The Little Blue Reasoning Book: 50 Powerful Principles for Clear and Effective Thinking

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A Polynomial Approach to Linear Algebra Springer-Verlag New York Paul A. Fuhrmann (auth.) Year: 2012 Language: english File: PDF, 1.86 MB

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Manuel de coréen, volume 1 Langues et Mondes L'Asiathèque André Fabre, Seung-Ja Shim Year: 2006 Language: french File: PDF, 7.21 MB

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 mechanical↜—↜including
photocopying, recording, or any information storage and retrieval
system↜—↜without 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, Canada╇ 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 systems↜—↜primary, secondary, and post-secondary↜—↜has
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 tools↜—↜boxes
and trees↜—↜are 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 col�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.
—↜La 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 thinking↜
—↜
thinking that
encompasses both sides of an issue or topic↜—↜is 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 Reid↜—↜one 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 situation↜—↜“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 novel↜—↜typing 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 intended↜—↜ice 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 championship↜—↜the “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 producer↜—↜all 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 details↜—↜the
pieces of the puzzle at hand↜—↜while 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.
—↜Loris Malaguzzi

CREATIVE THINKING

Overview
Loosely speaking, there are two types of thinking↜—↜analytical 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.
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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).

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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

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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

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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 on↜—↜and produces↜—↜a
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.

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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 divergence↜—↜
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.

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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

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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?

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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.
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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
sticks↜—↜mind 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.

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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.

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THE LITTLE BLUE REASONING BOOK

Exhibit 2.1

“The World of Wine” Mind Map by Sandi Hotchkiss

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CREATIVE THINKING

Exhibit 2.2

“Happiness” Mind Map by Paul Foreman

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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 fool↜—↜these are the
three greatest creativity inhibitors.

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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, illegal↜—↜it
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.”

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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
image↜—↜one 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
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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.

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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.

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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.

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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!

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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” ideas↜—↜the 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.
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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.

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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?)
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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?
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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 quality↜—↜for 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.)

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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
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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 born↜—↜a 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.
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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 makers↜—↜your
real audience↜—↜and 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.
—↜Napoleon

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,
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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
hypothesis↜—↜a 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
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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 thinking↜—↜thinking that
encompasses both sides of an issue↜—↜let’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.

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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.

•

•

•

•

•

•

•

•

•

•

•

•

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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.

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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.

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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.

•

•

•

•

•

•

•

•

•

•

•

•

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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.

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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

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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
profitability↜—↜margin and volume↜—↜accelerate 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.
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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
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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:
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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 dimensions↜
—↜
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 efficient↜—↜that is, when
“accessible” (dimension 1) and “summarized” (dimension 2).
It is the purpose of this chart to highlight the importance of
effectiveness↜—↜“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.

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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

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f
f
e
c
t
i
v
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n
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s
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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?
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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.

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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.

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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.

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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

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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 events↜—↜the 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:
Event↜1 × Weight↜1 = xx
Event↜2 × Weight↜2 = 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:

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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 criteria↜
—↜
technical skills, people skills, and track
record↜—↜are 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.

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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

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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

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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

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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

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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.
Utility╅ Probability╅╇╛╛╛╛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.
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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