We all make decisions of varying importance every day, so the idea that decision making can be a rather sophisticated art may at first seem strange. However, studies have shown that most people are much poorer at decision making than they think. An understanding of what decision making involves, together with a few effective techniques, will help produce better decisions.
What is Decision Making?
Some Definitions
A good place to start is with some standard definitions of decision making.
1. Decision making is the study of identifying and choosing alternatives based on the values and preferences of the decision maker. Making a decision implies that there are alternative choices to be considered, and in such a case we want not only to identify as many of these alternatives as possible but to choose the one that best fits with our goals, desires, lifestyle, values, and so on.
2. Decision making is the process of sufficiently reducing uncertainty and doubt about alternatives to allow a reasonable choice to be made from among them. This definition stresses the information gathering function of decision making. It should be noted here that uncertainty is reduced rather than eliminated. Very few decisions are made with absolute certainty because complete knowledge about all the alternatives is seldom possible. Thus, every decision involves a certain amount of risk.
Kinds of Decisions
There are several basic kinds of decisions.
1. Decisions whether. This is the yes/no, either/or decision that must be made before we proceed with the selection of an alternative. Should I buy a new TV? Should I travel this summer? Decisions whether are made by weighing reasons pro and con. The PMI technique discussed in the next chapter is ideal for this kind of decision.
It is important to be aware of having made a decision whether, since too often we assume that decision making begins with the identification of alternatives, assuming that the decision to choose one has already been made.
2. Decisions which. These decisions involve a choice of one or more alternatives from among a set of possibilities, the choice being based on how well each alternative measures up to a set of predefined criteria.
3. Contingent decisions. These are decisions that have been made but put on hold until some condition is met.
For example, I have decided to buy that car if I can get it for the right price; I have decided to write that article if I can work the necessary time for it into my schedule.
Most people carry around a set of already made, contingent decisions, just waiting for the right conditions or opportunity to arise. Time, energy, price, availability, opportunity, encouragement--all these factors can figure into the necessary conditions that need to be met before we can act on our decision.
Decision Making is a Recursive Process
A critical factor that decision theorists sometimes neglect to emphasize is that in spite of the way the process is presented on paper,
decision making is a nonlinear, recursive process. That is, most decisions are made by moving back and forth between the choice of criteria (the characteristics we want our choice to meet) and the identification of alternatives (the possibilities we can choose from among). The alternatives available influence the criteria we apply to them, and similarly the criteria we establish influence the alternatives we will consider. Let's look at an example to clarify this.
Suppose someone wants to decide, Should I get married? Notice that this is a decision whether. A linear approach to decision making would be to decide this question by weighing the reasons pro and con (what are the benefits and drawbacks of getting married) and then to move to the next part of the process, the identification of criteria (supportive, easy going, competent, affectionate, etc.). Next, we would identify alternatives likely to have these criteria (Kathy, Jennifer, Michelle, Julie, etc.). Finally we would evaluate each alternative according to the criteria and choose the one that best meets the criteria. We would thus have a scheme like this:
decision whether ... select criteria ... identify alternatives ... make choice
However, the fact is that our decision whether to get married may really be a contingent decision. "I'll get married if I can find the right person." It will thus be influenced by the identification of alternatives, which we usually think of as a later step in the process. Similarly, suppose we have arrived at the "identify alternatives" stage of the process when we discover that Jennifer (one of the girls identified as an alternative) has a wonderful personality characteristic that we had not even thought of before, but that we now really want to have in a wife. We immediately add that characteristic to our criteria. Thus, the decision making process continues to move back and forth, around and around as it progresses in what will eventually be a linear direction but which in its actual workings is highly recursive.
The Components of Decision Making
The Decision Environment
Every decision is made within a decision environment, which is defined as the collection of information, alternatives, values, and preferences
available at the time of the decision. An ideal decision environment would include all possible information, all of it accurate, and every possible alternative. However, both information and alternatives are constrained because time and effort to gain information or identify alternatives are limited. The time constraint simply means that a decision must be made by a certain time. The effort constraint reflects the limits of manpower, money, and priorities. (You wouldn't want to spend three hours and half a tank of gas trying to find the very best parking place at the mall.) Since decisions must be made within this constrained environment, we can say that
the major challenge of decision making is uncertainty, and a major goal of decision analysis is to reduce uncertainty. We can almost never have all information needed to make a decision with certainty, so most decisions involve an undeniable amount of risk.
The fact that decisions must be made within a limiting decision environment suggests two things. First, it explains why hindsight is so much more accurate and better at making decisions that foresight. As time passes, the decision environment continues to grow and expand. New information and new alternatives appear--even after the decision must be made. Armed with new information after the fact, the hindsighters can many times look back and make a much better decision than the original maker, because the decision environment has continued to expand.
The second thing suggested by the decision-within-an-environment idea follows from the above point. Since the decision environment continues to expand as time passes, it is often advisable to put off making a decision until close to the deadline. Information and alternatives continue to grow as time passes, so to have access to the most information and to the best alternatives, do not make the decision too soon. Now, since we are dealing with real life, it is obvious that some alternatives might no longer be available if too much time passes; that is a tension we have to work with, a tension that helps to shape the cutoff date for the decision.
Delaying a decision as long as reasonably possible, then, provides three benefits:
1. The decision environment will be larger, providing more information. There is also time for more thoughtful and extended analysis.
2. New alternatives might be recognized or created.
3. The decision maker's preferences might change. With further thought, wisdom, maturity, you may decide not to buy car X and instead to buy car Y.
The Effects of Quantity on Decision Making
Many decision makers have a tendency to seek more information than required to make a good decision. When too much information is sought and obtained, one or more of several problems can arise. (1) A delay in the decision occurs because of the time required to obtain and process the extra information. This delay could impair the effectiveness of the decision or solution. (2) Information overload will occur. In this state, so much information is available that decision-making ability actually declines because the information in its entirety can no longer be managed or assessed appropriately. A major problem caused by information overload is forgetfulness. When too much information is taken into memory, especially in a short period of time, some of the information (often that received early on) will be pushed out.
The example is sometimes given of the man who spent the day at an information-heavy seminar. At the end of the day, he was not only unable to remember the first half of the seminar but he had also forgotten where he parked his car that morning.
(3) Selective use of the information will occur. That is, the decision maker will choose from among all the information available only those facts which support a preconceived solution or position. (4) Mental fatigue occurs, which results in slower work or poor quality work. (5) Decision fatigue occurs, where the decision maker tires of making decisions. Often the result is fast, careless decisions or even decision paralysis--no decisions are made at all.
The quantity of information that can be processed by the human mind is limited. Unless information is consciously selected, processing will be biased toward the first part of the information received. After that, the mind tires and begins to ignore subsequent information or forget earlier information.
Decision Streams
A common misconception about decision making is that decisions are made in isolation from each other: you gather information, explore alternatives, and make a choice, without regard to anything that has gone before. The fact is, decisions are made in a context of other decisions. The typical metaphor used to explain this is that of a stream. There is a stream of decisions surrounding a given decision, many decisions made earlier have led up to this decision and made it both possible and limited. Many other decisions will follow from it.
Another way to describe this situation is to say that most decisions involve a choice from a group of preselected alternatives, made available to us from the universe of alternatives by the previous decisions we have made. Previous decisions have "activated" or "made operable" certain alternatives and "deactivated" or "made inoperable" others.
For example, when you decide to go to the park, your decision has been enabled by many previous decisions. You had to decide to live near the park; you had to decide to buy a car or learn about bus routes, and so on. And your previous decisions have constrained your subsequent ones: you can't decide to go to a park this afternoon if it is three states away. By deciding to live where you do, you have both enabled and disabled a whole series of other decisions.
As another example, when you enter a store to buy a VCR or TV, you are faced with the preselected alternatives stocked by the store. There may be 200 models available in the universe of models, but you will be choosing from, say, only a dozen. In this case, your decision has been constrained by the decisions made by others about which models to carry.
We might say, then, that every decision (1) follows from previous decisions, (2) enables many future decisions, and (3) prevents other future decisions. People who have trouble making decisions are sometimes trapped by the constraining nature of decision making. Every decision you make precludes other decisions, and therefore might be said to cause a loss of freedom. If you decide to marry Terry, you no longer can decide to marry Shawn. However, just as making a decision causes a loss of freedom, it also creates new freedom, new choices and new possibilities. So making a decision is liberating as well as constraining. And a decision left unmade will often result in a decision by default or a decision being made for you.
It is important to realize that every decision you make affects the decision stream and the collections of alternatives available to you both immediately and in the future. In other words, decisions have far reaching consequences.
Concepts and Definitions
1. Information. This is knowledge about the decision, the effects of its alternatives, the probability of each alternative, and so forth. A major point to make here is that while substantial information is desirable, the statement that "the more information, the better" is not true. Too much information can actually reduce the quality of a decision. See the discussion on The Effects of Quantity on Decision Making above
. 2. Alternatives. These are the possibilities one has to choose from. Alternatives can be identified (that is, searched for and located) or even developed (created where they did not previously exist). Merely searching for preexisting alternatives will result in less effective decision making.
3. Criteria. These are the characteristics or requirements that each alternative must possess to a greater or lesser extent. Usually the alternatives are rated on how well they possess each criterion. For example, alternative Toyota ranks an 8 on the criterion of economy, while alternative Buick ranks a 6 on the same criterion.
4. Goals. What is it you want to accomplish? Strangely enough, many decision makers collect a bunch of alternatives (say cars to buy or people to marry) and then ask, "Which should I choose?" without thinking first of what their goals are, what overall objective they want to achieve. Next time you find yourself asking, "What should I do? What should I choose?" ask yourself first, "What are my goals?"
A component of goal identification should be included in every instance of decision analysis.
5. Value. Value refers to how desirable a particular outcome is, the value of the alternative, whether in dollars, satisfaction, or other benefit.
6. Preferences. These reflect the philosophy and moral hierarchy of the decision maker. We could say that they are the decision maker's "values," but that might be confusing with the other use of the word, above. If we could use that word here, we would say that personal values dictate preferences. Some people prefer excitement to calmness, certainty to risk, efficiency to esthetics, quality to quantity, and so on. Thus, when one person chooses to ride the wildest roller coaster in the park and another chooses a mild ride, both may be making good decisions, if based on their individual preferences.
7. Decision Quality. This is a rating of whether a decision is good or bad. A good decision is a logical one based on the available information and reflecting the preferences of the decision maker.
The important concept to grasp here is that the quality of a decision is not related to its outcome: a good decision can have either a good or a bad outcome. Similarly, a bad decision (one not based on adequate information or not reflecting the decision maker's preferences) can still have a good outcome.
For example, if you do extensive analysis and carefully decide on a certain investment based on what you know about its risks and your preferences, then your decision is a good one, even though you may lose money on the investment. Similarly, if you throw a dart at a listing of stocks and buy the one the dart hits, your decision is a bad one, even though the stock may go up in value.
Good decisions that result in bad outcomes should thus not be cause for guilt or recrimination. If you decide to take the scenic route based on what you know of the road (reasonably safe, not heavily traveled) and your preferences (minimal risk, prefer scenery over early arrival), then your decision is a good one, even though you might happen to get in an accident, or have a flat tire in the middle of nowhere. It is not justified to say, "Well, this was a bad decision."
In judging the quality of a decision, in addition to the concerns of logic, use of information and alternatives, three other considerations come into play:
A. The decision must meet the stated objectives most thoroughly and completely. How well does the alternative chosen meet the goals identified?
B. The decision must meet the stated objectives most efficiently, with concern over cost, energy, side effects. Are there negative consequences to the alternative that make that choice less desirable? We sometimes overlook this consideration in our search for thrills.
C. The decision must take into account valuable byproducts or indirect advantages. A new employee candidate may also have extra abilities not directly related to the job but valuable to the company nonetheless. These should be taken into account.
8. Acceptance. Those who must implement the decision or who will be affected by it must accept it both intellectually and emotionally.
Acceptance is a critical factor because it occasionally conflicts with one of the quality criteria. In such cases, the best thing to do may be to choose a lesser quality solution that has greater acceptance.
For example, when cake mixes first were put on the market, manufacturers put everything into the mix--the highest quality and most efficient solution. Only water had to be added. However, the mixes didn't sell well--they weren't accepted. After investigation, the makers discovered that women didn't like the mixes because using the mixes made them feel guilty: they weren't good wives because they were taking a shortcut to making a cake. The solution was to take the egg and sometimes the milk out of the mix so that the women would have something to do to "make" the cake other than just adding water. Now they had to add egg and perhaps milk, making them feel more useful. The need to feel useful and a contributor is one of the most basic of human needs. Thus, while the new solution was less efficient in theoretical terms, it was much more acceptable. Cake mixes with the new formula became quite popular.
Thus, the inferior method may produce greater results if the inferior one has greater support. One of the most important considerations in decision making, then, is the people factor. Always consider a decision in light of the people implementation.
A decision that may be technologically brilliant but that is sociologically stupid will not work. Only decisions that are implemented, and implemented with thoroughness (and preferably enthusiasm) will work the way they are intended to.
Approaches to Decision Making
There are two major approaches to decision making in an organization, the authoritarian method in which an executive figure makes a decision for the group and the group method in which the group decides what to do.
1. Authoritarian. The manager makes the decision based on the knowledge he can gather. He then must explain the decision to the group and gain their acceptance of it. In some studies, the time breakdown for a typical operating decision is something like this:
make decision, 5 min.; explain decision, 30 min.; gain acceptance, 30 min.
2. Group. The group shares ideas and analyses, and agrees upon a decision to implement. Studies show that the group often has values, feelings, and reactions quite different from those the manager supposes they have. No one knows the group and its tastes and preferences as well as the group itself. And, interestingly, the time breakdown is something like this:
group makes decision, 30 min.; explain decision, 0 min.; gain acceptance, 0 min.
Clearly, just from an efficiency standpoint, group decision making is better. More than this, it has been shown many times that people prefer to implement the ideas they themselves think of. They will work harder and more energetically to implement their own idea than they would to implement an idea imposed on them by others. We all have a love for our own ideas and solutions, and we will always work harder on a solution supported by our own vision and our own ego than we will on a solution we have little creative involvement with.
There are two types of group decision making sessions. First is free discussion in which the problem is simply put on the table for the group to talk about. For example, Joe has been offered a job change from shift supervisor to maintenance foreman. Should he take the job?
The other kind of group decision making is developmental discussion or structured discussion. Here the problem is broken down into steps, smaller parts with specific goals. For example, instead of asking generally whether Joe should take the job, the group works on sub questions: What are Joe's skills? What skills does the new job require? How does Joe rate on each of the skills required? Notice that these questions seek specific information rather than more general impressionistic opinions.
Developmental discussion (1) insures systematic coverage of a topic and (2) insures that all members of the group are talking about the same aspect of the problem at the same time.
Some Decision Making Strategies
As you know, there are often many solutions to a given problem, and the decision maker's task is to choose one of them. The task of choosing can be as simple or as complex as the importance of the decision warrants, and the number and quality of alternatives can also be adjusted according to importance, time, resources and so on. There are several strategies used for choosing. Among them are the following:
1. Optimizing. This is the strategy of choosing the best possible solution to the problem, discovering as many alternatives as possible and choosing the very best. How thoroughly optimizing can be done is dependent on
A. importance of the problem
B. time available for solving it
C. cost involved with alternative solutions
D. availability of resources, knowledge
E. personal psychology, values
Note that the collection of complete information and the consideration of all alternatives is seldom possible for most major decisions, so that limitations must be placed on alternatives.
2. Satisficing. In this strategy, the first satisfactory alternative is chosen rather than the best alternative. If you are very hungry, you might choose to stop at the first decent looking restaurant in the next town rather than attempting to choose the best restaurant from among all (the optimizing strategy). The word satisficing was coined by combining satisfactory and sufficient. For many small decisions, such as where to park, what to drink, which pen to use, which tie to wear, and so on, the satisficing strategy is perfect.
3. Maximax. This stands for "maximize the maximums." This strategy focuses on evaluating and then choosing the alternatives based on their maximum possible payoff. This is sometimes described as the strategy of the optimist, because favorable outcomes and high potentials are the areas of concern. It is a good strategy for use when risk taking is most acceptable, when the go-for-broke philosophy is reigning freely.
4. Maximin. This stands for "maximize the minimums." In this strategy, that of the pessimist, the worst possible outcome of each decision is considered and the decision with the highest minimum is chosen. The Maximin orientation is good when the consequences of a failed decision are particularly harmful or undesirable. Maximin concentrates on the salvage value of a decision, or of the guaranteed return of the decision. It's the philosophy behind the saying, "A bird in the hand is worth two in the bush."
Quiz shows exploit the uncertainty many people feel when they are not quite sure whether to go with a maximax strategy or a maximin one: "Okay, Mrs. Freen, you can now choose to take what you've already won and go home, or risk losing it all and find out what's behind door number three."
Example: I could put my $10,000 in a genetic engineering company, and if it creates and patents a new bacteria that helps plants resist frost, I could make $50,000. But I could also lose the whole $10,000. But if I invest in a soap company, I might make only $20,000, but if the company goes completely broke and gets liquidated, I'll still get back $7,000 of my investment, based on its book value.
Example: It's fourth down and ten yards to go on your twenty yard line. Do you go for a long pass or punt? Maximax would be to pass; Maximin would be to punt.
Decision Making Procedure
As you read this procedure, remember our discussion earlier about the recursive nature of decision making. In a typical decision making situation, as you move from step to step here, you will probably find yourself moving back and forth also.
1. Identify the decision to be made together with the goals it should achieve. Determine the scope and limitations of the decision. Is the new job to be permanent or temporary or is that not yet known (thus requiring another decision later)? Is the new package for the product to be put into all markets or just into a test market? How might the scope of the decision be changed--that is, what are its possible parameters?
When thinking about the decision, be sure to include a clarification of goals: We must decide whom to hire for our new secretary, one who will be able to create an efficient and organized office. Or, We must decide where to go on vacation, where we can relax and get some rest from the fast pace of society.
2. Get the facts. But remember that you cannot get all the facts. Get as many facts as possible about a decision within the limits of time imposed on you and your ability to process them, but remember that virtually every decision must be made in partial ignorance. Lack of complete information must not be allowed to paralyze your decision. A decision based on partial knowledge is usually better than not making the decision when a decision is really needed. The proverb that "any decision is better than no decision," while perhaps extreme, shows the importance of choosing. When you are racing toward a bridge support, you must decide to turn away to the right or to the left. Which way you turn is less important than the fact that you do indeed turn.
As part of your collection of facts, list your feelings, hunches, and intuitive urges. Many decisions must ultimately rely on or be influenced by intuition because of the remaining degree of uncertainty involved in the situation.
Also as part of your collection of facts, consult those who will be affected by and who will have to implement your decision. Input from these people not only helps supply you with information and help in making the decision but it begins to produce the acceptance necessary in the implementers because they feel that they are part of the decision making process. As Russell Ackoff noted in The Art of Problem Solving, not consulting people involved in a decision is often perceived as an act of aggression.
3. Develop alternatives. Make a list of all the possible choices you have, including the choice of doing nothing. Not choosing one of the candidates or one of the building sites is in itself a decision. Often a non decision is harmful as we mentioned above--not choosing to turn either right or left is to choose to drive into the bridge. But sometimes the decision to do nothing is useful or at least better than the alternatives, so it should always be consciously included in the decision making process.
Also be sure to think about not just identifying available alternatives but creating alternatives that don't yet exist. For example, if you want to choose which major to pursue in college, think not only of the available ones in the catalog, but of designing your own course of study.
4. Rate each alternative. This is the evaluation of the value of each alternative. Consider the negative of each alternative (cost, consequences, problems created, time needed, etc.) and the positive of each (money saved, time saved, added creativity or happiness to company or employees, etc.). Remember here that the alternative that you might like best or that would in the best of all possible worlds be an obvious choice will, however, not be functional in the real world because of too much cost, time, or lack of acceptance by others.
Also don't forget to include indirect factors in the rating. If you are deciding between machines X, Y, and Z and you already have an employee who knows how to operate machine Z, that fact should be considered. If you are choosing an investigative team to send to Japan to look at plant sites and you have very qualified candidates A, B, and C, the fact that B is a very fast typist, a superior photographer or has some other side benefit in addition to being a qualified team member, should be considered. In fact, what you put on your hobbies and interests line on your resume can be quite important when you apply for a job just because employers are interested in getting people with a good collection of additional abilities.
5. Rate the risk of each alternative. In problem solving, you hunt around for a solution that best solves a particular problem, and by such a hunt you are pretty sure that the solution will work. In decision making, however, there is always some degree of uncertainty in any choice. Will Bill really work out as the new supervisor? If we decide to expand into Canada, will our sales and profits really increase? If we let Jane date Fred at age fifteen, will the experience be good? If you decide to marry person X or buy car Y or go to school Z, will that be the best or at least a successful choice?
Risks can be rated as percentages, ratios, rankings, grades or in any other form that allows them to be compared. See the section on risk evaluation for more details on risking.
6. Make the decision. If you are making an individual decision, apply your preferences (which may take into account the preferences of others). Choose the path to follow, whether it includes one of the alternatives, more than one of them (a multiple decision) or the decision to choose none.
And of course, don't forget to implement the decision and then evaluate the implementation, just as you would in a problem solving experience.
One important item often overlooked in implementation is that when explaining the decision to those involved in carrying it out or those who will be affected by it, don't just list the projected benefits: frankly explain the risks and the drawbacks involved and tell why you believe the proposed benefits outweigh the negatives. Implementers are much more willing to support decisions when they (1) understand the risks and (2) believe that they are being treated with honesty and like adults.
Remember also that very few decisions are irrevocable. Don't cancel a decision prematurely because many new plans require time to work--it may take years for your new branch office in Paris to get profitable--but don't hesitate to change directions if a particular decision clearly is not working out or is being somehow harmful. You can always make another decision to do something else.
Risking
Because making decisions involves a degree of risk, it would be helpful to examine risk and risk analysis in this chapter in order to gain an understanding of what is involved. Risk and uncertainty create anxiety, yet they are necessary components of an active life.
General Comments on Risk Taking
1. Only the risk takers are truly free. All decisions of consequence involve risk. Without taking risks, you cannot grow or improve or even live.
2. There is really no such thing as permanent security in anything on earth. Not taking risks is really not more secure than taking them, for your present state can always be changed without action on your part. If you don't take the risk of dying by driving to the store, your house could collapse on you and kill you anyway.
3. You are supposed to be afraid when you risk. Admit your fears--of loss, of rejection, of failure.
4. Risking normally involves a degree of separation anxiety--the anxiety you feel whenever you are removed from something that makes you feel secure. Many children feel this when they first leave their parents for school. Some college students feel this when they go off to college. Travelers sometimes feel it when they get homesick. The way to overcome separation anxiety is to build a bridge between the familiar and secure and the new. Find out what the new place--school or country--is like and how its elements compare to familiar and secure things at home. Take familiar things with you--books, teddy bear, popcorn popper, whatever.
The same is true of all risks. Make the opportunity as familiar as possible and learn as much about it as you can before you release the security of the old. Find out about the new job, its location, the lifestyle of those who live there, and so on.
The Orthodox Theory of Risk Evaluation
The traditional strategy for evaluating risks is to use an expected value calculation, based on the simple idea that the expected value of a risk is the value of the possible outcome discounted by the probability of its realization. The formula is
EV=PR or expected value equals prize times risk (or chance). Thus, if you have one chance in a million of winning a million dollars, your expected value is one dollar (which is one millionth of a million dollars). Expected value calculations are often used when comparing an amount of money to be invested with the probable payoff. (Note: if the risk is, for example, one in twenty, you can divide the prize by twenty, which is the same as multiplying the prize by one twentieth.)
Let's take a typical state lottery, for example. The investment for a ticket is a dollar. The usual prize is about $6,500,000 and the chance of winning is about one in 14,800,000. By discounting the possible outcome by the chance of winning (dividing $6.5 million by 14.8 million), we discover that the expected value of the lottery ticket is about 43.9 cents. Since a ticket costs $1.00 (more than twice as much as its expected value), we would conclude that this is a poor risk. Only when the expected value meets or exceeds the required expense is the risk considered worth taking, according to this theory.
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Try It Yourself
Expected Value. Calculate the expected value of each of the following risks. Divide the prize by the chance, and compared the answer with the cost of the ticket to decide whether the risk is worth taking.
1. Irish Sweepstakes. Ticket: $2.50 Prize: $100,000,000 Chance: 1 in 60,000,000
2. State Lottery. Ticket: $1.00 Prize: $42,300,000 Chance: 1 in 14,800,000 (Note: Calculate the expected value for just a single winner and for the number of winners you'd expect based on 80,000,000 entries.)
3. Reader's Digest Sweepstakes. Ticket: 32 cent stamp to return the entry Prize: $6,000,000 Chance: 1 in 256,000,000
4. Publisher's Clearinghouse Sweepstakes. Ticket: 32 cent stamp to return the entry Prize: $10,000,000 Chance: 1 in 140,000,000
5. Charity Raffle. Ticket: $5.00 Prize: $12,400 (new car) Chance: 1 in 3,000
6. Vegas Roulette #1. Ticket: $20 bet Prize: $380 Chance: 1 in 35
7. Reno Roulette #2 Ticket: $25 bet Prize: $975 Chance: 1 in 35
8. Pearl in Oyster Ticket: $10 Prize: $50 Chance: 1 in 8
9. Extended Warranty Ticket (Price of Extended Warranty): $45 Prize (Cost of average covered warranty repair): $180 Chance: 1 in 12
10. In Your Dreams Ticket: $1.00 Prize: $500,000 Chance: 1 in 250
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Many risks have multiple possible outcomes, each outcome with its own probability of occurrence and its own value. The expected value of a given decision in such cases is the sum of all the values of each outcome, each diminished by its individual probability. The formula is
EV = sumn (pn x rn)
where p is the probability and r is the reward or value of the risk. Note in the following examples that the value of an outcome is represented numerically, but it does not need to represent dollars, or even physical units. A 10 could be units of happiness, pleasure, pain, embarrassment, and so forth, as well as dollars.
Example: Should I go scuba diving this weekend? If I do, there is a ninety percent probability that I will have a lot of fun. I quantify this great fun as 10 fun points. There is also a ten percent probability that I will get hurt, which I quantify as minus 20 fun points. If I make the other decision, to stay home, there is a ninety-nine percent probability that I will be bored, represented by a minus 2 fun points, and a one percent probability that something exciting will happen, which I represent as five fun points (half as exciting as going scuba diving). Our expected value worksheet looks like this:
Probability Reward
_____ .9 x +10 = +9
|
|_____ .1 x -20 = -2
Y|
_Scuba?_| Total = 7
N|
|_____ .99 x -2 = -1.98
|
|_____ .01 x +5 = + .05
Total = -1.93
Here we see that the expected value of going diving is 7, which is much higher than the expected value of staying home, which is a negative 1.93.
As another example, suppose I'm trying to decide whether or not to attempt a repair on my computer or whether to have a dealer fix it. If I attempt the repair, there are three possible outcomes. One is that I'll succeed, which I value both financially, experientially, and egotistically, so I give that a +10. Second is that I will increase the cost of repairing the computer by damaging something. This I rate at -8. The third possibility is that I will ruin the computer and be totally humiliated. This I rate at -20. The probability I see for each of these possibilities is, in order, 50%, 30%, and 20%. Do note that for any given decision, the probabilities of all possible outcomes must add up to 100%.
On the other hand, if I have a dealer repair the computer, there are two possibilities. One is that it will cost a modest amount of money, which I rate at a -2, since I will be out a few bucks and will have to haul the computer into the shop and back. The other possibility is that the repair will cost major money, which I rate at a -9. The probabilities for each of these I predict at 20% for a cheap repair and 80% for an expensive one. Our EV worksheet would then look like this:
Probability Reward
_____ .5 x +10 = +5
|
|_____ .3 x -8 = -2.4
|
|_____ .2 x -20 = -4
Y|
Me Fix?_| Total -1.4
N|
|_____ .8 x -9 = -7.2
|
|_____ .2 x -2 = -0.4
Total -7.6
Here we see that both expected values are negative, meaning that this decision will probably result in discomfort either way. However, the expected value for doing the repair is "higher" (less negative) than that for having the dealer do it, so that is the way our calculations tell us to go. Note, of course, that if we decide our probabilities are different, or if we decide that our rewards are different, the expected values will change.
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Try It Yourself
Expected Value. Work out each of these for expected value and determine which decision is best.
1. You want to decide whether or not to take the freeway home from an event you've attended. From experience, you calculate that if you take the freeway, you will either speed home, which you rate at a +8 on the happiness scale, or you will get into a traffic jam, which you rate at a -6 on the happiness scale. If you take the side streets, you will either get home okay, which is a +4 on the happiness scale (since it's only half as fast as the freeway) or you will hit another traffic jam, which you rate as a -7, slightly worse than a jam on the freeway. The probability of a freeway jam is 60% (you'll have to figure out the probability for speeding home). The probability for getting home okay on the side streets is 30%.
2. Your crop of cotton is infested with insects and you want to decide which pesticide to use. Some of the insects are probably resistant to the different available pesticides, so you sit down and figure out the following probabilities. If you use ToxiBug, there is a 22% probability that it will kill 95% of the bugs on your crops. There is a 49% probability that it will kill only 71% of the bugs, and a 29% probability that it will kill only 43% of the bugs. (Use the bug percentages as reward numbers, so that 95% is a reward of 95.)
If you use Bug-O-Kill, there is a 71% probability that it will kill 90% of the bugs, a 24% probability that it will kill 11% of the bugs, and a 5% probability that it will kill 19% of the bugs.
If you use MegaDeath Bug Viability Terminator, there is a 90% chance that 60% of the bugs will be killed, and a 10% chance that 5% will be killed.
3. You have been retained by Amalgamated Pencil Sharpeners, Inc. to help determine whether the company should export its new sharpener model XT-S to Brazil. If APS does export, there are three foreseen possibilities. First, there is a 25% probability that the product will sell well, earning the company (after startup costs) $280,000. Second, there is a 40% probability that the sharpeners will have only modest performance, earning the company a net of only $15,000. Lastly, the product might be rejected, causing the company to lose its startup costs of $175,000. The probability for this is 35%.
If the company decides not to export the sharpeners, it could invest the startup money with a 90% probability of making a net of $18,000 and a 10% probability of losing a net of $27,000.
What should the company do?
4. As a diving buff, you have been asked to help salvage a sunken treasure ship off the coast of Florida. Your only problem is an abundance of riches: There are three ships to choose from. And, to make life interesting, there is a little uncertainty about whether each has already been salvaged. (If the ship has already been salvaged, there will be no treasure at all left, and the attempt will result in a net loss equal to the cost of mounting the expedition.) Judging by the records of each ship's inventory and the probability of previous salvaging, you have this information:
If you salvage the Jacques D'Ambois, there is a 60% probability of finding the $20,000,000 in gold and silver bars on board. Cost of salvaging this wreck is $5,000,000.
If you salvage the Acana, there is a 75% probability of finding $11,000,000 in doubloons and jewels. Cost of salvaging this wreck is $3,000,000.
If you salvage the Princess Avanti, there is a 20% probability of finding $30,000,000 in gold and a 25% probability of finding only $15,000,000. Cost of salvaging this wreck is $4,000,000.
Hint: Subtract the cost of salvaging from the hoped for return in each case. Subtract the probability of success from 100% to find the probability of failure. Failure results in the expense of salvaging (a net loss).
Which ship should be salvaged?
5. Penelope has a serious illness for which doctors have recommended surgery. If she has the operation, there is a 60% chance she will recover and live another 50 years. There is a 20% chance she will live only 20 more years. And there is a 20% percent chance that she will die on the operating table or shortly thereafter. If she does not have the operation, there is a 60% chance that she will live only five years. There is a 15% percent chance that she will live 15 years. And there is a 25% chance that she will spontaneously recover and live 50 years. For each case, let the number of years to live equal the possible reward. For the possibility of dying on the operating table, make that equal to a negative of the expected value of not having the operation at all (so calculate the not having the operation EV first).
Should she have the operation?
6. You have $250,000 to invest for a year. If you put it in stocks, there is a 50 percent chance that you will net a return of $40,000. There is, however a 20 percent chance that you'll lose $2,000 and a 30 percent chance that the market will really decline and you'll lose $50,000.
If you put the money in the bank, there is a 95 percent chance that you'll earn $17,500 in interest. There is, however, just a small chance--5 percent--that the bank will go broke, and since the FDIC insurance covers only $100,000, you would lose $150,000.
Which investment has the highest expected value?
7. You are trying to decide between three used cars, all of which are priced the same. If you buy used car number one, there is a 70 percent probability that you'll have to spend $400 to get the engine back in shape. However, there is a 30 percent probability that the engine will have to be replaced, which will cost you $2,000.
If you choose car number 2, there is a 50 percent probability that you won't have to spend any money at all, a 30 percent probability that emission repairs will cost only $200, but there is a 20 percent chance that the car will require a California smog conversion (since it may be a European import that hasn't been built for California). This will cost you $5000.
If you choose car number three, you will face a 60 percent probability of an $800 transmission repair, a 35 percent probability of a small transmission adjustment, and a 5 percent possibility that you'll need to spend $1600 to fix the engine and the transmission.
Which car should you buy? Consider the costs as negative values and choose the one with the lowest negative total.
8. Your true love comes up to you and says, "Darling, I can't decide whether we should go to the beach or to a movie, because while the beach would be twice as much fun if it doesn't rain, there is a 30 percent chance of rain today. And if it rains, the beach would be no fun at all." You smile knowingly and reply, "Well, sweetheart, I just happen to know how to calculate expected values. I'll solve the problem for us." If the fun you would have at the beach is a 10, what should you decision be?
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Advice on Risking
1. Decide whether the risk is necessary or desirable. Spend some careful thought before acting, so that you will not end up taking unnecessary risks.
2. Risk for the right reasons and when you are calm and thoughtful. Don't take a risk because you are angry, hurt, depressed, desperate, or frightened. Don't take risks just to get revenge or to harm someone else. Don't risk when you are incapable of rational thought.
3. Have a goal. When you take a risk, have a clear purpose in mind so that you will know, after the fact, whether you succeeded or not. What will taking the risk accomplish?
4. Determine the possible loss as well as the gain. That is, know exactly what the consequences of failure will be. Unless you know pretty accurately what both loss and gain will be, you do not understand the risk. There is a tendency either to underestimate or to overestimate the consequences of risk. Underestimation can result in surprising damage, cost, setbacks, pain, whatever. But overestimation is just as problematic, because it can keep us from taking the risks we should be taking. Many times, upon reflection, the worst case event of a failed risk is much less harmful or negative that we originally believed.
It's a good idea in fact to list all the good expected effects of a successful outcome and all the bad expected effects of an unsuccessful outcome.
5. Try to make an accurate estimate about the probability of each case. Is the probability of success one in two, one in ten, one in a hundred, one in a million? This can be sometimes difficult to do, but usually you can guess the probability within an order of magnitude.
6. When possible, take one risk at a time. Divide your actions or goals wherever possible so that you are not combining risks unless absolutely necessary. Simultaneous risking increases anxiety, creates confusion, and makes failure analysis very difficult.
7. Use imaging or role playing to work through the various possibilities, successes and failures, so that you will be mentally prepared for any outcome. Think about what can go right and what can go wrong and how you will respond to or adjust to each possibility.
8. Use a plan. Set up a timetable with a list of steps to take. Use the plan as a guideline, but be flexible.
9. Act decisively. When you have evaluated the risk and decided that it's worth it, act. Go for it. Don't hesitate at the threshold or halfway through. Once you get going, be courageous. Grit your teeth and move forward. Don't procrastinate and don't act half heartedly.
10. Don't expect complete success. You may get it, of course, but chances are the result of your risk will not be exactly what you had imagined and there will be more a degree of success than absolute success or failure.
Risk Management Strategies
In order of precedence, the strategies are:
1. Dismiss extremely remote or unrealistic possibilities. For example, in the decision, Shall I go to the store? there are risks like dying on the freeway, being shot by robbers, buying poisoned food, and so forth, but these should not normally enter into the risk evaluation because they are highly if not extremely improbable. Remember that all life is accompanied by risk. Ten thousand television sets catch fire each year, a hundred thousand people walk through plate glass each year, 125,000 do-it-yourselfers injure themselves with power tools each year, 70,000 children are injured by toys each year, ten thousand people are poisoned by aspirin each year. But what are we willing to give up? Some of these are not really remote, but we are willing to take the risk. E.g. automobile deaths. 1 chance in 4000 each year of dying.
And of course whenever you trust someone, you risk betrayal; when you open yourself, you risk exploitation or ridicule; whenever you hand over a dollar, you risk being defrauded.
2. Insofar as possible, avoid catastrophes. If there is a small but significant chance for catastrophe, then the regular expected value calculations may not apply.
A major principle of risk management is to avoid any real risk of catastrophe at any reasonable cost. The difficulty of applying this principle comes from the uncertainty of what is a real risk and what is a reasonable cost.
3. Recognize the tradeoffs. Remember that every action of life has some risk to it. Even when we don't take the risk upon ourselves, risk is often put upon us by the nature of life and society. Eating you risk food poisoning or choking, but you have to eat or you'll die. Socializing you risk disease, driving or flying you risk crashing, but in some sense you have to socialize and travel. Lying in the sun you risk skin cancer; smoking you risk lung cancer; eating French fries you risk heart disease.
Don't deny the risks involved in living and don't worry excessively about the consequences of modern life.
4. Maximize Expected Values. Normally, the expected value of each alternative shows its relative preferability. That is, you are opting for the greatest probability of the greatest good. Remember, though, that these calculations are guides, and are based on what may be very subjective probabilities and rewards. You are not "required by law" to choose any particular alternative. If you believe that the alternative with the highest EV is a poor choice, you should reconsider the probabilities and rewards you have assigned to all the alternatives.
With these ideas in mind, you'll better understand why some people pursue dangerous sports like skiing, sky diving, race car driving and so forth. The risk/benefit ratio is acceptable to them. It may be useful to note here, too, that most people are not rational risk takers. They take some risks all out of proportion to any expected return and avoid other risks that have a large expected value compared to the risk.
via: virtualsalt
