone to think in a muddled, whimsical, or irrational manner. Critical reasoning, also referred to as critical thinking, may be defined broadly as “the process by which we evaluate information.” Often, the information we seek relates to problems or opportunities, and the process relates to how we arrive at our conclusions based upon the information we have. Individuals who possess critical thinking skills can identify problems or opportunities, gather relevant information, analyze information in a “proper” way, and come to reliable conclusions by themselves, without necessarily relying on others. Notwithstanding our ability to read, no other single skill is more important than our ability to reason. Yet, strangely, no required course dedicated to reasoning skills exists as a part of our regular school curriculum or as part of any on-the-job training program. This book provides a distillation of the most useful academic and real-life reasoning concepts. Teaching in our school systemsâ†œ—â†œprimary, secondary, and post-secondaryâ†œ—â†œhas traditionally been skewed toward instructing us “what to think” as opposed to “how to think.” An all-rounded education must balance the teaching of course content with new and better ways of understanding and interpreting the material at hand. 9 This book contains fifty reasoning tips interspersed throughout five sections. Perception & Mindset (chapter 1) provides an initial framework for reasoning. We live in a world of imperfect information and of imperfect abilities, where subjectivity is a key ingredient. As no two individuals have the same perspective or mindset, we must make allowances for this when mastering the tools of reasoning and logic. Creative Thinking (chapter 2) introduces non-traditional thinking methods. Creative thinking is subjective or non-linear thinking, and is often referred to as “out-of-the-box” thinking. One of the most useful topics is reframing problems. An important step in problem solving involves asking, “Is the perceived problem really the problem?” The ability to use creativity to better define problems bolsters the ability to solve problems. Decision Making (chapter 3) focuses on applied reasoning and introduces various tools, the major benefit of which is to structure or quantify the decision-making process. The basic toolsâ†œ—â†œboxes and treesâ†œ—â†œare devices that allow problems to be approached in an efficient, organized manner. Other tools, such as weighted ranking and utility analysis, allow us to quantify qualitative decisions (e.g., hiring decisions, career choices), which may or may not involve monetary considerations. Analyzing Arguments (chapter 4) shows us how to break arguments down according to classic argument structure: conclusion, evidence, and assumption. The ability to understand, attack, and defend arguments is one of the most fundamental uses of reasoning skills. Mastering Logic (chapter 5) contains some of the more technical material in this book, but it also provides the foundation for understanding some of the most relevant examples of reasoning flaws found in everyday conversation and speech. Let’s get started. 10 Quiz Try these ten basic, but occasionally tricky, reasoning concepts. Mark each statement as being either true or false. Answers can be found on the final pages of this book. 1. The Prisoner’s Dilemma provides an example of how competition is superior to cooperation. ❑ Trueâ•… ❑ False 2. The statement “some doctors are rich people” does not imply reciprocality because “some rich people might not be doctors.” ❑ Trueâ•… ❑ False 3. The ad hominem fallacy consists in attempting to hide a weakness by drawing attention away from the real issueand emphasizing a side issue. ❑ Trueâ•… ❑ False 4. The halo effect occurs when a person so wishes something to be true that, in his or her mind, the situation is believed to be true. ❑ Trueâ•… ❑ False 5. The following represents the formulaic relationship among the three elements of classic argument structure: Evidence − Assumption = Conclusion. ❑ Trueâ•… ❑ False 6. The words “inference” and “assumption” may be used interchangeably. ❑ Trueâ•… ❑ False 7. The beauty of matrixes lies in their ability to summarize data across rows and colÂ�umns. However, data must be “collectively exclusive and mutually exhaustive.” ❑ Trueâ•… ❑ False 11 8. In formal logic, the statement “Every A is a B” may be translated as “Only As are Bs.” ❑ Trueâ•… ❑ False 9. Left-brain thinking might be described as “floodlight” thinking while rightbrain thinking might be described as “spotlight” thinking. ❑ Trueâ•… ❑ False 10. Utility analysis takes into account the desirability of outcomes by multiplying a given value by the probability of its occurrence; all resultant values will total to 100%. ❑ Trueâ•… ❑ False 12 Chapter 1 Perception & Mindset Many complain about their memory, few about their judgment. —â†œLa Rochefoucauld PERCEPTION & MINDSET Selective Perception aâ•–Tip #1: Selective perception is the tendency to see the world the way we would like it to be rather than how it really is. The sound thinker suspends judgment and is not unduly influenced by stereotypes, prejudices, isolated experiences, or preconceived notions. Imagine recovering your sight after thirty years of blindness. Pioneering psychologist K. F. Muenzinger captured the words of a person who had made this remarkable journey: When I could see again, objects seemed to hurl themselves at me. One of the things normal people know from long habit is what not to look at. Things that don’t matter, or that confuse, are simply shut out of their minds. I had forgotten this, and tried to see everything at once; consequently I saw almost nothing. This interesting but extreme case is virtually the opposite of what most of us typically experience. The active thinker struggles to gain more latitude, differing viewpoints, and corroborating information. We hardly worry about seeing too much, but rather about seeing too little. All-rounded thinkingâ†œ —â†œ thinking that encompasses both sides of an issue or topicâ†œ—â†œis probably the greatest asset that training in critical thinking can lend us. Age, culture, gender, education, and work and life experience are major reasons why no two individuals see the world in exactly the same way. Perhaps the most basic way to view the world is from a positive or negative perspective. Is the cup half full or half empty? Are we perennial pessimists or incurable optimists? Consider the following truncated profiles that describe the life and times of Remus Reid. Folklore has it that two separate newspaper accounts surfaced regarding the death of cowboy Remus Reidâ†œ—â†œone from the sheriff’s office and one from a close relative who lived in Remus’ hometown: 15 THE LITTLE BLUE REASONING BOOK From the sheriff’s office: “Remus Reid, horse thief, sent to prison in 1885, escaped in 1887, robbed the local train six times. Caught by local detectives, convicted and hanged in 1889.” From Remus’ dotting relative: “Remus Reid was a famous cowboy whose business empire grew to include acquisition of valuable equestrian assets and intimate dealings with the regional railroad. Beginning in 1883, he devoted several years of his life to government service, finally taking leave to resume his dealings with the railroad. In 1887, he was a key player in a vital legal investigation. In 1889, Remus passed away during an important civic function held in his honor when the platform upon which he was standing collapsed.” We have a tendency to interpret events selectively. If we want things to be “this way” or “that way” we can most certainly select, stack, or arrange evidence in a way that supports such a viewpoint. Selective perception is based on what seems to us to stand out. However, what seems to us to be standing out may very well be related to our goals, interests, expectations, past experiences, or current demands of the situationâ†œ—â†œ“with a hammer in hand, everything looks like a nail.” The preceding quote highlights the phenomenon of selective perception. If we want to use a hammer, then the world around us may begin to look as though it is full of nails! The Magic of Coincidence Ponder this rather astounding comparison of the assassinations of two famous American presidents: Abraham Lincoln was elected to Congress in 1846. John F. Kennedy was elected to Congress in 1946. 16 PERCEPTION & MINDSET Abraham Lincoln was elected president in 1860. John F. Kennedy was elected president in 1960. The names Lincoln and Kennedy each contain seven letters. Both were particularly concerned with civil rights. Both wives lost children while living in the White House. Both presidents were shot on a Friday. Both were shot in the head. Lincoln’s secretary was named Kennedy. Kennedy’s secretary was named Lincoln. Both were assassinated by Southerners. Both were succeeded by Southerners. Both successors were named Johnson. Andrew Johnson, who succeeded Lincoln, was born in 1808. Lyndon Johnson, who succeeded Kennedy, was born in 1908. John Wilkes Booth, who assassinated Lincoln, was born in 1839. Lee Harvey Oswald, who assassinated Kennedy, was born in 1939. Both assassins were known by their three names. The names of both assassins comprise fifteen letters. Booth ran from a theatre and was caught in a warehouse. Oswald ran from a warehouse and was caught in a theatre. Booth and Oswald were both assassinated before their trials. A week before Lincoln was shot he was in Monroe, Maryland. A week before Kennedy was shot he was with Marilyn Monroe. 17 THE LITTLE BLUE REASONING BOOK Despite how enticing the above comparison may appear, we must keep in mind that there are likely just as many differences as there are similarities between these two events. Care must be exercised so as to not overestimate the veracity of such a compilation. Recall the well-known saying: “If a billion chimpanzees were to sit down in front of a billion computers with a billion hours to spare, eventually one of them would type Tolstoy’s War and Peace.” Eventually one chimpanzee would arrange the letters exactly as they appear in that novelâ†œ—â†œtyping the identical letters to form those identical words, in the right order, with the right spaces, and the correct punctuation. Here the magic of chance or coincidence reminds us that almost anything is possible. At the crossroads of selective perception and coincidence is something known as the “halo effect.” The halo effect is the tendency to view a person, place, or thing favorably based on only a single incident, trait, or characteristic. For example, if someone arrives at our firm to answer a job ad and happens to be impeccably dressed, we may view this person favorably and overlook certain technical qualifications required for the job. Sometimes the halo effect is tied to coincidence. Say, for example, the candidate who arrives at our company for an interview happens to be from our hometown. Perhaps they also know someone we know. These coincidences may cause us to view the candidate favorably in an overall way. Here’s some offhanded Commonwealth humor. Year 1981: e e e e Prince Charles got married. Liverpool crowned Champions of Europe. Australia lost the Ashes tournament. The Pope died. 18 PERCEPTION & MINDSET Year 2005: e e e e Prince Charles got married. Liverpool crowned Champions of Europe. Australia lost the Ashes tournament. The Pope died. Lesson learned: The next time Prince Charles gets married, would someone please warn the Pope! The Four Classic Mindsets Each of us learns early that different people see the world differently. Our experience, background, and predispositions play a unique role in shaping our outlook. Ponder this simple but revealing question: Which of the following five sports is least like the other four? A) B) C) D) E) Baseball Cricket Soccer (Football) Golf Ice Hockey This is indeed an interesting question highlighting the possibility of multiple solutions and subjective interpretations. Not only would such a question never be chosen for an IQ test, but it also hints at ambiguity so often present whenever individuals make choices. Most people find themselves choosing choice D insofar as golf is primarily an individual sport while the other sports are team sports. Golf is also the only sport here in which a lower score beats a higher score. Some pontificate whether the distinction rests on the degree to which golf is more mental than physical while the other four sports are more physical than mental. Certainly physical speed is of obvious importance in all sports except golf. 19 THE LITTLE BLUE REASONING BOOK Choice E is likely the next most popular. Ice hockey is essentially a winter sport, whereas the other sports are typically played in warmer weather. In ice hockey, players use skates, whereas in the other sports players use sporting shoes. Ice hockey is also played with a puck, the others, with balls! (Pun intendedâ†œ—â†œice hockey is notorious for being one of the roughest of sports and the only one listed above where you can legitimately “check” another player.) A number of people see soccer (football) as least like the other three. After all, the other sports are played with stick-like objects: golf requires clubs, irons, and putters; ice hockey requires sticks, and baseball and cricket require bats. Football (soccer) also is played with an air-filled object, not a solid ball or puck. People who choose choice A point to the fact that baseball has no true world championshipâ†œ—â†œthe “World Series” is an American phenomenon. Choice B (cricket) represents a sport that is played primarily in Commonwealth countries. Every answer choice is both right and wrong! In summary, there are at least four distinct ways in which individuals draw broad contrasts among these different sports. Some people tend to focus first on the number of people who play the sport (individual vs. team sport), some focus on the speed with which each sport is played (walking vs. running), some focus on the objects used to play the sport (puck vs. ball, inflatable object vs. non-inflatable object, stick-like object vs. non-stick-like object), while others see these sports in the context of when (winter vs. summer, cold weather vs. warm weather) or where they are played (within a particular country or region). In terms of thinking about how different people think, it is useful to massage the concept of “mindset.” Many schemas exist which seek to classify mindsets. For instance, if we were to spend time reviewing how various people choose an answer to the above multiple-choice question, we might find the following: some people are more analytical, some more holistic, some are more results-oriented, and some are more process-oriented. Case in 20 PERCEPTION & MINDSET point: People who are analytically minded tend to focus on the instruments used to play the sport. People who are holistically minded tend to see the sport in terms of when and where (i.e., geography) it is played. People who are results-oriented are more likely to see the end result, contrasting the desirable low scores in golf with the desirable high scores in the other four sports. Process-oriented individuals will likely see contrasts in the number of players who play each sport, their physical size, and their athletic movements. aâ•–Tip #2: Think of mindsets as divided into four basic types: Analysts, Idealists, Realists, and Synthesists. These mindsets can be further contrasted based on levels of practicality and emotional attachment. Our natural dispositions with respect to how we see the world come with their inherent strengths and weaknesses. Such dispositions, often referred to as mindsets, can help us in understanding how others around us are motivated. To understand the importance of mindsets, ponder why it might be difficult, apart from obvious time constraints, to be a movie actor, director, and producerâ†œ—â†œall at the same time. The answer lies in competing skills and personalities. An actor needs to be dynamic and spontaneous, a director needs to be systematic and creative, and a producer needs to be persuasive, commercial, and administrative. The chart below summarizes the four mindsets of the Realist, Idealist, Analyst, and Synthesist. Realist: Describes a person whose primary goal is “getting the job done” (results-oriented). Idealist: Describes a person whose primary goal is “finding the ‘right’ answer” (process-oriented). 21 THE LITTLE BLUE REASONING BOOK Analyst: Describes a person whose primary goal is “obtaining a thorough evaluation” (analytically oriented). Synthesist: Describes a person whose primary goal is “achieving a composite view” (holistically oriented). Exhibit 1.1 below may be used to further contrast the four classic mindsets in terms of practicality and emotion. In short, Realists and Analysts are deemed more practical than Idealists or Synthesists (this is fairly empirical). Also, Realists and Idealists are deemed to be more emotional than are Analysts or Synthesists. Realists and Idealists tend to deal more with people in moving their goals forward. Realists know where they are going and need to enlist people’s help, while Idealists seek to marshal support in determining the proper course of action. On the other hand, Analysts and Synthesists favor the intellectual more than the emotional. The Analyst deals with detailsâ†œ—â†œthe pieces of the puzzle at handâ†œ—â†œwhile the Synthesist tries to draw themes from the information presented; thus, there is less need for emotional attachment. Exhibit 1.1 The Four Classic Mindsets Practicality More Less More Realist Idealist Less Analyst Synthesist Emotion Exhibit 1.2 presents a stereotypical list of traits for individuals working across different fields. Naturally, a “good” thinker must not be unduly influenced by such stereotypes. 22 PERCEPTION & MINDSET Exhibit 1.2 Perceptions of the Professions 1. Accountant Perceived Strengths Perceived Weaknesses • Good technical, • Not dynamic; not a quantitative skills • Good at reality checks • Diligent 2. Administrator/Personnel 3. Artist • Organized; detail minded • Trained to take care of people; team player leader • Lacks big-picture view despite exposure to different industries • Doesn’t know how to build a business • Stuck on rules and procedures • Flexible mindset; • Not quantitatively creative • Unique viewpoint • Doesn’t know how to skilled manage people 4. Computer/ Internet/ Techno Geek • Quantitatively skilled • Understands tech- 5. Consultant • Can think outside • Doesn’t care about the box; good business sense • Articulate; smart • Too theoretical; too • Methodical; hard- • Myopic; can’t see the 6. Engineer nology and uses hands-on approach working • Quantitatively and technologically skilled 23 • Lacks people skills • Lacks big-picture view detail much style at the expense of substance forest for the trees • Lacks communication skills THE LITTLE BLUE REASONING BOOK 7. Entrepreneur • Dynamic; high en- • Chaotic; disorga- ergy level • Hands on; a real doer nized; easily bored; impatient • Averse to theory 8. Investment Banker • Savvy; resourceful; • Callous; uncaring; 9. Lawyer 10. Marketer/ Salesperson 11. Military knows the bottom line; good at networking • Facility with numbers “ends” at the expense of the “means” • Smart; clever com- • Works alone; set in municator • Well trained; good organizational skills • Not quantitatively • Strong personality; self-confident • Understands the consumer • Obeys rules; disciplined • Team player 12. Scientist arrogant • Focuses on the his or her ways skilled • Lacks number sense • Doesn’t see value in theory or book learning • Commercial misfit • Too focused on executing orders; not enough vision • Intelligent; unique • Lacks business viewpoint • Quantitatively skilled • Can’t “bullshit”; sense; inhibited unwilling to develop soft skills 24 Chapter 2 Creative Thinking Our task, regarding creativity, is to help children climb their own mountains, as high as possible. No one can do more than that. —â†œLoris Malaguzzi CREATIVE THINKING Overview Loosely speaking, there are two types of thinkingâ†œ—â†œanalytical and creative. Analytical thinking is the focus of chapters 3, 4, and 5. Because so much emphasis is placed on traditional, analytical problem-solving techniques, this chapter “reverses the order” and precedes with non-traditional, creative techniques for use in analyzing and solving problems. Lateral thinking, an offshoot of creative thinking, is discussed first. The problems titled Stroke, Pattern, and Nine Dots are examples of puzzles that highlight the power of programmed responses. As a follow-up, we explore differences between convergent thinking and divergent thinking and the strengths and weaknesses of both abilities. The primary goal is to broaden the mind and develop an all-around thinking process. Because fresh ideas are the bloodline of creativity, a discussion of how to generate ideas includes sections on brainstorming as well as “idea growers” and “idea killers.” In terms of problem-solving ability, the technique of reframing problems to determine whether the problem is really the problem is an extremely valuable tool. Finally, we address some issues regarding the “selling” of creative ideas within the context of organizations, where other individuals will have an impact on the success or failure of those ideas being presented. Lateral Thinking aâ•–Tip #3: Creative thinking is “backdoor” thinking. Creative thinking is often used synonymously with the term “lateral” thinking. Although lateral thinking is not a new term, Dr. Edward De Bono was the person who coined it, and much of the term’s popularity has arisen from his book of the same title. Here are some differences between traditional or “vertical” thinking and creative or lateral thinking. 27 THE LITTLE BLUE REASONING BOOK Creative or Lateral Thinking Traditional or Vertical Thinking ❧ Creative thinking is sideways thinking. ❧ Vertical thinking is straightforward thinking. ❧ Creative thinking is backdoor thinking. ❧ Vertical thinking is frontdoor thinking. ❧ Creative thinking is spontaneous thinking. ❧ Vertical thinking is logical thinking. ❧ Creative thinking is lowprobability thinking. ❧ Vertical thinking is highprobability thinking. ❧ Creative thinking is primarily right-brain thinking. ❧ Vertical thinking is primarily left-brain thinking. ❧ Creative thinking is “outside-the-box” thinking. ❧ Vertical thinking is “inside-the-box” thinking. ❧ ❧ Creative thinking is like a river which overflows and moves in new directions. Vertical thinking is like a river which follows a set course. The concept of creative thinking is somewhat more difficult to describe than to illustrate. The following story suffices as a noteworthy example. Many years ago, a hapless merchant owed a substantial sum of money to a wealthy moneylender. Unable to pay back his debt, the merchant knew that the moneylender could see to it that he was put in jail. The moneylender was old, ugly, and ill-tempered, but he couldn’t help but notice how beautiful the merchant’s teenage daughter was. He proposed a deal to relinquish 28 CREATIVE THINKING the debt and ensure that the daughter would not starve as a result of her father’s going to jail. The moneylender said he would place two small stones, one white and one black, into an empty money-bag and permit the splendid young lady to choose her fate. If she reached into the bag and chose the white stone, her father’s debt would be canceled and she would be free from any obligation to marry him. If the stone was black, the father’s debt would be canceled, but the young girl would have to marry the moneylender. If she refused to choose, the father would immediately go to jail. Horrified by their present predicament, the father and daughter knew they could not refuse the moneylender’s proposal for debt relief. What would you have done if you had been the unfortunate girl? If you had been asked to advise her, what would you have told her to do? You may believe that careful, logical analysis would solve the problem, if there were a solution. This type of traditional, straightforward thinking is not much help to the girl in this story. In this respect, there are but two possibilities: 1. The girl should take a black pebble and sacrifice herself in order to save her father from prison. 2. The girl should refuse to choose a pebble, show that there are two black pebbles in the bag, expose the moneylender as a cheat, and demand a fair retrial. This story shows the difference between traditional thinking and creative thinking. Traditional thinkers are concerned with the fact that the girl has to take the pebble and on how the parameters of the “game” are fixed. Creative thinkers are concerned with changing the focus or parameters of the game. Traditional thinkers take the reasonable view of a situation and then proceed logically and carefully to work it out. Creative thinkers tend to explore all the different ways of looking at something, rather than accepting the most promising and proceeding from that. 29 THE LITTLE BLUE REASONING BOOK Soon the moment of truth had arrived. The three of them met on the garden path of the moneylender’s large home. The moneylender bent over to pick up two small rocks. The girl grimaced with fright upon noticing that the moneylender had picked up two small rocks, both of them black, which he now placed in the money bag. “Please choose, my fair maiden,” he said. The young woman reached into the money bag and pulled out a rock, which she purposefully let fall to the ground and disappear within the camouflage of the stone path beneath her. “How clumsy of me,” she said, while looking toward the moneylender. “No matter though. If you look at the stone held in the bag, we’ll be able to tell which color I must have chosen.” With a sense of shock, and with no intention of admitting his dishonesty, the moneylender allowed the girl to reach back into the bag and reveal a black stone. “I chose the white stone!” the girl shouted with joy. In this way, by using creative thinking, the girl changes what seems an impossible situation into an extremely advantageous one. The girl is actually better off than if the moneylender had been honest and had put one black and one white pebble into the bag, for then she would have had only an even chance of being saved. As it is, she is sure of remaining with her father and at the same time having his debt canceled. Creative thinking might result in two possibilities: 1. Before choosing, the girl should demand the opportunity to change colors, even offering to let the moneylender reach into the bag and choose a stone for her. 2. The girl should choose a stone, fumble it to the ground to conceal its color, and ask to see the color of the remaining stone in the money bag (just as she did in this story). 30 CREATIVE THINKING What types of things most hinder our ability to unleash creative thinking? The answer lies in distinguishing between programmed versus non-programmed responses. Programmed responses are essential in everyday life, saving us from having to engage in deep thought in order to do routine tasks, e.g., going to the store, driving a car, or saying “hello” while anticipating a familiar response. However, programmed responses form barriers when we encounter novel situations, requiring non-programmed responses. Problem 1 Stroke Add one stroke or character to solve or make sense of the following: IX = 6 Note: For answers and proposed solutions to exercises and problems, see the Answers and Explanations that follow at the back of this book. Problem 2 Mop Make sense of the following: “The floor is dirty because Sally mopped it.” Problem 3 Pattern Based on the pattern below, place each of the characters “E F G H I” in their proper position both above and below the line. A BCD 31 THE LITTLE BLUE REASONING BOOK Problem 4 Nine Dots Draw no more than four straight lines (without lifting the pencil or pen from the paper) in order to cross through all nine dots. ••• ••• ••• Problem 5 Two Water Buckets A circus owner sends one of his clowns to bring water back from a nearby river. The owner wants to mix the water with a special health concentrate to give to the elephants, and needs exactly seven gallons of water. He gives the clown a five-gallon bucket and a three-gallon bucket and tells him to bring back exactly seven gallons of water. How can the clown measure out exactly seven gallons of water using nothing but these two buckets and not guessing at the amount? Five-Gallon Bucket Three-Gallon Bucket 32 CREATIVE THINKING Divergent vs. Convergent Thinking aâ•–Tip #4: Convergent thinking focuses the mind; divergent thinking opens the mind. At any point in the analytic process, from the very beginning to the very end, we are engaged in one of two thinking modes: convergence or divergence. Convergence means bringing together and moving toward one point. Whenever we take a narrower view of a problem, focusing our mind on a single aspect of the puzzle, we are in a convergent mode. Whenever we take a broader view of a problem, whether by examining evidence more thoroughly, gathering new evidence, or entertaining alternative solutions, we are in a divergent mode. While divergent thinking opens the mind to new ideas and thoughts, convergent thinking closes the mind by viewing a problem ever more narrowly until it focuses onâ†œ—â†œand producesâ†œ—â†œa single solution. An apt simile is a camera lens that can zoom in until the subject fills the aperture (convergence) or adjust to broaden the field of view around the subject (divergence). An even more dramatic contrast occurs when using a microscope or telescope. Both divergence and convergence are necessary for effective problem solving. Divergence opens the mind to creative alternatives; convergence winnows out the weak alternatives, focusing on and choosing among the strong alternatives. Without divergence, we could not analyze a problem creatively or objectively; without convergence, we would just keep on analyzing, never coming to closure. It is therefore vital to effective problem solving that an individual be prepared to shift back and forth between divergent and convergent approaches easily and at will, using each mode to its best effect as the problem solving process dictates. 33 THE LITTLE BLUE REASONING BOOK Unfortunately, it is extremely difficult for individuals to shift back and forth between these two ever-opposite, ever-warring approaches. Most of us are inherently better convergers than divergers. Divergence is not as instinctual as is convergence. Indeed, most of us habitually resist divergenceâ†œ—â†œ sometimes passionately, even angrily. Discussion of divergent versus convergent thinking dovetails with the following overview of right-brain versus left-brain thinking. In 1981, Dr. Roger Sperry was awarded the Nobel Prize for his proof of the split brain theory. Research confirmed that the brain has two hemispheres with different, but overlapping functions. The right and left hemispheres of the brain each specialize in distinct types of thinking processes. In the most basic sense, the left brain is the analytical side while the right brain is the creative side. In 95 percent of all right-handed people, the left side of the brain controls analytics while the right side controls creative endeavors. In most left-handed people, the hemisphere functions are reversed. The passage below, relevant to the topic at hand, is excerpted from The Little Red Writing Book, where it is used to show how to structure written documents. The left side of the brain is responsible for analytical, linear, verbal, and rational thought. Left-brain thinking is characterized as “spotlight” thinking. It is the left brain that a person relies on when balancing a checkbook, remembering names and dates, or setting goals or objectives. The right side of the brain is holistic, imaginative, nonverbal, and artistic. Right-brain thinking is characterized as “floodlight” thinking. Whenever a person recalls another person’s face, becomes engrossed in a symphony, or simply daydreams, that person is engaged in right-brain functions. 34 CREATIVE THINKING Since most of the Western concepts of thinking are derived from Greek logic, which is a linear logic system, left-brained processes are most rewarded in the Western education system. Right-brain processes are, to the chagrin of many, less often rewarded in school. The primary abilities of the left and right brain include: Left Brain Right Brain h Analysis h Artistic ability h Classification h Emotion h Language h Imagery h Logic h Imagination h Memory h Intuition h Numbers h Music h Sequence h Rhythm/Physical coordination h Seriation h Synthesis h Writing h Theatrics h Convergent thinking processes h Divergent thinking processes 35 THE LITTLE BLUE REASONING BOOK Here is a snapshot summarizing right-brain versus left-brain thinking: Left-Brain Thinking Right-Brain Thinking ❧ Left-brain thinking is characterized as “spotlight” thinking. ❧ Right-brain thinking is characterized as “floodlight” thinking. ❧ The functions of the left brain are characterized by sequence and order. ❧ The functions of the right brain are characterized as holistic and diffuse. ❧ The left brain can put the parts together into an organized whole. ❧ The right brain instinctively sees the whole, then the parts. ❧ The left hemisphere controls our analytical, scientific, logical, mathematical, and verbal leanings. ❧ The right hemisphere of the brain governs our artistic, musical, innovative, imaginative, entrepreneurial, political, theatrical, and visual tendencies. Although it would be difficult, perhaps impossible, to find a task that requires the exclusive use of the right or left brain, the following exercise is an example of a strong right-brain activity. Reflect on the statement below and try to come up with at least six responses. You may write your answers on a separate sheet of paper. How is a good idea like an Iceberg? 36 CREATIVE THINKING Possible answers: A good idea is cool! A good idea stands out. A good idea may get a chilly reception. A good idea can easily disappear. Good ideas are fleeting. A good idea sure seems natural. A good idea has a big effect on its surroundings. A good idea takes time to form. Good ideas come in bunches. Good ideas are only created when conditions are right, and then, many are created. If you overlook a good idea, it can sink you. You have to go a long way to find a good idea. If you’re looking in the wrong place, you’ll never find one. You only see part of a good idea because there is more to it than meets the eye. There is a lot of depth in a good idea, but not everyone appreciates it. One-tenth of the benefit of a good idea is clearly visible, but nine-tenths of the long-term benefits lie below the surface. 37 THE LITTLE BLUE REASONING BOOK Mind Maps Mind maps, also generically known as concept maps or idea maps, are a note-taking technique that uses both visual and linear thought processes. They provide an alternative to traditional linear note-taking skills. Tony Buzan is the best-known advocate and practitioner of concept maps, and although he didn’t originate the technique, he did manage to come up with a name that sticksâ†œ—â†œmind maps! The technique used to create mind maps is based on the workings of our bicameral brain (right and left side). The idea is that since linear note taking only appeals to one side of our brain, it would be more effective to take notes in such a manner as to appeal to both sides of our brain, thereby increasing retention and comprehension. Accordingly, concept maps traditionally use an organic structure, usually centered on a large sheet of paper, with branches that radiate from the central topic. Use of illustrations and color appeal to the right side of the brain, which is normally neglected in traditional linear note-taking approaches. The somewhat freewheeling format of mind maps facilitates problem solving by making it easier to visualize the “big picture.” While this technique has benefits for everyone, a visual learner will especially appreciate mind maps. One useful variation is to combine mind mapping (organic structure) with a linear structure in a two-column format. This format is useful when taking notes in real time; it allows the note taker to spontaneously jot down points and related ideas during the course of the lecture or presentation. Rules for creating mind maps: c Put the main ideas in the middle of the sheet of paper and box it in. c Add a branch from the center for each key point. 38 CREATIVE THINKING c Use a different color for each branch. c Write one key word or short phrase on each branch and keep building out. c Use arrows to show connections between branches. c Use symbols or illustrations. c Use CAPITAL letters. c Let the size of the ideas reflect their relative importance. c Use underlines and bold letters. c Make it personal! c Be creative! Devil’s Advocate Technique aâ•–Tip #5: The devil’s advocate technique imposes objectivity and compels divergent thinking. Your Side Pros Opponent’s Side Cons Pros Cons Definition: Devil’s advocate – a person who advocates an opposing or unpopular cause for the sake of argument or to expose it to a thorough examination. 39 THE LITTLE BLUE REASONING BOOK Exhibit 2.1 “The World of Wine” Mind Map by Sandi Hotchkiss 40 CREATIVE THINKING Exhibit 2.2 “Happiness” Mind Map by Paul Foreman 41 THE LITTLE BLUE REASONING BOOK The devil’s advocate technique forces us to consider the merits of the “other side” of an issue or topic. What we actually do is act as if we believe our opponent’s side is right! In this way we can gain a greater degree of objectivity. This technique is excellent for use in negotiations because it forces us to understand the other party’s position and leads to a more realistic, effective bargaining process. Consider that you are an analyst working at a leading market research firm. Your objective is to write a report on the market economics for product A. You have a strong idea that the market for product A is becoming more price-sensitive, and that the greater variations in price observed in the market are due to widening differences in product quality and branding (or perceptions of that product’s quality or brand strength). You need to confirm your suspicion, and you’re off to an interview with the marketing director of a major company who is responsible for marketing product A. But wait! If you and other analysts hold a similar view then you risk simply confirming something you already believe. Play the devil’s advocate. Go into the meeting and ask questions designed to “disconfirm” what you think is true. You might ask, “So, is it true that the market for product A is becoming less pricesensitive?” The responses elicited may be essential to gaining a more complete understanding of the situation. Idea Killers and Idea Growers aâ•–Tip #6: Not challenging the obvious, evaluating ideas too quickly, and fear of looking the foolâ†œ—â†œthese are the three greatest creativity inhibitors. 42 CREATIVE THINKING Not challenging the obvious Creativity may suffer whenever we as individuals accept the status quo. We have to challenge the obvious. “Does one plus one really equal two”? It could indeed equal two. But it might equal eleven, as in “1 + 1 = 11.” Or it could equate to “T,” the result of placing one bar on top of the other. Management consultants are constantly faced with the need to challenge the obvious. For instance, a client calls the consultant in and says, “Profitability is down because product costs are too high. Can you help me find a way to reduce them?” The consultant will instinctively challenge the obvious, asking whether it is the case that costs are too high. Perhaps it is another factor in the profitability mix (i.e., price or volume) that is really to blame. Evaluating ideas too quickly One way of confronting this barrier is to look at your hands. Think of your right hand as representing “idea production” and your right hand as representing “idea evaluation.” Often an idea produced is immediately evaluated and possibly killed, e.g. by the phrase, “That won’t work.” Success in creative thinking demands that the two hands should be separated, and that the left hand (idea evaluator) should be put to one side for the moment. All ideas are acceptable in a creative situation, regardless of the quality. They may be good, bad, useful, useless, legal, illegalâ†œ—â†œit doesn’t matter. Subsequently, the evaluation hand is brought back, and at that stage, a strange thing happens. Some of the ideas which originally would have been dismissed are looked at afresh, possibly with the comment: “Wait a minute, there may be something in that idea after all.” 43 THE LITTLE BLUE REASONING BOOK Fear of looking the fool Failing to challenge the obvious and evaluating ideas too quickly may well be the by-products of being afraid to look like a fool. We learn to fear ridicule from an early age, and it follows us into later life. Many excellent examples are found in the world of management. In a hierarchical organization, junior team members are less likely to put forth wild, wacky ideas for fear that more senior team members will see them as silly. The junior does not want to destroy his or her chances of promotion, and therefore sticks to well-tried, analytical routines. At the other end of the scale, the most senior manager seeks to protect his imageâ†œ—â†œone that been built up over many years. That senior manager doesn’t want to confirm to his or her underlings that he or she is a silly old fool. As a consequence, he or she does not propose any wild ideas either. In short, we must fight apathy, hastiness, and insecurity. History abounds with instances of people who haven’t been proactive enough in evaluating new ideas or who have been overly dismissive of new inventions or artistic or literary styles. This is particularly true where individuals are deemed authorities in their fields and err on the side of protecting their reputations. Here are several examples taken from the domain of science and art. w Walt Disney was fired by a newspaper editor of the Kansas City Star newspaper because “he lacked imagination and had no good ideas.” Years later, the Disney company bought ABC which owned the Kansas City Star. w Although Vincent van Gogh produced some 800 paintings, he was able to sell only one painting during his lifetime. The Red Vineyard at Aries was sold to the sister of one of his friends for 400 francs (approximately $50). w In 1921, Newton Baker, U.S. Secretary of War, reacted to Brigadier General Billy Mitchell’s claim that airplanes could 44 CREATIVE THINKING sink battleships by dropping bombs on them: “That idea is so damned nonsensical and impossible that I’m willing to stand on the bridge of a battleship while that nitwit tries to hit it from the air.” w “Can’t act. Can’t sing. Can dance a little.” MGM summary of a screen test of some guy named Fred Astaire, 1928. w A Paris art dealer refused Pablo Picasso shelter when he asked if he could bring in his paintings from out of the rain. w “Where a calculator on the ENIAC is equipped with 19,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes and perhaps weigh only 1.5 tons.” Popular Mechanics, March 1949. w “I have traveled the length and breadth of this country and talked with the best people, and I can assure you that data processing is a fad that won’t last out the year.” The editor in charge of business books for Prentice Hall, 1957. w “We don’t like their sound, and guitar music is on the way out.” Decca Recording Co. on rejecting the Beatles, 1962. w “But whatâ•›…â•›is it good for?” Engineer at IBM’s Advanced Computing Systems Division, 1968, commenting on the microchip. w Madonna, the best-selling female rock artist of the 20th century, was rejected by several music labels in the early 1980s. One talent agent is said to have commented that her voice wasn’t unique enough to stand out in a crowded marketplace. w In the early 1990s, J.K, Rowling’s Harry Potter and the Philosopher’s Stone was rejected by more than a dozen UK publishers, the majority of which believed that the story wasn’t mainstream enough. 45 THE LITTLE BLUE REASONING BOOK The process of making mistakes in judgment and/or missing opportunities can be further illustrated within the framework of Type I and Type II errors. These two types of errors also are discussed within the topic of Hypothesis Testing in chapter 3. Type I errors are really errors of commission, while Type II errors are errors of omission. Type I errors result in failure. Type II errors result in missed opportunities. A Type I error occurs when we take an action and it turns out to be a mistake. For example, whenever a top movie executive “green-lights” (okays) a movie project that turns out to be a failure, a Type I error is committed. The executive’s career could suffer in a very public way, as these kinds of errors are very visible. A Type II error occurs when we don’t take an action, and the mistake comes from missing an opportunity. If one movie executive passes on a decision to make a movie, and another movie house later produces it, turning it into a blockbuster, a Type II error is committed. Type II errors are often hard to see, even if they are common. The problem is that most Type II errors are never discovered. This is because many opportunities never immediately resurface. Projects or ideas, once killed or shelved, seldom get a second opinion. They are stopped without being shown to other people or organizations to see if someone else wants to take on the risk to pursue them. Because Type II errors are mostly invisible, they come at less cost to people and organizations than do Type I errors. It’s often easier to say no to something that might be a huge success than it is to say yes, because most of the time, no one will ever know what the outcome might have been. As long as most individuals (and the departments or organizations they work for) are evaluated based on the outcomes of their decisions, and not on what opportunities they might have missed, Type II errors will never be fully monetized. 46 CREATIVE THINKING aâ•–Tip #7: Keep a mental list of idea “killers” and idea “growers.” Idea Killers We tried it before. It would cost too much. That’s not my job. That’s not your job. That’s not how we do it. Why don’t you put that in writing? It’s impossible. That sounds crazy to me. Maybe next year. You may be right, butâ•›… If it ain’t broke, don’t fix it. Our customer would never go for that. It would take too much time. I don’t think that’s important. My mind is definitely made up. Our company is too small. Our company is too big. It’s good enough. That’s a stupid idea. We don’t have time right now. I don’t need any more information. You can’t do that here. 47 THE LITTLE BLUE REASONING BOOK I dea Growers Are there any questions? Before we make a final decision, let’s review all the options. Where else can we go for additional information on that? May I ask a question? What would happen ifâ•›…? In light of the new information, I’ve changed my mind. How could we improveâ•›….? Let me ask you for some ideas onâ•›… I’d like to get your help with an idea I’m working on. Is this what you meant? Who else would be affected? What have we missed? Who else has a suggestion? I don’t know much about that. How about you? Why do we always do it like that? Wouldn’t it be fun ifâ•›…? What ideas have you come up with? How many ways could weâ•›…? Thank you! 48 CREATIVE THINKING Brainstorming aâ•–Tip #8: Brainstorming has rules: quantity of ideas is preferred, wacky ideas are welcome, delayed evaluation is mandatory, and “hitchhiking” is encouraged. Ideas are the lifeblood of creativity, and brainstorming is a method to generate ideas. Brainstorming sessions are usually conducted in a group of between six and fifteen people. The setting is a room equipped with a whiteboard (or flip chart) so that ideas can be written down. The goal of brainstorming is to produce “novel but appropriate” ideasâ†œ—â†œthe very heart of creativity. To achieve this goal, one must adhere to the “rules” of brainstorming. First, quantity of ideas is the primary objective. Ideas should flow right from participants’ tongues to the whiteboard. Second, to get people to come up with truly novel ideas, we say “wackier is better.” Let the ideas flow by themselves. No one should fear looking the fool. All ideas, however wild or silly, are accepted. Third, delayed evaluation is mandatory. It is contradictory to try to create ideas and evaluate them at the same time. Any such attempt will curtail the creative process. Fourth, as the session progresses, people will naturally “hitchhike” on ideas. “Oh that idea reminds of this” and “If that is so, then how aboutâ•›…” Hitchhiking means that one person is able to use another person’s idea to go further and supply another idea. Toward the end of the brainstorming session, ideas will be scattered haphazardly from one end of the whiteboard to the other. This is perfectly natural. This may cause some participants to giggle or burst out laughing because very rarely does anyone experience this kind of free-flowing activity, especially in an office environment. Once ideas are regrouped and summarized, the results may be truly surprising. Managers, for example, who are unfamiliar with the power of brainstorming sessions are typically amazed at how many commercially viable ideas exist in the “collective mind” of their staff members and employees and that have never been uncovered previously. 49 THE LITTLE BLUE REASONING BOOK Business Brainstorming Questionnaire The business questionnaire per exhibit 3.1 yields the best results if completed as a group brainstorming session. The brainstorming session should take place on company premises. It is a deceptively thought-provoking tool for increasing our understanding of our company, its products, and the current market opportunities. This questionnaire includes a most intriguing question: “What business are we really in?” Participant responses to this question may help a company redefine its business by enlarging its scope (or sometimes by narrowing it). Many business leaders have used this question to find new market opportunities. Too often, the business we believe we are in has been too narrowly defined or has become narrowed over the passage of time. Consider a company that prints newspapers. What business are they in? The likely answer is “the newspaper business.” But what business are they really in? A possible answer is “the information business.” Such a newly defined business scope conjures up new possibilities. The opportunity faced by such a company may be the challenge, not of selling more newspapers, but rather of entering new but related markets. Is an airline company in the airline business or the transportation business? How about Coca-Cola? Coke used to define itself as being in the carbonated soft drink market, where it enjoyed an 80 percent market share. When Coke redefined its market in terms of ready-to-drink beverages, its market share fell to 10 percent. The ready-to-drink beverage market includes bottled water, orange juice, milk, and any other drink sold in a bottle, can, or container. Such a redefinition radically altered the company’s perception of its market potential, and led to reinvigorated marketing efforts. 50 CREATIVE THINKING Exhibit 2.3 I. What Business Are We Really In? What is our business? 1a. What business are we really in? 1b. What business should we be in? 1c. What business(es) are we in, but perhaps shouldn’t be? 1d. Where do we see ourselves in a year? Two years? Five years? Ten years? (And why?) 1e. How will macroeconomic and political changes affect our business? II. Who are we? 2a. Exercise: Create a one-page résumé for our company and include: Experience Education Accomplishments References 2b. What are we really good at doing? (What are our core competencies?) 2c. Ask yourself: What assets do or can I bring to our company? What skills? What contacts? 2d. What things should we be good at (but aren’t yet)? III. What are we selling, to whom? 3a. Who are our customers? Who buy(s) from our company? (Who buys each product?) 51 THE LITTLE BLUE REASONING BOOK 3b. Why do they buy? 3c. What are we really selling? What benefits are our customers buying?â•›…â•›receiving? 3d. Who doesn’t buy (but could or should)? 3e. Why don’t they? IV. Who is our competition? 4a. Who competes with us? What business are they in? 4b. What are their unique selling points/advantages vis-àvis our company? 4c. What are their weaknesses vis-à-vis our company? 4d. How do they advertise and promote? 4e. What are their pricing and discount policies? 4f. What are their customer service policies and practices? 4g. Who are their key people? What do we know about them? Experience and qualifications? Strengths and weaknesses? Personality traits? V. What is our competitive position? 5a. What markets are we in? 5b. Who is our competition (in each market)? 5c. How are we positioned against the competition? 5d. How or where are we stronger? How or where are we weaker? 52 CREATIVE THINKING 5e. If we worked for a competitor, how would we go about attacking our company to steal our company’s business? VI. How can we improve customer service? 6a. How do our customers feel about our company’s service? Why? 6b. Where is our service strong? What do people compliment us on, or thank us for? 6c. Where can we improve our service? What complaints have we had (even if they were not our fault)? How are complaints handled? Can this be improved? 6d. What customer service practices are established as our company’s policies? Are they written down? Where? Does everyone know about them? 6e. How can we make our customers feel like “part of the team”? 6f. V. How many ways can you think of regarding how we can offer better service and/or value to our customers? (At this stage, let your imagination run riot: no matter how outrageous, think of as many ideas as you can: quantity, not qualityâ†œ—â†œfor now, at least.) Advertising and Promotion How many ways can you think of to promote our company’s business? (At this stage, let your imagination go wild: wacky, impractical ideas are as welcome as practical ones. Quantity over quality: the list can be whittled down later.) 53 THE LITTLE BLUE REASONING BOOK Reframing Problems aâ•–Tip #9: Consider whether a problem is really the problem. Think in terms of redefining the problem. Ponder the following problem: “A restaurant is losing customers because customers are annoyed at how long it takes to line up outside in order to get a seat inside the restaurant.” If you were hired as a consultant, reporting to the headquarters of the restaurant chain, what would you suggest? Typical solutions to be anticipated include: Enlarging the restaurant facilities in order to serve more customers Streamlining the menu in order to make ordering and delivery of food faster Refusing to let customers occupy tables if not ordering food; no “drinking-only” tables These are all potential solutions. Nevertheless, they address only one of a number of possible general objectives: to speed up the process of getting customers through the dining process. An alternative goal is to find ways to keep people from getting annoyed at lining up. This suggests a host of potential strategies, such as installing televisions that customers could watch while they wait for a table, giving them free snacks while they wait in line, conducting market research while they wait in line, or having live or videotaped entertainment (e.g., magicians) to amuse persons in the line. Still another objective is to keep the restaurant from having too many customers at one particular time of day. One idea/strategy would be to get more of the regular restaurant customers to come at non-peak hours. This might be accomplished by giving special 54 CREATIVE THINKING dinner or drink discounts during certain hours of the day or holding special promotional events, such as corporate cocktail parties, speaking engagements, book signings, guitar solos, or birthday parties for the elderly. It is rare for people to step back and try to define alternative goals. Instead, most people read or hear of a problem and almost immediately begin generating strategies. One way to become more creative is by explicitly defining a minimum of two or three different goals for each problem situation. Here is another example: An agricultural importer’s association was attempting to seek a way to reduce the number of bruised pears which occurred when these fruits were transported. The importers initially defined their goal as “decreasing the rate with which pears became bruised or damaged when shipped.” This led to various strategies for modifying distribution systems and packing procedures, such as including more padding around the pears and using smaller packing boxes. Although all of these strategies provided partial solutions, none was considered a breakthrough. Reframing the problem led to a new goal: “creating a pear that is less likely to be bruised!” This entailed hiring individuals to look into the process of breeding pears. By exploring strategies to modify the pear, a portion of the problem was eventually solved. An “apple-pear” was bornâ†œ—â†œa fruit with some of a pear’s taste but with an apple’s sturdiness Now grocery stores could be supplied with large quantities of unblemished pear hybrids. Get into the habit of asking if the problem really is the problem. Is the goal really the goal? Selling Creative Ideas aâ•–Tip #10: In selling creative ideas, most people are moved more by the depth of a person’s conviction and commitment than they are by the details of a logical presentation. 55 THE LITTLE BLUE REASONING BOOK To turn any creative idea into an innovative reality, an individual must obtain the support of key persons in an organization. In reality, the acceptance of a creative idea will have as much or more to do with company politics as with technical considerations. First, think of everybody as being your ally. Get initial feedback from people lower in the organizational structure and use it as a trial session to see what questions people have and what weaknesses and strengths are attributed to your idea. Never think you can please everyone; there will always be objectors. In fact, one way to gather support for your project is to ask for input from those you expect will be most affected. Note that most good ideas are defeated by irrelevant issues. It should come as no surprise that the people who are most affected by the potential implementation of an idea tend to have a knack for raising irrelevant issues. Use this fact to your advantage. Make note of such issues and prepare to defend against them. Assuming your idea is good, people will want to invest in it. Let them. It is important to give the impression that you do not want to take total credit for the idea you have created. People who do invest in your idea will hope to get something in return. Upon their acceptance of your idea, you have to determine what that “something” is. Never believe that you will not have to alter your idea; compromise is an inevitable reality. Last, think hard about your ultimate decision makersâ†œ—â†œyour real audienceâ†œ—â†œand do some research. The better you know who your audience is, the better you can tailor your presentation. The ultimate presentation is customized, organized, and passionate. Strive to combine logic and novelty, but remember, above all else, that research indicates that people are persuaded more by passion and dedication to an idea than they are by a logical, detailed presentation. 56 Chapter 3 Decision Making Nothing is more difficult, and therefore more precious, than to be able to decide. —â†œNapoleon DECISION MAKING Overview This chapter introduces a variety of tools that can be used in making decisions for the purpose of solving problems or capturing opportunities. In this respect, it addresses applied reasoning. Perhaps the most important benefit of these techniques lies in our ability to use them to structure the thinking process. Imagine building a house without a plan! Adding structure to the decisionmaking process is like having a blueprint before building a house. Certainly a house could be built without a blueprint, but not as accurately or efficiently as it would be with one. A crucial distinction between structuring and decision making is that structuring doesn’t make decisions; people do. The tools presented here are principally “trees” and “boxes.” Trees impose order and hierarchy; boxes summarize data or information. Using trees is similar to flowcharting, and decisionevent trees provide a classic example of techniques used to diagram information and visualize outcomes. Using boxes is similar to using a table to sort information or data, although in this material, “boxes” most often refers to matrixes. Frequently the need exists to contrast information according to two (or more) variables, and this leads to four (or more) distinct outcomes. Work done in a factory might involve making small and large widgets and silver-colored and gold-colored widgets. Matrixes help us to set up the information in a table to quickly see how many items fall within each category: silver-colored widgets that are small, silver-colored widgets that are large, gold-colored widgets that are small, and gold-colored widgets that are large. Weighted ranking is a technique to help us quantify the decisionmaking process in order to evaluate outcomes or options. We rank items and assign weights to them. An example occurs if we are buying a house and want to make the best decision. Say we believe, for example, that the ideal house is a combination of having the right location, size, and livability. By ranking prospective houses not only under each of the three categories, 59 THE LITTLE BLUE REASONING BOOK but by also assigning weights (or probabilities) to them, the optimal choice is quantifiable. Hypothesis testing is useful when we want to test an idea or theory. It provides a framework for testing ideas and it begins with a hypothesisâ†œ—â†œa statement that we are trying to prove. Statements begin as questions and run the gamut of social science, business, or science: “Are green-eyed people more gregarious?” (social science); “Do stockbrokers really make better stock investment decisions than regular business people?” (business); “Do I have cancer?” (science). Lastly, in examining the Prisoner’s Dilemma, a mixed-motive game, we gain insights into the benefits of cooperation versus competition as they relate to individual versus group decisions. Pros-and-Cons Analysis aâ•–Tip #11: Pros-and-cons analysis may be illustrated using a “T-Account,” with pros on one side and cons on the other side. Pros Cons • • • • • • How many sides are there to every issue? Actually there are three. There are two distinct sides, as well as the “middle” view. But in pros-and-cons analysis, we assume for simplicity that there are 60 DECISION MAKING two sides to every issue. The advantages are called “pros” and the disadvantages are called “cons.” Our practical goal is to evaluate a topic or issue by generating three support points for each side prior to beginning to write. Seeing both sides of an issue is the cornerstone of an all-around thinking process. A secondary benefit of pros-and-cons analysis is that it forces a person to consider positive points, not just negative ones. Most people are naturals at finding flaws! Prosand-cons analysis brings balance. The benefits of high school or college debate is that it trains students to consider two sides of any issue. During a given tournament, a debater must be prepared to both defend and attack different sides of the same topic. Note that pros-and-cons analysis should include both qualitative and quantitative support points, if applicable. Replace an Old Historical Building? Imagine for a moment working as a professional for the urban planning department of a major city. As a staff member, you must make a recommendation on whether to replace an historical building located in the city’s downtown center with a modern building. In order to engage all-around thinkingâ†œ—â†œthinking that encompasses both sides of an issueâ†œ—â†œlet’s fill in the chart on the next page, placing support examples next to each bullet point. Topic: “Although most people would agree that historical buildings represent a valuable record of any society’s past, municipal governments should resolve doubt in favor of removing old buildings when such buildings stand on ground that planners feel could be better used.” Outline the likely pros and cons behind any decision to remove or keep an historical building. 61 THE LITTLE BLUE REASONING BOOK Outline Template for Pros and Cons Cons Pros Quantitative Support Points Qualitative Support Points In general, I agree that we should resolve doubt in favor of replacing old buildings. In general, I disagree that we should resolve doubt in favor of replacing old buildings. • • • • • • • • • • • • 62 DECISION MAKING Filling in the Pros and Cons Qualitative Support Points Quantitative Support Points Pros Cons In general, I agree that we should resolve doubt in favor of replacing old buildings. In general, I disagree that we should resolve doubt in favor of replacing old buildings. •Revenue streams: New buildings earn more money in rent or sales. •Revenue streams: Old buildings earn money from tourists. •Revenue streams: New buildings earn more money in taxes. •Revenue streams: Wealthy individuals often donate money to preserve old historical buildings. •Costs: Old buildings have high maintenance costs which could be avoided if we built a new building. •Costs: There is a huge capital outlay to begin construction on a new building which ties up valuable municipal funds. •Educational: There is cultural, educational, and historical worth in old buildings. •Safety: New buildings are safer. •Architectural: New buildings are more visually harmonious with other modern buildings (“harmony in parity”). •Architectural: Old buildings offer an interesting visual contrast to modern buildings (“harmony in contrast”). •Aesthetics: New buildings are a sign of power and progress. •Aesthetics: Old buildings bear a sense of nostalgia. 63 THE LITTLE BLUE REASONING BOOK Problem 6 Corporate Training One more! Fill in the chart on the following page with hypothetical but plausible support points to illustrate the pros and cons of providing on-site corporate training. Topic: “The Head of the Human Resources Department of Super Corp. believes that a formal in-house training program is required to build employee skills in order for employees to perform new tasks and to avoid the costs associated with hiring for new positions from outside the company. Certain key executives, however, believe that formal in-house training will either take up valuable company time without proven effectiveness or be lost due to the high rate of employee turnover.” Using pros-and-cons analysis, evaluate the case for and against corporate in-house training. 64 DECISION MAKING Outline for Pros and Cons Cons Pros Quantitative Support Points Qualitative Support Points Yes, I agree that we should provide inhouse training. No, I don’t think we should provide inhouse training. • • • • • • • • • • • • 65 THE LITTLE BLUE REASONING BOOK Matrixes aâ•–Tip #12: A matrix is a useful tool to summarize data that can be contrasted across two variables and sorted into four distinct outcomes. Understanding Matrixes The most common matrixes appear as two-column, two-row tables. A matrix is used to effectively present data, as is always the case, where two items are being contrasted with two other items and there are four possibilities or outcomes. The matrix below is based on a famous time management principle highlighting the need to concentrate on “important but not urgent” tasks. Exhibit 3.1 Urgent Tasks Not Urgent Tasks Time Management Matrix Important Tasks Unimportant Tasks Important and Urgent Tasks Unimportant but Urgent Tasks • Example: A major project is due in three days! • Results in crisis management • But time management problems are not found here. • Example: The phone rings and you need to pick it up (this is an unimportant but urgent task; it is not related to the project at hand). • Good time management means putting limits here. Important but not Urgent Tasks Unimportant and Not Urgent Tasks • Example: A major project is assigned but is not due for three months. • Never get around to it • Not enough time devoted here • Divides effective and ineffective individuals • Time management problems found here. • Example: You attend a community service event by day (unrelated to the project at hand); later that night you watch TV. • Busywork; tension-relieving work; wasted time • Low-priority items • Good time management means putting limits here. 66 DECISION MAKING Our job with respect to matrix problems is to fill in known information, and through simple mathematical deduction, find the unknown information. Take for example a batch of toys, fresh off the production line. Each toy has exactly two of four characteristics: each is either blue or green and either large or small. A matrix must total across as well as down. This is the figure that appears in the bottom righthand corner of the extended matrix, represented by three “xxxs.” The dotted lines are merely useful extensions of the basic fourbox matrix. Here is the template used to set up this problem: Toy Production Here is the nine-box table used to set up this problem: Color Blue Green Large x x xx Small x x xx xx xx xxx Size 67 THE LITTLE BLUE REASONING BOOK Say we have a batch of 100 toys. The number 100 will be placed in the extended bottom right corner. Based on available data, the matrix might be filled in as follows: Color Blue Green Large 20 45 65 Small 10 25 35 30 70 100 Size Why do matrixes work so neatly? Things work neatly as long as all data is “mutually exclusive and collectively exhaustive.” What does this mean? Mutually exclusive is a fancy way of saying that the data does not overlap; it is distinct. In other words, toys must be either blue or green and either large or small. We can’t have toys which are both blue and green (e.g., colored blue-green or striped) or both large and small (i.e., medium-sized). Collectively exhaustive means that the number of data is finite. There are exactly 100 toys, of which 30 are blue, 70 are green, 65 are large, and 35 are small. Data which is mutually exclusive and collectively exhaustive ensures that everything will total both “down” and “across.” Matrixes also work with information (see exhibit 3.1), in addition to numbers, as long as information makes sense when read across as well as down. Because matrixes handle information so neatly, it is not surprising that they are a consultant’s favorite presentation tool. Folklore has it that one junior management consultant became so enamored with matrixes that he called them “boxes of joy”! The truth is that matrixes are wonderful tools that can encapsulate a great deal of information. Case in point: The following write68 DECISION MAKING up sheds light on just how much information can be gleaned from The Lots-Little Matrix (exhibit 3.2), which can be used to understand how the two basic components of a company’s profitabilityâ†œ—â†œmargin and volumeâ†œ—â†œaccelerate or trade-off with each another in a competitive business marketplace. Exhibit 3.2 The Lots-Little Matrix Margin High Low High 1. Lots (Q), Lots ($) 2. Lots (Q), Little ($) Low 3. Little (Q), Lots ($) 4. Little (Q), Little ($) Volume Notes: (Q) = Volume = quantity of product sold ($) = Margin = dollar “profit” per unit of product sold The Lots-Little Matrix is useful for pinpointing where specific companies or industries are competitively positioned: 1. Sell a lot (Q), at a lot ($) “Selling large quantities at high margins.” The computer software industry has provided examples of companies (Apple and Microsoft in their early days) that are/were able to sell large volumes of product at high margins, within limited time frames. 2. Sell a lot (Q), at a little ($) “Selling large quantities at low margins.” The airlines industry is known for selling large volumes of product (seats) at low margins. 69 THE LITTLE BLUE REASONING BOOK 3. Sell a little (Q), at a lot ($) “Selling small volumes at high margins.” Companies within the fashion industry (haute couture) are known for being able to sell relatively smaller volumes of product at high margins (sometimes very high). 4. Sell a little (Q), at a little ($) “Selling small volumes at low margins.” Sam’s Fish & Chips (a generic, local food vendor) sells small volumes of product at low margins. The Lots-Little Matrix helps tell a story about how businesses thrive and survive. Certainly companies would love to operate in category 1 and enjoy the best of both worlds: high margins and high volumes. But practically, the competitive marketplace does not usually allow such occurrences to be long lived. A company initially operating in category 1 would likely be forced into one of categories 2 or 3, as a result of competitors entering their marketplace. Many businesses operate in categories 2 or 3. That is, they either have good margins but lower volumes (category 2) or lower margins but good margins (category 3). Category 4 would invariably represent those small businesses that can sustain themselves, but are not able to grow to compete in categories 2 or 3. Generally, no major company within an established industry can sell only small volumes at low margins and survive for any extended time frame. Matrixes vs. Tables Confusion often arises regarding the use of tables and matrixes. While it is true that matrixes look like tables (actually, all matrixes are tables but not all tables are matrixes), they are distinctly different tools. As previously illustrated, matrixes must total across and down and do so because the data or information contained 70 DECISION MAKING in them is mutually exclusive and collectively exhaustive. Tables simply display or group related information. However, tables should not be used to sort random data. Table A works well because the information is related. Here, the study of marketing is displayed by breaking it down into four distinct areas. Table A – The Marketing Mix Product Promotion Price Place (Distribution) The information in Table B is not presented effectively because the words appear random and arbitrary. Table B – Medical Discoveries in Europe Paris Madrid London Amsterdam The cities mentioned above should, in all likelihood, be enumerated in a list: 1) 2) 3) 4) Paris London Madrid Amsterdam Exhibit 3.3 is not a matrix (although it certainly looks like one) because the information only “reads” down, but not across. The following write-up would likely accompany this chart: 71 THE LITTLE BLUE REASONING BOOK We hear so much about information today. But when is information deemed “good” information? Information is best understood by looking at it in terms of its four quality dimensionsâ†œ —â†œ accessible, summarized, relevant, and customized. When information touches all of these dimensions it becomes both efficient and effective. The dimensions of “accessible” and “summarized” relate to the efficiency of information. The dimensions of “relevant” and “customized” relate to the effectiveness of information. The terms effective and efficient are, in casual conversation, often used interchangeably because information has traditionally been thought to be effective as soon as it has been deemed efficientâ†œ—â†œthat is, when “accessible” (dimension 1) and “summarized” (dimension 2). It is the purpose of this chart to highlight the importance of effectivenessâ†œ—â†œ“relevant” (dimension 3) and “customized” (dimension 4). Unless information is effective as well as efficient, it will not be easily adopted or internalized by the user. Without becoming effective, information cannot be easily recalled or acted upon. Information that has all four elements may be said to be “transparent.” It is so ready and usable that it takes on the appearance of always being in the mind of the user. 72 DECISION MAKING Exhibit 3.3 E f f i c i e n c y The Effective Information Chart Dimension 1: “Accessible” Dimension 3: “Relevant” Information must be constantly accessible and mobile. It can’t be just stored in boxes. Information must be targeted and relevant so that it has meaning and significance to the user. Key concept: readily locatable Key concept: readily applicable Catchwords: getable, findable Catchwords: targeted, applicable, pertinent Dimension 2: “Summarized” Dimension 4: “Customized” Information must be kept in summarized form. It must be distilled and condensed. Information must be able to be modified and tweaked to conform to the user’s style or needs. Key concept: readily digestible Key concept: readily adaptable Catchwords: compact, essential, distilled Catchwords: “ownable,” styled, personalized 73 E f f e c t i v e n e s s THE LITTLE BLUE REASONING BOOK Using Matrixes Job search: Of thirty-five applicants applying for a job, twenty had at least seven years’ work experience, twentythree had degrees, and three had less than seven years’ work experience and did not have a degree. How many of the applicants had at least seven years’ work experience and a degree? Step #1: Sketch a matrix and enter given information into the appropriate boxes. The shaded box depicts the value we’re trying to find. < 7 years’ work v 7 years’ work experience experience With degrees No degrees ? 23 20 35 3 Step #2: Let’s total the numbers on the side and bottom of the matrix, filling in the dotted boxes. < 7 years’ work v 7 years’ work experience experience With degrees No degrees ? 3 23 12 15 20 74 35 DECISION MAKING Step #3: Since data must total down and across, we simply fill in remaining numbers within the middle four boxes. < 7 years’ work v 7 years’ work experience experience With degrees 12 11 23 No degrees 3 9 12 15 20 35 Eleven of the candidates, therefore, have at least seven years’ work experience and hold degrees. For each of the following problems, use matrix analysis to calculate the desired outcomes. Problem 7 Singles In a graduate physics course, 70% of the students are male and 30% of the students are married. If 20% of the male students are married, what percentage of students are female and single? Problem 8 Batteries For every batch of 100 batteries manufactured at a certain upstart factory, one-fifth of the batteries produced by the factory are defective and one-quarter of all batteries produced are rejected by the quality control technician. If one-tenth of the non-defective batteries are rejected by mistake, and if all the batteries not rejected are sold, then what percent of the batteries sold by the factory are defective? 75 THE LITTLE BLUE REASONING BOOK Problem 9 Interrogation Police who are trained in criminal interrogation techniques use questions to obtain information and evidence about the guilt or innocence of the subject being interrogated. There are four possible outcomes: (1) a person did commit a crime and is telling the truth (confessing to a crime they really did do); (2) a person did commit a crime and is not telling the truth (claiming to be innocent when they really did do it); (3) a person did not commit a crime and is telling the truth (claiming to be rightfully innocent for a crime they didn’t do); and (4) a person did not commit a crime and is not telling the truth (confessing to a crime they actually didn’t do). Interrogators have past statistics to guide them. In short, police interrogators contend that when someone is accused of a crime and interrogation takes place, there is a 75% chance that a given person did not commit the crime, a 20% chance that a person is not telling the truth, and a 2% chance that a person will confess to a crime they didn’t commit. Based on these statistics, what is the chance that a person actually committed the crime and is telling the truth (confessing to a crime they actually committed)? Decision-Event Trees aâ•–Tip #13: Decision-event trees are a way to represent graphically the multiple outcomes involved in a decision scenario. Terms such as felony, infraction, misdemeanor, and tort are potentially very confusing for the layperson. How might a firstyear law student put these words into a decision tree to help make sense out of case law? One idea would be to view each term in terms of the severity of punishment that a court/jury could impose on a guilty verdict. 76 DECISION MAKING How are the following ten terms connected? Felonies Civil Wrongs (private) Infractions Torts Homicide Treason Offenses Crimes (public) Misdemeanors Breach of Contract The decision-event tree per exhibit 3.4 acts as a flowchart to depict logical relationships among legal terms. Civil wrongs, also known as “private wrongs,” occur between or among individuals. A breach of contract occurs when one party “breaks” a legal agreement. A tort is a general term used to describe acts that result in injury to another person (e.g., assault). Crimes, on the other hand, involve the state (public). Informally speaking, infractions are “minor offenses” (e.g., parking violations), misdemeanors are “minor criminal offenses” (e.g., shoplifting), and felonies are “major criminal offenses,” of which homicide (murder) and treason are considered the most serious offenses. Understandably, the above paragraph is difficult to read. We need a visual representation to summarize the type of crime and the severity of crime. Refer to exhibit 3.4. 77 THE LITTLE BLUE REASONING BOOK Exhibit 3.4 Decision-Event Tree – Legal Offenses Breach of Contract E.g., rental agreement Civil Wrongs (private wrongs) Torts E.g., assault Offenses Infractions E.g., parking violation Crimes (public wrongs) Misdemeanors E.g., shoplifting Felonies Homicide E.g., manslaughter Treason E.g., selling state secrets Exhibit 3.5 provides an example of a decision-event tree showing the outcomes associated with tossing a coin three times? There are eight possibilities when a coin is tossed three times: HeadsHeads-Heads (HHH), Heads-Heads-Tails (HHT), Heads-TailsHeads (HTH), Heads-Tails-Tails (HTT), Tails-Heads-Heads (THH), Tails-Heads-Tails (THT), Tails-Tails-Heads (TTH), and Tails-Tails-Tails (TTT). Even though writing out the possibilities using abbreviated letters is compact, it is not as easy to grasp until supplemented with a visual format. Decision-event trees are notably user-friendly. 78 DECISION MAKING Exhibit 3.5 Decision-Event Tree – Coin Tosses Heads HHH Heads Tails HHT Heads HTH Tails HTT Heads THH Tails THT Heads TTH Tails TTT Heads Tails Coin Heads Tails Tails 79 THE LITTLE BLUE REASONING BOOK Exhibit 3.6 Probability Tree – Coin Tosses Heads HHH 1 8 Heads 1 4 Tails HHT 1 8 Heads 1 2 Heads Tails 1 4 HTH 1 8 Tails HTT 1 8 Coin Heads 1 8 Heads 1 4 THH Tails THT 1 8 Tails 1 2 Heads Tails 1 4 1 8 Tails 1 8 80 TTH TTT DECISION MAKING Problem 10 Set Menu A restaurant offers a set lunch menu. Diners have the choice of choosing between one of two appetizers (soup or salad), one of three main courses (pasta, chicken, or fish), one of two deserts (pie or cake), as well as coffee or tea. Draw a decision tree showing the total number of ways a diner can choose his or her meal. Probability Trees aâ•–Tip #14: The end branches of a probability tree must total to 1, which is equal to the aggregate of all individual probabilities. Exhibit 3.6 illustrates the probabilities associated with each event. Note that probabilities always total to 1, if we add the probabilities at the endpoints (i.e., 8 × 1 = 1.0 ). Each endpoint equals 1 , which 8 8 is the resultant probability of three consecutive tosses of a coin (i.e., 1 × 1 × 1 = 1 ). 2 2 2 8 Weighted Ranking aâ•–Tip #15: Weighted ranking is a tool for finding solutions using a weighted average. To calculate weighted average, we multiply each event by its associated weight and total the results. In the case of probabilities, we multiply each event by its respective probability and total the results. Snapshot The weighted average concept is actually quite intuitive. To find a weighted average, we multiply events by their respective weight and total the results. Events are the things that we wish to rate, rank, or judge. Weights refer to the amount of emphasis we want to attribute to each event and are commonly expressed as percentages, fractions, decimals, or probabilities. The beauty of 81 THE LITTLE BLUE REASONING BOOK weighted average is that we can assign different weights based on the relative importance of eventsâ†œ—â†œthe more important the event, the more weight it is given. Below is the weighted average formula for two events: Weighted Average = (Event1 × Weight1) + (Event2 × Weight2) An alternative format is: Eventâ†œ1 × Weightâ†œ1 = xx Eventâ†œ2 × Weightâ†œ2 = xx xx Exam Time A student scores 60 out of 100 points on his midterm exam and 90 out of 100 points on his final exam. If the exams are both weighted equally, counting for 50% of the student’s final course grade, then what is his course grade? 60 × 50% = 30 90 × 50% = 45 75 Based on the same information above, what is the student’s final course grade if the midterm exam is weighted 40% and the final exam is weighted 60%? 60 × 40% = 24 90 × 60% = 54 78 Note that the weights above could also be expressed using fractions or decimals: 82 DECISION MAKING 40 = 24 100 60 90 × = 54 100 78 60 × â•…â•…â•…â•… 60 × 0.4 = 24 90 × 0.6 = 54 78 Hiring and promotion decisions are classic examples of situations in which subjective influences can override an objective decisionmaking process. Weighted ranking therefore presents a method to quantify decision opportunities. Consider a company with ten salespersons, one of whom is to be named National Sales Manager. As depicted in exhibit 3.7, the ten candidates are first ranked from 1 to 10 (10 being the highest rating) across three criteria. The three criteriaâ†œ —â†œ technical skills, people skills, and track recordâ†œ—â†œare weighted using the weights of 0.2, 0.3, and 0.5, respectively (see exhibit 3.8). Note that instead of using decimals (0.2, 0.3, 0.5), we could also use percents (i.e., 20%, 30%, 50%), fractions (i.e., 2 , 3 , 5 ), or even whole numbers such as 2, 3, 10 10 10 and 5. Based on the results from weighting the data (per exhibit 3.9), Patricia receives the highest ranking while George gets the next highest ranking. The weights used will typically add up to 1 or 100%, as is the case when dealing with percentages, fractions, decimals, or probabilities. Sometimes problems will use arbitrary weights which are not equal to 1. 83 THE LITTLE BLUE REASONING BOOK Exhibit 3.7 Performance of Salespersons Technical skills and product knowledge People skills and ability to communicate Track record and ability to get things done Albert 2 3 7 Betty 5 2 6 George 4 5 9 Jed 3 7 1 Jono 7 10 3 Martha 10 1 2 Patricia 1 4 8 Randy 8 9 4 Sabrina 3 6 10 William 6 8 5 84 DECISION MAKING Exhibit 3.8 Performance Using Weighted Average Technical skills and product knowledge People skills Track record and ability to and ability communicate to get things done Weight = 0.2 Weight = 0.3 Weight = 0.5 Albert 2 × 0.2 = 0.4 3 × 0.3 = 0.9 7 × 0.5 = 3.5 4.8 Betty 5 × 0.2 = 1.0 2 × 0.3 = 0.6 6 × 0.5 = 3.0 4.6 George 4 × 0.2 = 0.8 5 × 0.3 = 1.5 9 × 0.5 = 4.5 6.8 Jed 3 × 0.2 = 0.6 7 × 0.3 = 2.1 1 × 0.5 = 0.5 3.2 Jono 7 × 0.2 = 1.4 10 × 0.3 = 3.0 3 × 0.5 = 1.5 5.9 Martha 10 × 0.2 = 2.0 1 × 0.3 = 0.3 2 × 0.5 = 1.0 3.3 Patricia 1 × 0.2 = 0.2 4 × 0.3 = 1.2 8 × 0.5 = 4.0 5.4 Randy 8 × 0.2 = 1.6 9 × 0.3 = 2.7 4 × 0.5 = 2.0 6.3 Sabrina 3 × 0.2 = 0.6 6 × 0.3 = 1.8 10 × 0.5 = 5.0 7.4 William 6 × 0.2 = 1.2 8 × 0.3 = 2.4 5 × 0.5 = 2.5 6.1 85 Total THE LITTLE BLUE REASONING BOOK Exhibit 3.9 Ranking of Salespersons Total votes Rank Weight = 0.5 (The higher the better) (The lower the better) 6 × 0.3 = 1.8 10 × 0.5 = 5.0 7.4 1 4 × 0.2 = 0.8 5 × 0.3 = 1.5 9 × 0.5 = 4.5 6.8 2 8 × 0.2 = 1.6 9 × 0.3 = 2.7 4 × 0.5 = 2.0 6.3 3 William 6 × 0.2 = 1.2 8 × 0.3 = 2.4 5 × 0.5 = 2.5 6.1 3 Juno 7 × 0.2 = 1.4 10 × 0.3 = 3.0 3 × 0.5 = 1.5 5.9 5 Patricia 1 × 0.2 = 0.2 4 × 0.3 = 1.2 8 × 0.5 = 4.0 5.4 6 Albert 2 × 0.2 = 0.4 3 × 0.3 = 0.9 7 × 0.5 = 3.5 4.8 7 Betty 5 × 0.2 = 1.0 2 × 0.3 = 0.6 6 × 0.5 = 3.0 4.6 8 Martha 10 × 0.2 = 2.0 1 × 0.3 = 0.3 2 × 0.5 = 1.0 3.3 9 Jed 7 × 0.3 = 2.1 1 × 0.5 = 0.5 3.2 10 Technical skills and product knowledge People skills Track record and ability to and ability communicate to get things done Weight = 0.2 Weight = 0.3 Sabrina 3 × 0.2 = 0.6 George Randy 3 × 0.2 = 0.6 86 DECISION MAKING Chess In chess, a pawn is worth one point, a knight or bishop is worth three points, a rook is worth five points, and a queen is worth nine points. Player A has two rooks, a knight, and three pawns. Player B has a bishop, four pawns, and a queen. Who is ahead and by how much? Player A Player B Pawns: 3 × 1 = 3 pts 4 × 1 = 4 pts Bishops: 1 × 3 = 3 pts Knights: 1 × 3 = 3 pts Rooks: 2 × 5 = 10 pts Queens: 1 × 9 = 9 pts ____________ ____________ 16 points 16 points Answer: Both players are tied at 16 points each. Sweet Sixteen On her sixteenth birthday, Jane received $500 from each of her two uncles. Both amounts had been deposited in two local banks, one bank paying 6% per annum and the other paying 7% per annum. How much in total did she earn from these two investments over the course of exactly one year? $500 × 6% = $30 $500 × 7% = $35 $65 87 THE LITTLE BLUE REASONING BOOK Problem 11 Investor An investor is looking at three different investment possibilities. The first investment opportunity has a chance of returning $90,000, a $50,000, and a 1 3 $100,000 and a $100,000, a 1 2 chance of returning chance of losing $50,000. The third investment opportunity has a 1 4 chance of returning chance of losing $60,000. A second investment opportunity has a 1 2 1 2 1 6 1 4 chance of returning chance of returning $60,000, a of losing $40,000, and a 1 4 1 4 chance chance of losing $80,000. Assuming the investor chooses to invest in all three investments, what will be his or her expected return? Utility Analysis aâ•–Tip #16: Utility analysis takes into account desirability of outcomes, which may be different from monetary payoffs. Utility is “desirability.” Utility analysis is useful in those situations in which we seek to match utility with probability. In other words, these two terms must be distinguished at the outset. Utility is “what we want”; probability is “what we get.” Consider for a moment the dilemma of a fourth-year college student who is trying to decide what to do with his or her future. The student knows that he or she wants to do one of three things: pursue work as a travel writer, join the diplomatic service, or go into business and work as a sales representative. In terms of how rewarding these experiences would be, the student believes that pursuing work as a travel writer is to be rated first, joining the diplomatic service is to be rated second, and going into business is to be rated third. But how do we assign a value to the desirability 88 DECISION MAKING of these options? Money will not be an appropriate utility because the person is likely not thinking in terms of how much money can be earned, but rather how much he or she would like to pursue each of these options. The world might be our “oyster,” but how do we evaluate our options? Expected Value (EV) is defined as the product (multiplication) of a given utility and its corresponding probability. Utilityâ•… Probabilityâ•…â•‡â•›â•›â•›â•›EV Work as travel writer Join diplomatic corps Go into business 100 × 0.10 = 10 70 × 0.40 = 28 40 × 0.50 = 20 Note that the probabilities assigned incorporate the risk and/or skill level required to pursue each option. According to the above analysis, “Join the diplomatic service” provides the greatest Expected Value (EV) and, objectively, this option should be chosen. The following rules can be used to choose values for utilities. Always pick a value of 100 for the most desirable (non-monetary) outcome. This provides an analytical boundary and makes choosing other values easier. In reality, “Work as a travel writer” might be less than 100. A “100” might represent a dream scenario in which a person wins the lottery and retires to a deserted island to paint sunsets. This is not showed as an option owing to the incredibly low probability associated with it. One more rule is to make each utility a multiple of 10 (i.e., 10, 20, 70, 100), for any more precision would be suspect. Of course, utility could still be calculated in terms of money. Utility measured in monetary terms is the focus of our next problem. Four teams have made the semi-finals of the NBA Championships. It is time to place a bet. 89 THE LITTLE BLUE REASONING BOOK If there were costs associated with the opportunity to place a bet, then we would have to subtract this cost from our Expected Value in order to arrive at our price. However, such a fixed cost would not affect the result of our Utility Analysis. The team with the highest Expected Value would be the best bet. In the summary that follows, we see that option 1 has the highest probability and option 4 has the highest payoff (utility), but neither results in the highest expected value (EV). It turns out that placing a bet for team 2 or team 3 leads to the highest expected value (EV). This is because expected payoff must be tempered with probability of the outcome. The analysis below helps us see the optimal outcomes quickly. (Bet) Optionâ•…â•…â•…â•…â•‡Outcomeâ•…â•‡Utilityâ•…â•‡Probabilityâ•…â•‡EV Option 1 Option 2 Option 3 Team 1 $200 × 0.50 = $100 Team 2 $0 × 0.20 = $0 Team 3 $0 × 0.20 = $0 Team 4 $0 × 0.10 = $0 Team 1 $0 × 0.50 = $50 Team 2 $600 × 0.20 = $120 Team 3 $0 × 0.20 = $0 Team 4 $0 × 0.10 = $0 Team 1 $0 × 0.50 = $0 Team 2 $0 × 0.20 = $0 Team 3 $600 × 0.20 = $120 Team 4 $0 × 0.10 = $0 90 $100 $120 $120 DECISION MAKING Option 4 Team 1 $0 × 0.50 = $0 Team 2 $0 × 0.20 = $0 Team 3 $0 × 0.20 = $0 Team 4 $900 × 0.10 = $90 $100 Sunk Costs aâ•–Tip #17: Sunk costs are irrelevant to future decision making. Suppose you bought a discounted, nonrefundable plane ticket for $500, which you had planned to use when going on vacation. No sooner had you bought the ticket did an important meeting arise, one that you had been waiting months to arrange. It could definitely help move your career forward. You have a dilemma. How do you decide in a logical way what to do? Do you use the plane ticket you paid good money for or forfeit it and attend the important meeting? According to economic theory, any past costs, also known as sunk costs, have no affect on future decision making. The only thing that affects future decisions are the cost and benefits of the two (or more) alternative courses of action. This means that if the net benefits of this meeting are deemed greater than the net benefits of attending this trip, then we forget about the trip and attend the meeting. Of course, we must factor in both costs and benefits. The benefits of attending the meeting might involve securing a large account, getting promoted, or perhaps finding out about a new job opportunity. The costs involved might include travel to the meeting and/or the time and effort needed to prepare for the meeting. The benefits of going on vacation may well involve having a relaxi