The Little Blue Reasoning Book Part 3

6e. How can we make our customers feel like apart of the teama?

6f. 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: quant.i.ty, not quality a" for now, at least.) Advertising and Promotion How many ways can you think of to promote our companyas business? (At this stage, let your imagination go wild: wacky, impractical ideas are as welcome as practical ones. Quant.i.ty over quality: the list can be whittled down later.) REFRAMING PROBLEMS.

Tip #9: Consider whether a problem is really the problem. Think in terms of redefining the problem.

Ponder the following problem: aA 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.a If you were hired as a consultant, reporting to the headquarters of the restaurant chain, what would you suggest?

Typical solutions to be antic.i.p.ated include: a' Enlarging the restaurant facilities in order to serve more customers a' Streamlining the menu in order to make ordering and delivery of food faster a' Refusing to let customers occupy tables if not ordering food; no adrinking-onlya 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 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 dinner or drink discounts during certain hours of the day or holding special promotional events, such as corporate c.o.c.ktail 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.

Consider another example: An agricultural importeras a.s.sociation 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 adecreasing the rate with which pears became bruised or damaged when shipped.a 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: acreating a pear that is less likely to be bruised!a 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 aapple-peara was born a" a fruit with some of a pearas taste but with an appleas st.u.r.diness Now grocery stores could be supplied with large quant.i.ties 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.

Tip #10: In selling creative ideas, most people are moved more by the depth of a personas conviction and commitment than they are by the details of a logical presentation.

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.

a.s.suming 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 asomethinga 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 a" your real audience a" 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 pa.s.sionate. Strive to combine logic and novelty, but remember, above all else, that research indicates that people are persuaded more by pa.s.sion and dedication to an idea than they are by a logical, detailed presentation.

Chapter 3.

Decision Making.

Nothing is more difficult, and therefore more precious, than to be able to decide.

a"Napoleon.

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 decision-making 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 doesnat make decisions; people do.

The tools presented here are princ.i.p.ally atreesa and aboxes.a Trees impose order and hierarchy; boxes summarize data or information. Using trees is similar to flowcharting, and decision-event trees provide a cla.s.sic 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, aboxesa 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 decision-making process in order to evaluate outcomes or options. We rank items and a.s.sign 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, but by also a.s.signing 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" a statement that we are trying to prove. Statements begin as questions and run the gamut of social science, business, or science: aAre green-eyed people more gregarious?a (social science); aDo stockbrokers really make better stock investment decisions than regular business people?a (business); aDo I have cancer?a (science).

p.r.o.nS-AND-CONS a.n.a.lYSIS.

Tip #11: Pros-and-cons a.n.a.lysis may be ill.u.s.trated using a aT-Account,a with pros on one side and cons on the other side.

How many sides are there to every issue? Actually there are three. There are two distinct sides, as well as the amiddlea view. But in pros-and-cons a.n.a.lysis, we a.s.sume for simplicity that there are two sides to every issue. The advantages are called aprosa and the disadvantages are called acons.a 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 a.n.a.lysis is that it forces a person to consider positive points, not just negative ones. Most people are naturals at finding flaws! Pros-and-cons a.n.a.lysis brings balance. Students who study debate in high school or college gain concrete exposure to viewing 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 a.n.a.lysis should include both qualitative and quant.i.tative 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 cityas downtown center with a modern building. In order to engage all-around thinking a" thinking that encompa.s.ses both sides of an issue a" letas fill in the chart on the next page, placing support examples next to each bullet point.

aAlthough most people would agree that historical buildings represent a valuable record of any societyas past, munic.i.p.al governments should resolve doubt in favor of removing old buildings when such buildings stand on ground that planners feel could be better used.a Outline the likely pros and cons behind any decision to remove or keep an historical building.

Outline Template for Pros and Cons Filling in the Pros and Cons Problem 6: Corporate Training One more! Fill in the chart on the following page with hypothetical but plausible support points to ill.u.s.trate the pros and cons of providing on-site corporate training.

aThe 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 a.s.sociated 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.a Using pros-and-cons a.n.a.lysis, evaluate the case for and against corporate in-house training.

Outline for Pros and Cons See solution MATRIXES.

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 aimportant but not urgenta tasks.

Exhibit 3.1 a" Time Management Matrix 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 right-hand corner of the extended matrix, represented by three ax.x.xs.a The dotted lines are merely useful extensions of the basic four-box 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: 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: Why do matrixes work so neatly? Things work neatly as long as all data is amutually exclusive and collectively exhaustive.a 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 canat 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 adowna and aacross.a 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 consultantas favorite presentation tool. Folklore has it that one junior management consultant became so enamored with matrixes that he called them aboxes of joya!

The truth is that matrixes are wonderful tools that can encapsulate a great deal of information. Case in point: The following write-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 companyas profitability a" margin and volume a" accelerate or trade-off with each another in a compet.i.tive business marketplace.

Exhibit 3.2 a" The Lots-Little Matrix Notes: (Q) = Volume = quant.i.ty of product sold ($) = Margin = dollar aprofita per unit of product sold The Lots-Little Matrix is useful for pinpointing where specific companies or industries are compet.i.tively positioned: 1. Sell a lot (Q), at a lot ($) aSelling large quant.i.ties at high margins.a 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 ($) aSelling large quant.i.ties at low margins.a The airlines industry is known for selling large volumes of product (seats) at low margins.

3. Sell a little (Q), at a lot ($) aSelling small volumes at high margins.a 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 ($) aSelling small volumes at low margins.a Samas 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 compet.i.tive 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 compet.i.tors 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 ill.u.s.trated, matrixes must total across and down and do so because the data or information contained 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 a" The Marketing Mix The information in Table B is not presented effectively because the words appear random and arbitrary.

Table B a" Medical Discoveries in Europe The cities mentioned above should, in all likelihood, be enumerated in a list: 1.*Paris 2.*London 3.*Madrid 4.*Amsterdam Exhibit 3.3 is not a matrix (although it certainly looks like one) because the information only areadsa down, but not across. The following write-up would likely accompany this table or chart: We hear so much about information today. But when is information deemed agooda information? Information is best understood by looking at it in terms of its four quality dimensions a" accessible, summarized, relevant, and customized. When information touches all of these dimensions it becomes both efficient and effective.

The dimensions of aaccessiblea and asummarizeda relate to the efficiency of information. The dimensions of arelevanta and acustomizeda 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 a" that is, when aaccessiblea (dimension 1) and asummarizeda (dimension 2). It is the purpose of this chart to highlight the importance of effectiveness a" arelevanta (dimension 3) and acustomizeda (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 atransparent.a It is so ready and usable that it takes on the appearance of always being in the mind of the user.

Exhibit 3.3 a" The Effective Information Paradigm Using Matrixes Job search: Of thirty-five applicants applying for a job, twenty had at least seven yearsa work experience, twenty-three had degrees, and three had less than seven yearsa work experience and did not have a degree. How many of the applicants had at least seven yearsa work experience and a degree?

Step #1: Sketch a matrix and enter given information into the appropriate boxes. The shaded box depicts the value weare trying to find.

Step #2: Letas total the numbers on the side and bottom of the matrix, filling in the dotted boxes.

Step #3: Since data must total down and across, we simply fill in remaining numbers within the middle four boxes.

Eleven of the candidates, therefore, have at least seven yearsa work experience and hold degrees.

For each of the following problems, use matrix a.n.a.lysis 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?

See solution 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?

See solution 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 didnat do); and (4) a person did not commit a crime and is not telling the truth (confessing to a crime they actually didnat 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 didnat 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)?

See solution DECISION-EVENT TREES.

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 first-year 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.

How are the following ten terms connected?

aFelonies aaaaaaCivil Wrongs (private) aaaInfractions aaaaaaaaaTorts aaHomicide aaaaaaTreason aaaOffenses aaaaaaaaCrimes (public) aMisdemeanors aaaaaBreach 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 aprivate wrongs,a occur between or among individuals. A breach of contract occurs when one party abreaksa a legal agreement. A tort is a general term used to describe acts that result in injury to another person (e.g., a.s.sault). Crimes, on the other hand, involve the state (public). Informally speaking, infractions are aminor offensesa (e.g., parking violations), misdemeanors are aminor criminal offensesa (e.g., shoplifting), and felonies are amajor criminal offenses,a 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.

Exhibit 3.4 a" Decision-Event Tree of Legal Offenses Exhibit 3.5 provides an example of a decision-event tree showing the outcomes a.s.sociated with tossing a coin three times? There are eight possibilities when a coin is tossed three times: Heads-Heads-Heads (HHH), Heads-Heads-Tails (HHT), Heads-Tails-Heads (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.

Exhibit 3.5 a" Decision-Event Tree: Coin Tosses Exhibit 3.6 a" Probability Tree: Coin Tosses 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.

See solution PROBABILITY TREES.

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 ill.u.s.trates the probabilities a.s.sociated with each event. Note that probabilities always total to 1, if we add the probabilities at the endpoints (i.e., 8 - 1a"8 = 1.0). Each endpoint equals 1a"8, which is the resultant probability of three consecutive tosses of a coin (i.e., 1a"2 - 1a"2 - 1a"2 = 1a"8a).

WEIGHTED RANKING.

Tip #15: Weighted ranking is a tool for finding solutions using a weighted average. To calculate weighted average, we multiply each event by its a.s.sociated 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 weighted average is that we can a.s.sign different weights based on the relative importance of events a" 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: 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 studentas final course grade, then what is his course grade?

Based on the same information above, what is the studentas final course grade if the midterm exam is weighted 40% and the final exam is weighted 60%?

Note that the weights above could also be expressed using fractions or decimals: Hiring and promotion decisions are cla.s.sic examples of situations in which subjective influences can override an objective decision-making 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 a" technical skills, people skills, and track record a" 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., 2a"10, 3a"10, 5a"10a), or even whole numbers such as 2, 3, 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.

Exhibit 3.7 a" Performance of Salespersons Exhibit 3.8 a" Performance Using Weighted Average Exhibit 3.9 a" Ranking of Salespersons Chess In chess, a p.a.w.n 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 p.a.w.ns. Player B has a bishop, four p.a.w.ns, and a queen. Who is ahead and by how much?

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?

Problem 11: Investor An investor is looking at three different investment possibilities. The first investment opportunity has a 1a"6 chance of returning $90,000, a 1a"2 chance of returning $50,000, and a 1a"3 chance of losing $60,000. A second investment opportunity has a 1a"2 chance of returning $100,000 and a 1a"2 chance of losing $50,000. The third investment opportunity has a 1a"4 chance of returning $100,000, a 1a"4 chance of returning $60,000, a 1a"4 chance of losing $40,000, and a 1a"4 chance of losing $80,000. a.s.suming the investor chooses to invest in all three investments, what will be his or her expected return?

See solution UTILITY a.n.a.lYSIS.

Tip #16: Utility a.n.a.lysis takes into account desirability of outcomes, which may be different from monetary payoffs.

Utility is adesirability.a Utility a.n.a.lysis 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 awhat we wanta; probability is awhat we get.a 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 a.s.sign a value to the desirability 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 aoyster,a but how do we evaluate our options? Expected Value (EV) is defined as the product (multiplication) of a given utility and its corresponding probability.

Note that the probabilities a.s.signed incorporate the risk and/or skill level required to pursue each option. According to the above a.n.a.lysis, aJoin the diplomatic servicea 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 a.n.a.lytical boundary and makes choosing other values easier. In reality, aWork as a travel writera might be less than 100. A a100a 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 a.s.sociated 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.

If there were costs a.s.sociated 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 a.n.a.lysis. The team with the highest Expected Value would be the best bet.