Going through the goop: An introduction to decision making (1989)

Jonathan Baron, Katherine Laskey, Rex V. Brown

Every day, we make hundreds of choices. We choose what to wear, what to do when we get home from work or school, and how to respond when someone makes fun of us. Sometimes we also make big decision, such as what kind of school to go to, what career to pursue, whether to get married, and whether to have a child. Sometimes people make decisions that are even bigger than these because the decisions affect hundreds or millions of people - decisions about war and peace or about changes in the laws. Even if we ourselves don't make such big decisions, we need to understand how they are made.

Most of the time, we make these choices without thinking. For small, routine choices such as how to respond when your friend starts a conversation with you, you do not need to think. You have learned how to talk and how to behave in a friendly way without thinking at all, and your habits serve you well. You could behave differently than you do, of course, but your behavior is probably fine as it is.

In other cases, though, you THINK about your decisions, from what to wear in the morning to how to spend your money. Sometimes people make choices without thinking when they really ought to think a bit. For example, we sometimes say things that hurt people's feelings and then we feel bad for having said them. Can you think of other examples of things we do because we didn't think first?

The purpose of this book is to help you improve your decision making. It will teach you WHEN it is worth thinking about decisions and, mostly, HOW to think about them once you start thinking.

It will teach by example. You will be given a problem about decision making. First, think about the problem and try to answer it. You can discuss the problem with someone else. Then turn the page and look at the answer carefully.

Where do these answers come from, and why are they right? The answers come from a field of study called decision theory. It is taught in colleges and graduate schools. It is sometimes used as a way of making very important decisions such as whether to have surgery or where to locate an airport.

People who study decision theory and write about agree about some things and disagree about others. In our answers, we make our own best effort to give the right answer. All of us are scholars who have written about decision theory, and the answers we give are, in most cases, the same as the answers that any other scholar in this field would give. However, in some cases, other scholars would disagree with us.

You might disagree with us too, and you might be right. But give us a chance. Don't just assume that your first answer is the right one. Don't think that if an answer FEELS wrong it must BE wrong. Our feelings are not always the best guide to good decisions. If we relied on our feelings, we'd never go to the dentist!

After you read our answer, you will be given other problems to work out, sometimes without the answers. Try to apply what you have learned from the worked-out examples to these new problems.

Decisions are GOOPy

Problem: Some definitions

An OPTION is something you can do or not do.

An OUTCOME is something that will happen or not happen.

A DECISION is a situation in which: You have more than one option. The option you choose can have some effect on the outcome. You can think about which option to choose.

Which of the following are decisions? 1. What to wear? 2. What to wear if you're a baby? 3. Whether to do your homework? 4. Whether you will get all the answers right if you do your homework as wel as you can? 5. Whether to go to college? 6. Whether to breathe? 7. Whether to vote for the Republican or Democratic candidate? 8. Whether the Republican or Democrat will be elected?

Answer: 1, 3, 5, and 7 are decisions. 2 is not a decision because babies can't think about what to wear. 4 is an outcome, not a decision, and the only decision (to do your homework as well as you can) has been made. 6 is not a decision because you do not have the option of not breathing. 8 is an outcome of many people's decisions, not a decision that anyone makes.

Problem: Sara's options and their outcomes

Since she was eleven years old, Sara has been working after school babysitting Josh between the time his mother leaves for work at 3:30 and the time his father gets home at 6:30. Josh, who is now five years old, has developed a close bond with Sara. Sara, who has just turned sixteen, has become pretty attached to Josh herself. In fact, she is thinking of a career in child development because she has had such a good experience sitting for Josh. Sara's friend Leslie has just gotten a job at Burger King, and she says there are openings there. "Come on," she says. "We could work together and Burger King will pay you lots more. Babysitting is a kid job." Burger King pays $5 per hour and Sara is now making $2 an hour sitting for Josh.

What are Sara's options? What are the possible outcomes?

Answer: Sara's two main options are:
  1. try to get a job at Burger King, and quit babysitting if she gets it.
  2. don't try to get the job.

She has other options too. For example, she could quit babysitting first and then try to get the job, but this is foolish because she could wind up with neither job. Or, she could ask for more money from Josh's parents.

The outcomes of trying to get the job are that she either gets the job or not. If she gets it, the outcomes are that she would make more money, be with her friend, miss Josh, lose the experience working with children, and hurt Josh. Notice that the last of these outcomes is something that affects Josh, but it still matters.

The outcomes of continuing to babysit are that things stay the way they are. We could also describe these outcomes by comparing them to the possible outcomes of the other option: she would make less money, not be with her friend, not miss Josh, get more experience working with children, and not hurt Josh.

Problem: Sara's decision - goals

What should Sara do? Why?

Answer: It depends on her goals, what she wants, and how strongly she feels about each goal. Is it more important to her to make money and be with her friend? Or is it more important to avoid upsetting Josh and prepare for her future?

GOALS are another important part of decisions, aside from options and outcomes.

Goals themselves result from decisions. Sara might decide that she cares more about the money. But she could also ask herself why she cares about money. She might decide that she really doesn't need the fancy clothes and jewlry she could buy with more money. She could also think about her future, and she could decide that, in 10 years, it won't matter whether she had a little more money or a little more time with her friend, but it will matter whether she has prepared herself for a career.

The other element of decisions is PROBABILITY. This has to do with how likely the outcomes are. We didn't need to think about probability very much in this decision, but there was some. It is not absolutely certain that Sara will get the job at Burger King if she applies for it. We could ask how likely she is to get it. But it really doesn't matter here, because the sensible thing is to apply for the job and see if she gets it before she quits.

There are four things to consider when making a decision:
The first letters of these make up the word GOOP. Making a decision well involves thinking about all four of these elements. It might be that we don't need to think much about one of these elements (such as probability), but we need to check to make sure.

Making a decision well, then, requires going through the GOOP. Going through the GOOP isn't always easy. Sometimes it can be downright uncomfortable. But if we do it we'll be more comfortable with our decision once it's made.

Problem: Quitting

What if Sara had to quit babysitting before she even applied for the job at Burger King? In order to apply for the job, she would have to miss babysitting on a very important day, and because of missing on that day, she would lose her job. Would the probability of getting the job at Burger King matter then? Why?

Answer: The probability would matter, but only if Sara has decided that the job at Burger King is better than babysitting. If she decides that babysitting is better, then she will not quit, and the probability of getting the job won't matter. If she decides that the Burger King job is better, however, she takes a risk by quitting her babysitting job in order to apply for it. If she almost sure to get the Burger King job, the risk is small and is worth taking. But if very few applicants are accepted, the risk will be too great, and she would do better to keep her babysitting job.

Two proverbs capture the two sides of this dilemma:
  Nothing ventured, nothing gained.
  A bird in the hand is worth two in the bush.

Neither one of these proverbs is always a good guide to follow. Sometimes you should follow one, sometimes, the other. It depends on the probability, on the outcomes, and on your goals.

Problem: Good and bad decisions

What if Sara said: "I want to make as much money as I can, so I'll work at Burger King." Would that be a good way to make the decision?

Answer: Perhaps that is the right decision, but this is not the right way to make it. Sara has considered only one possible outcome and one possible goal, her goal of making more money. She has not asked what she might be giving up, and whether the extra money is worth it.

When we think about any decision, we should try avoid thinking of only one side. When we favor one option, we should check our decision by thinking of reasons why we might be wrong. The reasons correspond to the four elements:
  Sara might have negelcted some of her GOALS, such as preparing for her future or not hurting Josh.
  She could have neglected other OPTIONS, such as doing more babysitting to earn extra money or asking for a raise.
  She could have neglected certain OUTCOMES, such as hurting Josh or losing the experience of babysitting.
  She could have failed to consider PROBABILITIES, such as the probability that she would not like working at Burger King once she takes the job.

Good decision making is ACTIVELY OPEN-MINDED. Good decision makers look for reasons why they might be wrong. Even if they don't change their decision, they can often modify it in ways that take these reasons into account. For example, if Sara decided to keep babysitting, she could ask for a raise to make up for the difference in money.

Problem: Simple vs. complex

Which is a sign of better decision making:

1. Sara thought to herself: "I can't quit my job. If I do, I'll miss Josh."

2. Sara thought to herself: "If I quit my job, I'll miss Josh, but I'll make more money. I guess Josh is more important to me than the money."

Answer: 2 is better because Sara is more actively open-minded. She considers reasons on both sides.

Why is this important? The best decision is the one that takes into account all the reasons on both sides. If you think of only the reasons on one side, you can make mistakes. It often happens that thinking helps you to change your mind and make a better decision, a decision that will achieve your goals more completely.

Thinking of the other side has other benefits: It make you aware of the things you are giving up when you choose one side, and it helps you understand people who see things differently.

Problem: Simple vs. complex again

Think of a bad decision that someone made, perhaps you. Then think of a reason that might have caused the person to choose a different option. Could the person have thought of this reason before the decision was made?

Problem: Sara and Joan

Suppose Sara and Joan both had the same choice to make, and Sara decided to work at Burger King but Joan decided not to. Could they both have made good decisions? Could they both have made bad decisions?

Answer: Both decisions could be good ones. A good decision depends on goals, and people can have different goals. Even if Sara and Joan have the same goals, Joan's goal of helping Josh (or some other goal) could be stronger than Sara's.

Problem: Bad outcomes

Suppose that Sara decided to take the new job and she hated it. Does that mean she made a bad decision?

Answer: Not necessarily. Perhaps there was no way for Sara to know that this would happen. Bad luck is not the same as bad decision making.

Problem: The lottery

John and Susan each bought a ticket in the state lottery. They both picked their birthday (518 for May 18, 220 for February 20). The winning number is also chosen at random: the digits 0-9 are written on ping-pong balls, which are mixed up thoroughly in a container. One ping-pong ball is taken out for each of the three digits in the number. (It is then put back and the numbers are mixed some more.)

John won the lottery that week but Susan didn't. Was John's decision to buy a tickt better than Susan'd decision?

Answer: The two decisions were equally good, or equally bad. Whether a decision is good or bad depends on what the decision maker knows at the time. We cannot predict the future perfectly. The fact that John won was a matter of luck, not a matter of good decision making. You can learn how to make good decisions, but you cannot learn how to be lucky.

Problem: The hitchhiker

Imagine now that I'm your friend. My parents have gone away for the weekend, and so I decided to have some fun myself. So I hitchhiked to a nearby city, did a little sightseeing, and hitchhiked home. You're a little surprised by this (I'm usually more levelheaded than that), but I say to you, "Come on. Nothing bad happened. I had fun and it was exciting." What would you say to me?

Answer: I was lucky, but I did not make a good decision. I didn't think about the bad things that could have happened.

Problem: The boyfriend

Now I'm another friend, and I tell you that I had a tough decision to make last week, about whether I should tell my friend that her boyfriend was saying mean things behind her back. I decided not to tell, but I want you to tell me whether you think it was a good decision. What would you say to me?

Answer: Whether it was a good decision depends on how it was made - whether I made it for the right reasons. Either telling or not telling might have been the better decision. Did I go through the GOOP? Did I think about Goals, Options, Outcomes, and Probabilities? Was I actively open-minded? Did I try to think of reasons against the option I liked as well as reasons for it?

If you want to help someone make a decision, try to help them think of Goals, Options, Outcomes, and Probabilities that they haven't thought of? Are you worried about your friend's boyfriend taking advantage of her? (A goal) Is there some way to make her aware of the situation without telling her? Could you get someone else to tell her? (An option) What will happen in a few months if you don't tell? (An outcome) How likely is it that she will no longer be your friend if you tell? (A probability) And try to get them to be actively open minded, to consider goals, options, and outcomes that they haven`t thought of yet.

Problem: Michael

Michael was born big, in fact, almost 12 pounds. When he started school, he towered above the other kids. Everyone thought he had stayed back at least two grades, but he actually never had much trouble with school. His father was tall too. His father had played basketball in high school, and he made sure to teach Mike how to dribble and shoot as soon as he could walk. As Mike grew older, he got really interested in basketball. He watched all the games on TV, and he decided that he wanted to be a professional basketball star when he grew up. He practiced every chance he got, sometimes with other kids and sometimes alone.

There was a magnet school near where Mike lived. He could go to this school for high school, or he could go to the regular high school nearby. The magnet school was clearly the best choice academically. Most of the graduating class went to college, even those from Mike's neighborhood. The kids from Mike's neighborhood who went to the local school hardly ever went to college. Many of them wound up in trouble with the law.

The choice would be clear, except that the local school had a really fine basketball team, and the magnet school had none at all. The local school's team had won the state championship twice in the last ten years. In the last ten years, three kids from this school had made it to the pros.

Go through the GOOP about this decision. After listing the four elements, what would you advise Michael to do.

Problem: Marian

Marian loves music and has played the flute since she was seven years old. She practices every night for at least an hour, and her music teacher thinks that she has the talent to make it into a good music school like Juliard when she reaches college age. Marian also likes sports and often joins the boys in her neighborhood for a game of pick-up basketball. Now that she is starting seventh grade, Marian has to decide whether to join the school band or the girls' basketball team. She is afraid that her music might suffer if she plays basketball because basketball practice and homework might squeeze out flute practice. Being in the band would be good for her music, but she doesn't want to be too one-sided. Also, Marain's best girlfriend is going out for basketball and wants Marian to play with her. Marian's flute teacher is strongly for her joining the band.

Go through the GOOP about this decision. After listing the four elements, what would you advise Marian to do.

Conflicting values and goals

Problem: Sam

Sam is going with Lisa and has already asked her to the homecoming dance. Sam has been thinking for a while that he might want to break up with Lisa, but he hasn't said anything to her. Now there's this new girl, Luanne, and Sam really likes her. Sam told his friend Jack that he's going to break up with Lisa so he can go to the dance with Luanne. "Don't you think Lisa might feel bad?" asked Jack. "I don't want to think about that," said Sam. "I have to do what's best for me."

a. What goals is Sam failing to consider?

b. What options does Sam have?

c. Write a description of how Sam could make an actively open-minded decision but still decide to take Luanne to the dance.

d. Write a description of how Sam could make an actively open-minded decision and decide not to take Luanne to the dance.

e. Is he neglecting future consequences or consequences to other people?


a. What goals is Sam failing to consider?

His goal of not hurting Lisa's feelings.

b. What options does Sam have?

Try to find a way to break up with Lisa without hurting her feelings so much. Or try to find out why he likes her less and change it.

c. Write a description of how Sam could make an actively open-minded decision but still decide to take Luanne to the dance.

He could consider the other options and decide that taking Luanne is still the best decision. He might think, for example, that the way he breaks up with Lisa will make only a small difference to Lisa but whether he takes Luanne to this dance will make a big difference to him.

d. Write a description of how Sam could make an actively open-minded decision and decide not to take Luanne to the dance.

He could think about all these things and then choose one of the other options, such as trying to change his relationship with Lisa so that he likes her more.

e. Is he neglecting future consequences or consequences to other people?

Mostly consequences to other people. But one future consequence he is neglecting is his reputation. If he becomes known as a person who flits from one girl to another, girls will not want to get serious with him.

The big mistake that people tend to make is called single-mindedness. Most of the time it isn't a problem. If people pick by the most important factor, they usually do pick the best option. But sometimes, they make mistakes.

Problem: Amy

Amy loves sports and plays on her high school basketball team. Lately she has been having trouble with her knee. Her family doctor referred her to a specialist who told her she has a hereditary knee problem. "If you keep on abusing your knee by playing basketball, you'll make the knee worse, and I expect you'll have real problems when you get older," the doctor told her. Amy's grandmother had the same knee problem, and, at seventy, she walks with a cane and is often in a great deal of pain. Amy says, "I don't want to think about what happens when I get older. I'm going to play basketball now."

a. What goals is Amy failing to consider? Is she neglecting future consequences or consequences to other people?

b. Write a description of how Amy could make an actively open-minded decision but still decide to continue playing basketball.

c. Write a description of how Amy could make an actively open-minded decision and decide not to play basketball.


a. What goals is Amy failing to consider? Is she neglecting future consequences or consequences to other people?

She is neglecting future consequences, to herself.

b. Write a description of how Amy could make an actively open-minded decision but still decide to continue playing basketball.

She could think about the future and decide that she would be willing to put up with the pain that her grandmother has in order to play basketball. She could also think about the probability that she would never develop the symptoms her grandmother has, either because the doctor was wrong, because she would die of something else first, or because medical researchers would find a simple cure for the condition.

c. Write a description of how Amy could make an actively open-minded decision and decide not to play basketball.

She could decide that the chance of future pain was not worth it, even taking into account the possibility that the pain would never happen even if she played.

Problem: The track star

You are training for the olympics as a runner. A friend offers you some steroid drugs, which will increase your strength and make it more likely that you will win. What goals and outcomes should you consider? How could you make this decision in a single-minded way?

Answer: The two main goals in conflict here are success in the olympics and your future health. You would be single minded if you don't think about them both. You would be single minded if all you think about is winning, or if you think only about your health. Even if you decide not to take the drugs, you might later regret your decision, if you fail to make it to the olympics, unless you have thought in advance about what you might be giving up.

Problem: The cafeteria

You are put in charge of a school cafeteria for a week. You must decide what to serve. How should you think about this decision?

Answer: You should think about all the goals that matter. The ones that most people think of are the cost of the food, nutrition and health, and how much kids like it. (Ease of preparation is another goal.) A single-minded decision would think about only one of these goals.

Problem: The governor

You are governor of a state. A group comes to meet with you, pointing out the need for more money to be spent on shelters for the homeless, on programs to help them get jobs, and on community mental-health programs. What should you say?

Answer: The goals are important, and you will consider them, but you must also worry about other goals, such as keeping taxes low and funding other important state programs such as education, law enforcement, and highways.

Problem (with no answer given here): The governor again

You are governor of a state. A group comes to meet with you, arguing that taxes need to be lowered in order to encourage businesses to come to the state.

Problem (with no answer given here): Sunday TV

Your friend invites you over to watch TV on Sunday afternoon. You have not done your homework for Monday, but your friend has. How should you think about this decision?

Future consequences

Problem: Conflict over time

We have already seen several cases in which someone must make a decision between goals for the present and goals for the future. Often, people tend to neglect the future or not weigh it enough in their decisions. When people smoke cigarettes, for example, they neglect their future health over whatver pleasure they get from the cigarettes at the time they start smoking. Can you think of other examples in which people neglect the future?

Answer: Here are some more, but there are many others:

1. Eating food that is not healthy.

2. Having sex without birth control when you don't want to get pregnant.

3. Not doing your homework.

4. Not saving money for the future.

Problem: More examples

Can you think of more examples now?


5. Drinking too much alcohol.

6. Not practicing an instrument when you are taking lessons or trying to learn it.

7. Not saving money.

8. Scratching a scab or bite.

9. Nations use up their oil, firewood, or other resources without thinking about what they will use to replace them.

10. People and nations borrow money without thinking about whether or how they can pay it back.

11. Not taking protective action like having your home checked for radon.

In all these cases, the bad effects are in the future, but the good effects are immediate. When people do these things, we say they are impulsive; they follow their impulses rather than their better judgment. Another way to think about this is that people are short-sighted. It is as though they are walking forward but they can see only a few feet ahead. They take paths that look good where they are, but they do not look down the paths to see where the paths go.

Problem: Why bother?

Should we care as much about the future as the present? After all, the present is now, and future may never come.

Answer: This is a question that has puzzled philosophers and poets throughout history. It has no simple answer. But here is one way to think about it. Imagine that you are really many different people, closely related: you-now, you-next-year, you-the-year-after that. Suppose that someone else had to make a decision that would be best for "you," that is, best for all of these different you's. If that person cared equally about all the different you's, then that person would care as much about future you's as about you-now.

Parents tend to care about their children in this way. Children worry more about themselves at the moment. Their parents try to protect the people their children will become when they grow up.

Problem: Why bother again?

But this doesn't answer the original question. The future may never come. Isn't there any good reason to neglect the future?

Answer: Yes, here are some good reasons for giving the future less weight:

1. It's less certain. For example, in the case of Amy, she wasn't sure that she would develop knee trouble like her grandmother's. Although she should think about her future self, she should not treat the decision as simply between herself wanting to play basketball and her future self suffering from knee trouble, for that particular future self might never come.

2. Your desires may change. For example, in the example in which you are a runner who wants to run in the olympics, you desire to run in the olympics may weaken over time. Even if the steroids seem worth it for this future goal, they might not seem worth it later.

3. The situation may change. In the case of Amy, a new medical treatment might be discovered. People who save lots of money for the future sometimes lose their savings because of high levels of inflation. Or these people may die before they have a chance to enjoy what they have saved.

All these reasons are reasons for giving the future less weight. They are not reasons for neglecting the future, that is, for not thinking about it at all. When we give the future less weight, we discount it.

Problem: What people really do

Are these the reasons that people discount the future? That is, do people discount the future only for good reasons? Or do they sometimes have bad reasons?

Answer: People sometimes neglect the future because they forget to think about it or because they act against their better judgment. These are bad reasons for neglecting the future. We all discount the future for these reasons at one time or another.

Problem: The psychology experiment

In a psychology experiment, a child is given a choice of one piece of candy now or two pieces in 24 hours. Which would he choose? Now suppose that he is given the same choice 24 hours sooner. So now the choice is one piece in 24 hours or two pieces in 48 hours. Which do you think he would choose?

Answer: In experiments like this, children (and sometimes even adults) pick the smaller reward when they can get it right away. They are impulsive. They cannot wait for the better reward later. But if they think about the issue in advance, they want the bigger reward.

What you decide ahead of time is your better judgment. What you do when temptation is at hand - if it is different - is impulsive. It is shortsighted because you do not see ahead to the future. Thinking in advance is the better decision.

This experiment shows something about impulsiveness. It violates a fundamental principle of decision making: The option you choose should depend only on your goals, the outcomes of each option, and their probabilities. This principle implies that the option you choose should not depend on when you do the choosing (so long as everything you know about the decision stays the same). When we are impulsive, we violate this principle. It is only at the moment of temptation that we want to go against our better judgment. The rest of the time, we want to stick with it.

Problem: What can we do?

Suppose you are faced with the choice now of doing your homework tonight or putting it off and watching television. Which would you choose? Have you ever made a resolution ahead of time to do something like this? study for a test? go on a diet? not fight with your dad? Have you ever gone back on the resolution?

Many people go back on resolutions like this. When temptation comes, they cannot avoid it. How can we avoid this kind of impulsiveness? There is more than one way. How many ways can you think of?


1. We can think about the future at the time we make the decision. For example, when you decide whether to do your homework or watch television, you can think about what it will be like not to have your homework done the next day, or about what it will be like several years from now when you wish you had been a better student.

2. We can try to bind ourselves, to prevent ourselves in advance from giving in to temptation. Ulysses - the main character in the Odyssey, an ancient story told by Homer - was sailing his ship past the island of the Sirens. The song of the Sirens was so beautiful that all sailors who heard it were tempted to visit the island, and, once there, they would never leave alive. Ulysses knew this, but he wanted to hear the song, so he had his crew bind him to the mast of the ship with strong ropes. He filled their ears with wax so that they would not hear the Sirens, or him, if he tried to order them to stop.

In the same way, people who want to stop drinking sometimes pour their liquor down the sink, so that they cannot get to it even if they want it. Some people make deals: they quite smoking by signing a contract to pay someone a large sum of money if they are ever caught with a cigarette.

3. People make personal rules for themseles, like, "I will run two miles a day," or "I will get my homework done before I watch TV." These rules work, in part, because people see breaking the rule as setting a precedent for breaking it again. If you skip a day of running, what's to stop you from skipping another day? and another? When you think about this, you are more likely to follow your rule.

Precedent-setting is an extremely important principle of all decision making.

4. People can control their own emotions, goals, and attention. You can, for example, convince yourself that homework is fun by thinking about the parts of it that you like.

If you are trying to avoid some temptation, you can distract yourself. You can count to ten before you get angry at someone. Expressing anger is often impulsive, and the counting distracts you and gives you a chance to think about whether you really want to start a fight.

You can also pay attention to helpful emotions. One emotion is looking forward to a pleasant event that you have to put off. Another is looking backward with relief to a bad event that you have gotten over with. These emotions work against two other emotions that are not helpful: the feeling of impatience about wanting a good thing as soon as possible and the feeling of dread about doing something painful or difficult.

Problem: TV

You can watch TV for an hour, because you have a lot of homework to do. You have a choice between one program that starts right now and another one that starts later, after you would be finished with your homework. You like the later one better, but you are tempted to watch TV right now and do your homework afterwards. What can you do to avoid giving in to this temptation? Think of the four methods we just reviewed.


1. You can think about the future, about how unhappy you will be when you have to be doing your homework while the better program is on.

2. You can ask your parents or someone else to keep you away from the TV until it's time for the better program.

3. You can make a rule to get your homework done before you watch TV.

4. You can think about what you like about your homework, and you can enjoy looking forward to the program you want to watch. You can also think about how good it will feel to have your homework over with.

Problem: Personal rules

Can you think of examples of good and bad personal rules? Why are they good and bad?

Answer: Some are vague (e.g., not too many cigarettes), leading to abuse, and others are clear and easy to follow (e.g., no cigarettes at all). Some are too strict, and do more harm than good (anorexia). Others are too strict to be followed by the person in question and lead to cycles (bulemia) and to more and more elaborate rules. Personal rules are one way to control yourself, but sometimes the other ways are better.

Problem: Conflict

What is the conflict between present and future in each of the following decisions? What could the decision maker to avoid impulsiveness or shortsightedness? (In some cases, this is not needed.)

1. Jean wants to lose weight. Every day on her way home from school she passes Burger King and she can't resist buying an ice-cream cone. Some days she gets french fries too.

2. Sylvia borrows $2,000 to take a vacation to the Carribean. She pays 18% interest. The bank gives her 5% interest on her savings account, which has been growing at the rate of about $400 per month.

3. John wants a new TV. He has his eye on a particular model at Radio Shack, which he passes every day. One day he notices that the model is on sale, so he goes in and buys it even though he has just enough in the bank to pay for it and make it until next payday.

4. After winning her first major tennis tournament, Martina took all the prize money and bought herself a house and a new car.

5. Henry knows that he could be a good student, but he would prefer to go out with his friends rather than study.

6. It is July. Susan has a chance to go on a weekend trip to the mountains right now or in a month. She decides to go now.

7. Jane is 16 years old, unmarried, and has gotten pregnant. She considered trying to prevent pregnancy, but she decided that she was really old enough to have a child.

8. The population of Kenya, a country in East Africa, grows at the rate of 4% per year. The production of food grows at the rate of 1% per year. The government has no plan to control population.

9. Albert notices that a mole on his forehead has gotten bigger. He has been outside in the sun a lot. He decides it's probably nothing, and he does not go to the doctor.


1. Jean vs. Burger King: The conflict is wanting to eat at the moment and wanting not to be fat later. Jean could find a different way home (physical binding).

2. Sylvia's vacation: If Sylvia borrows the money at 18%, she'll lose money in the long run. She should wait until she has saved the money, which won't be very long. She loses much less interest by taking the money out of her account than by paying for the loan. In the meantime, she can enjoy planning for the vacation.

3. John's TV: If John can make it until payday, he should but the TV. In this case, it would be worse if he waits, because the TV will cost more. Putting good things off is not always the best thing to do.

4. Martina`s winnings: Althletes should save their prize money for the future. Their careers are short. Only after saving enough for a comfortable future should an athlete spend money on luxuries. Martina should think about the future.

5. Henry's studies: Henry should think about the advantages of being a good student for his future. If he can be a good student, it will be easy for him to find things to like about his schoolwork. He could change his goals.

6. Susan's trip to the mountains: July is an excellent tinme to visit the mountains. There is no conflict here. She should go. (See #3.)

7. Jane's pregnancy: Jane's choice is not whether to have a child or not, but whether to have one now or later. Later, she will be in a much better position to raise the child. She will know more, and she will have more money. She should change her goals, and should try to find interests more suited to her age.

8. The population of Kenya, a country in East Africa, grows at the rate of 4% per year. The production of food grows at the rate of 1% per year. The government has no plan to control population.

9. Albert notices that a mole on his forehead has gotten bigger. He has been outside in the sun a lot. He decides it's probably nothing, and he does not go to the doctor.

Problem: Your own decision

Think of a decision you made that involved a conflict between present and future. What methods of self-control do you use? (or do you use any?) Can you think of any other methods that might work better than the ones you use? Share your answers to this with others.

Self and others

Problem: The C-D game

Suppose you play a game as a class. Let's imagine that your class has 20 students. Each student writes down a C or D on a piece of paper without showing it to anyone else. If a student writes a D, then that student gets $1. If a student writes a C, then all the others get $1. So each student gets $1 for every other student who wrote C, plus $1 if that student wrote D. Nobody knows what anyone else writes down or how much money anyone else gets. The game is played only once. What should you do (C or D) if all you cared about was getting as much money as possible?

Answer: You should write D. You get one more dollar that way, in addition to the dollars you get for all the other people who wrote C.

Problem: The C-D game again

What should you do if all you cared about was that the whole class got as much money as possible?

Answer: Your should write C. If you do that, the total winnings are increased by $19. If you write D, they increase by only $1.

Notice that this answer is different from the answer to the last question. There is a conflict here between what is good for you and what is good for everyone else.

Problem: The C-D game again

Suppose that at the end of the game, everyone's winnings will be put into an envelope, and then all the envelopes would be mixed up. You will pick an envelope, but you don't know whose it will be. What should you do now? Does it matter whether you care more about how much you win or how much everyone wins together?

Answer: You should choose C. The chance is 19 out of 20 that you will pick someone else's envelope. If you pick C, it will have one more dollar than if you pick D. There is only a 1 in 20 chance that you will pick your own envelope, in which case you would get an extra dollar for picking D. C is best for both you and the group as a whole.

One way to think about fairness is to imagine that you do not know whose position you will be in, whose envelope you will have. The decision here that is best for you is also the one that is best for everyone.

Problem: Another class

Suppose that some other class was going to play the game. You can send a message to one person in the class about whether to pick C or D, and you can be sure this person will do what you say. Each person in that class has agreed to let someone in your class tell him or her what to do. You do not know who the message will go to. What should you tell the person to do?

Answer: If you tell the person to pick C, 19 others will get a dollar more, but the person you tell will get one dollar less. On the whole, you should tell the person to pick C. Since your message could go to any one of the 20 others, the chances are 19 out of 20 that any student in the other class will be better off because you said to pick C, and only a 1 in 20 chance that the other person would be worse off.

Problem: Why doesn't everyone pick C?

When this game is played for real, some people pick D. What is the problem?

Answer: This game creates a conflict between self and others. Because of this, it is called a social dilemma. Some people do not care enough about others.

Suppose you care about each other person as much as you care about yourself. Then you will pick C, because the gain to others is 19 if you pick C, and the gain to you is 1 if you pick D.

But suppose you care about yourself 50 times as much as you care about anyone else. Then the gain to you will be 50 instead of 1. Your decision will be 50 for picking D and 19 for picking D.

It would be nice if we all cared about others as much as about ourselves, but it is very hard. We should all try to do the best we can. When we can do a lot of good for others by making only a small sacrifice ourselves, we should certainly do it.

We can think about decisions like this as multi-attribute problems. One attribute is benefit for us. Another is benefit to society or others. We need to think about how much weight we should give to society. We should try to encourage each other to give as much weight as possible, because we all benefit that way. (Illustrate this with a multi-attribute table for the game.)

Problem: The psychology experiment

A psychologist named van Avermaet did an experiment to test how people deal with the conflict between self and others. The subjects of the experiment, who were college students, were instructed to fill out questionnaires until they were told to stop. They expected to be paid, but they did not know how much. Each subject was given either three or six questionnaires (depending on the experimental condition) and was told to stop after either 45 or 90 minutes. When the subject finished, she was told that there had been another subject who had had to leave before he could be told that he was supposed to be paid. The experimenter, who also said he had to leave, gave the original subject $7 (in dollar bills and coins) and asked her to send the other subject his money (in the stamped, addressed envelope provided). The subject was told that the other subject had put in either more, the same, or less time and had completed more, the same, or fewer questionnaires. The "other subject" was actually a friend of the experimenter, who returned the money and reported how much each of the other subjects had paid. How much money do you think the original subject would send to the "other" subject in each condition?

Answer: When the original subjects were equal to the other on both dimensions, they sent almost exactly $3.50 on the average. (Almost all of them did this, which is heartwarming.) Subjects who either worked longer or completed more questionnaires than the "other" gave the other less than $3.50. Subjects apparently seized on any excuse to see themselves as deserving more. Only when subjects did worse on both dimensions (time and number of questionnaires) was there a tendency to send more than $3.50 to the other (however, the increase was not statistically significant). It appears that subjects seize on any excuse to send the others less than themselves; they divide the money equally only when there is no excuse to give more to themselves. Instead of weighing the two dimensions (time and number of questionnaires) equally, or at least consistently, subjects weigh one dimension more when it suits them, whichever dimension it is.

What appears to happen in this experiment, and in real-life, is that people seek a distinction between themselves and others in order to justify selfish behavior. When their is doubt about what is important, people give themselves the benefit of that doubt. To fight this tendency, we need to follow a simple rule: give the other guy the benefit of the doubt.

Problem: Feelings

In the C-D game, C is called cooperating, and D is defecting. How would you feel if everyone else defected and you cooperated? if everyone else cooperated and you defected?

Answer: A person who defects when most others cooperate is called a free rider, or a "fink." Most people get angry at free riders. A person who cooperates when others defect is sometimes called a "sucker." The idea is that suckers don't look out for themselves enough. They expecte everyone else to cooperate. We should not make fun of such people, though. If everyone were as optimistic as they were, we would all be better off.

Problem: Examples

Can you think of things that happen in the world that are social dilemmas like this game?

Answer: There are many examples. Here are a few:

Paying your taxes: If everyone pays what they owe willingly, without trying to cheat, we are all better off because our taxes don't have to pay for agents to enforce the tax laws. The same goes for following any law. Sometimes you can get away with breaking the law, but if everyone did this, people would live in fear, and they would spend a lot of money on police, so there would be less money for schools, roads, and other things.

Contributing to public TV: If nobody contributes, the station goes off the air. A free rider is someone who watches without contributing.

Pollution, garbage, littering: It is best for you not to recycle your garbage and to throw your trash on the sidewalk, but it is best for everyone if we all recycle and throw our trash in cans. It is best for each electric company and each business to pollute the air and water, saving money by not buying special equipment. But it is best for everyone if companies install special equipment to control pollution.

Doing your job: Most people can get away with a little loafing on the job. But if everyone loafs, things don't get done. The goods sold in stores are badly made. The clerks don't know what the store has or where to find it. It is best if everyone does their job wholeheartedly, they way they would do it if they really cared.

Taking just your share: When there is not enough of something to go around, it is best for each person to take more than their share, but best for all if each takes only what is fair, or nothing at all if she doesn't want it.

Having children: Most people want children. Some families want more than one or two children. But if many families have more than two children, the population grows, and there is not enough room or enough food for people. This is happening in some places now, such as Egypt and Kenya.

Problem: What to do

Individuals can cooperate or defect. But there are things groups can do to get their members to cooperate if they are willing to discuss it. What are some of these things?

Answer: Groups can do many things:

1. Elect a leader who will force people to cooperate, for everyone's benefit. For example, you could have the biggest kid in the class threaten to beat up everyone who doesn't put C on their paper. This is what the governnemt does when it passes laws.

2. The group could agree to cooperate without a leader. It could make a rule that everyone will put C. The group as a whole will find ways to punish people who defect. Often just disapproval is enough. One kind of rule to prevent people taking more than their share, or more than they need, is to make them pay. We use this kind of rule a lot. Because of it, we have private property. If people just took whatevery they wanted, they would just move into each others' houses, eat each others' food, drive each others' cars, and so on. (This happens in families, because families do not use this kind of rule.)

3. We could try to change our own goals so that we care more about others. This is how cooperation usually occurs in families, but it could work elsewhere. Some people are politically motivated. Can you think of any?

Problem: Cooperation and defection

In each of the following situations, what is the cooperative option (call if "C")? Which is the defect option ("D")? Which of the methods - leader, group rules, or mutual caring - might be helpful in solving this dilemma? (No answers are given.)

1. There is a water shortage. Nobody wants to cut back their use of water, but if people continue to use water, they will all run out.

2. A couple live together and need to clean up the house. Each would rather have a clean house than a dirty one, but each would rather watch TV than clean.

3. Tom, Dick, and Harry are roommates. They keep their refrigerator stocked with beer. Each person is supposed to buy roughly what he drinks, but the others can help themselves. (There are two issues here, buying the beer and drinking it. There is a cooperate and defect option for both.)

4. Each of the workers in a store would rather have Friday off than any other day, but if everyone has Friday off, the store will at risk of going out of business.

5. Many retired people would like to visit the doctor once a week in order to have the best chance of maintaining their health. But if they all did this, everyone's taxes (including theirs) would have to go up in order to cover the Medicare costs.

6. In Kenya, in East Africa, each family does best if it has as many children as possible, but the population is increasing much faster than the amount of food.


Problem: Sara again

Remember Sara, who had the job babysitting for Josh and was thinking about quitting to take a job at Burger King? She was getting $2 an hour for babysitting and would get $5 from Burger King. The money wasn't her only reason to quit, but it was one reason. She also had reasons to keep babysitting.

Suppose she decided to ask for more money from Josh's parents, the Jones's. How should she think about this?

a. Should she ask for the most she thinks the Jones's would be willing to pay and then quit if they say no?

b. Should she ask for the least she would be willing to accept and then stay if they say yes?

c. Neither of these.

Answer: The best answer is c. Here is a way to think about problems like this. Sara has to decide the least amount of money she would accept. It is a good idea to do this in advance. It might be as low as $2, or even less, if she really cares about Josh and about the experience she will get. Even if it is less, it still might make sense to ask for a raise, for she would rather have more money than less, and maybe the Jones's would not mind paying her more. The minimum that Sara would accept is called her reservation price.

The Jones's also have a reservation price, the most they are willing to pay. It could be as high as $5 per hour, or even higher. It could be as low as $2 per hour, the amount they are paying now. Sara does not know the Jones's reservation price, but she can estimate it.

If the Jones's reservation price is higher than Sara's, there is room to bargain. For example, if the Jones's are willing to pay as much as $5, and Sara is willing to accept $3 or more, then Sara will continue babysitting if her pay is anything between $3 or $5. If the Jones's reservation price is lower than Sara's, then it is impossible for Sara and the Jones's to agree, and she will have to quit.

Suppose that the Jones's are willing to pay $5 and Sara is willing to accept $3. In this case, something in the middle would probably be best, something like $4. How can the two sides - Sara and the Jones's - arrive at this figure?

If Sara simply announces that she is willing to accept $3, the Jones's might simply agree to that, and Sara would not do as well as she might. On the other hand, Sara could ask for $4, or $5, or $6, and then ask for less if the Jones's say no. This is called bargaining, or negotiating.

Just as there is a danger from asking for too little, there is also a danger from asking too much. The danger of asking too little is that Sara will not get as much as she could, and the Jones's might be willing to pay much more. The danger of asking for too much is that the Jones's might give up. They might think that a deal is impossible, even though the truth is that their reservation price is higher than Sara's, so that many deals would be acceptable to both sides. When people bargain "tough," they sometimes lose out on agreements they would like.

The way Sara bargains should depend on her relationship with the Jones's. If people trust each other, they could be perfectly honest. Sara could say that she would accept $3, and the Jones's could say that they would be willing to pay $5, and they could all agree to split the difference and settle on $4. If everyone were honest like this, nobody would ever lose out on deals that both sides would accept. On the other hand, if Sara and the Jones's did not trust each other, then Sara would do better to pretend that she wanted more than she did, and the Jones's would do better to pretend that they were willing to pay less than they were. When trust is missing, deals can fall through. Trust is better, but both sides have to do it.

Problem: Two-dimensional negotiation

Suppose that Sara and the Jones's are negotiating about two things at once, time and money. These are like two attributes in a multiattribute table. Suppose that the Jones's would like Sara to work more hours, but they don't care much about how much they pay her. Sara, on the other hand, does not care much about working extra time, but she does care a lot about more dollars per hour. Her weight is higher for money, and the Jones's weight is higher for time. How can both sides take advantage of a situation like this?

Answer: Sara could agree to work more hours if the Jones's would pay her more per hour. In situations like this, neither side has any reason to hold back the truth. Sara should tell the Jones's outright that she cares more about money than time, and they should tell her outright that they care more about time than money. Both sides always benefit from such information. This is like cooperation in social dilemmas.

The only problem is to try to think of pairs of dimensions that the two sides weigh differently. In this case it was pretty obvious, perhaps, but in complicated negotiations like those between the U.S. and the Soviet Union, it is often difficult to guess what matters to the other side. In general, when two sides are negotiating, they do better if they learn a lot about each other.

The meaning of probability

The lottery again

John and Susan both bought a ticket in the state lottery. They both picked their birthday. John won the lottery that week but Susan didn't. If they both buy tickets the next week in the same way, who is more likely to win, or are they equally likely? Does it make any difference if they switch numbers?

Answer: They are equally likely whether they switch or not. The number that wins the lottery is chosen at random. The ping-pong balls have no way of remembering what numbers were picked before.

Some people think that John is more likely to win the second time because he is a lucky person, whether he picks his own birthday or Susan's. But being lucky once does not make you any more likely to be lucky again. Again, remember the the ping-pong balls have no way of knowing what number they picked before, or whose number it was. And they certainly don't CARE whose number it was.

Other people think that John's birthday is unlikely to come up twice in a row, so Susan is more likely to win the second time, unless they switch numbers. But, again, the balls have no memory. John's number is just as likely to come up the second time as it was the first time.

Problem: Probabilities

This section is about probability, the P in GOOP. Probability is a way of talking about how likely something is to happen, when we don't know whether it will happen or not. The probability of an event is often expressed as a number from 0 to 1. A probability of 0 means that the event won't happen, and a probability of 1 means that that it will certainly happen. A probabnility of .5 means that it is as likely to happen as not. Probabilities are also often stated as percents: a proability of 60% is the same as a probability of .6. What do you think the probability is of:

it raining if the weather forecase says that the probability of rain is 50%

a baseball player getting a hit if his batting average is .250

a baseball game having at least one home run

a baseball game having five or more home runs

winning by only 1 or 2 points in pro basketball

a letter getting lost in the mail

having a cold in any given year

having a cold in two years

being fatally injured in a car crash (serious enough to require a tow truck) without a seat belt

being fatally injured in a car crash (serious enough to require a tow truck) with a seat belt

having no injury in a car crash (serious enough to require a tow truck) without a seat belt

having no injury in a car crash (serious enough to require a tow truck) with a seat belt


it raining if the weather forecase says that the probability of rain is 50% (.50)

a baseball player getting a hit if his batting average is .250 (.25, if this is all you know)

a baseball game having at least one home run (.64)

a baseball game having five or more home runs (.01)

winning by only 1 or 2 points in pro basketball (.12)

a letter getting lost in the mail (.0000004)

having a cold in any given year (.50)

having a cold in two years (.75)

being fatally injured in a car crash (serious enough to require a tow truck) without a seat belt (.01)

being fatally injured in a car crash (serious enough to require a tow truck) with a seat belt (.002)

having no injury in a car crash (serious enough to require a tow truck) without a seat belt (.84)

having no injury in a car crash (serious enough to require a tow truck) with a seat belt (.93)

One way to learn about probabilities is to look at data, at what happened in the past. In most of these examples, someone counted the relevant cases (Source: The odds on virtually everything, New York: G.P. Putnam's Sons). In the case of the weather forecase, someone looked at what happened when the forecast said 60% chance of rain, or 70%, and so on. It actually rained on 60% of the days on which the forecase said 60%, 70% of the days on which the forecase said 70%, etc. Weather forecasters may not be able to tell you whether it will rain or not, but the can tell you the probability.

Problem: The future basketball star

Suppose you are friends with an 8th grader who lives next door to you. He cuts classes in school almost every day so that he can spend four hours or more practicing basketball. When someone asked him why he did that, he said he wanted to be a professional basketball player so he could make lots of money. How would you help him think about this plan? What is the probability of the best player on a high-school basketball team making it to the pro's?

Answer: One thing he needs to think about is how likely it is that he will make it to the pros. He could try to get data, to find out how many kids like him have made it in the past. But that is hard. He can also think about the relative sizes of groups. He could compare the number of "kids like him" (his age) to the number of people who make it to the pros each year. How many kids like him are there? How many players join the pro's each year? Here is a rough estimate. Suppose that half of the high schools in the country have basketball teams, and suppose that this kid will be the best player on his team. The number of "best players" is half the number of high schools. This will be in the thousands. Let's guess 20,000. The number who make it into the pros each year is about 20. If these assumptions are right, his chance of making it to the pros is 20/20,000 or 1/1,000 or .001 (a tenth of a percent). Certainly, he thinks that he is special. But so do all the other kids. (You can improve on this estimate by getting some data.)

Problem: Subjective probabilities

What is the probability that you will be married before you are 25 years old? that the next president of the U.S. will be a Democrat? that cocaine will become legal in the U.S. in the next 10 years? that there will be a strike of professional football players in the next five years?

Answer: We cannot answer these questions just by looking at data or by comparing sizes of sets, although in some cases it might help to do those things. To answer these questions, you have to take into account things that you know about the individual case, not just other cases like it. For example, to answer the question about getting married, it will make a difference whether you now have plans that will either increase or decrease this probability: do you want to be a priest or a nun? do you have an itch to spend a few years seeing the world before you settle down? do you want very much to have children as soon as possible?

When we use facts like this, we are making subjective probability judgments. These judgments are based on what we think. We might not feel very confident about these judgments, but making them is a lot better than assuming that the probability is 1 or 0, which is what a lot of people do when they don't want to think about probabilities. For example, one person was afraid to ask for a raise because she said her boss would fire her if she did. When she was asked how likely that was, in numbers, she realized that the chance was about 1%, a risk well worth taking. This was a subjective judgment, but probably a good one.

Sometimes, people are very good at subjective probabilities. This is how weather forecasters make their predictions. They take into account everything they know about weather patters on the day in question. If we look at 100 different times that the forecast was "80% chance of rain," it rains about 80 of these times.

Problem: Repetition

Recall that the probability of having a cold in any given year is .50, and the probability of a baseball game having 5 home runs is .01. What is the proability of having a cold at least once in 3 years? What is the probability of 5 home runs in 100 games?

Answer: It is easiest to think about these things mathematically by looking at the opposite. What is the probability of not getting a cold in three years? If we look at a lot of people, half of them will go one year without a cold. Half of those people will go another year without a cold, so the number who will make it for two years is .5.5 or .25. Half of those will make it for three years, so that number is .5.25, or .125. Therefore, the chance of getting a cold at least once is 1-.125, or .875.

[figure needed]

Likewise, the chance of not having 5 home runs is .99. To figure the chance of not having 5 home runs in 100 games, we multiply this by itself 100 times. The answer is about .37, so this means that the chance of having 5 home runs at least once in 100 gamnes is about .63. If you watch a hundred baseball games, there is a good chance you will see one with 5 home runs.

Probabilities add up. When a behavior (having a cigarette, having sex without contraception, trying a drug, driving while drunk) has the potential of setting a precedent, we need to consider not just the probability of bad outcomes from the single episode but also the cumulative probability from a string of episodes. The probability of having a fatal accident because you did not wear a seattttbelt in one trip is miniscule, but if that trip sets a precedent for the thousands of trips you will take in your life, the probabiltiy is not miniscule at all.

Problem: The pinch hitter

You are a baseball manager. It's the bottom of the 9th and it's the pitcher's turn to bat. If you win, you get to the playoffs. You are one run behind. The bases are loaded and there are two outs. There are two batters you can put in for the pitcher. They are pretty much the same, except that one has a batting average of .300 and the other has a batting average of .225. Which would you put in? Why? If this happened again, would you do the same thing?

Answer: In this kind of sitaition, you are more likely to win if you put in the batter with the higher average. If you always make decisions this way, you will win more often. Probability is a good guide to making decisions.

Problem: Seat belts

Most people think they should wear seat belts because they limit injury in head-on collisions, but I heard of an accident where a car fell into a lake and a woman was kept from getting out in time because of wearing her seatbelt, and another accident where a seatbelt kept someone from getting out of the car in time when there was a fire. What should you do?

Answer: These accidents happen, but they are less likely than the kind of accident in which seat belts help. You should wear your seat belt. If you do, you are less likely to die in a car accident.

Problems: More examples

In each of the following cases, what should you do, and why?

1. Imagine you are a physician making a decision on behalf of a patient who has left the matter up to you. The patient has an unusual infection, which lasts for a short time. The infection has a 15% chance of causing permanent brain damage. Your may undertake a procedure that will prevent the brain damage from the infection (with 100% probability). However, the procedure itself has a 20% chance of causing brain damage itself. Should you undertake the procedure or not?

2. Some people consider buying a gun to protect themselves. Suppose all you care about is not getting killed. Suppose that the probability of getting killed accidentally with your own gun is .003, the probability of getting killed by an intruder if you have a gun is .002, and the probability of getting killed by an intruder if you do not have a gun is .004. Are you more likely to get killed by owning a gun or not?

3. The Salk polio vaccine uses killed virus, and it never causes polio itself. Sometime, however, it doesn't take, and a person who was vaccinated got polio anyway. The Sabin vaccine uses live viruses, taken orally. It never fails to make the person immune, but sometimes it causes polio itself. How would you decide which vaccine is best?

4. Jane has been working in a store for two years. She knows the stock in the store and does a good job with customers. She always gets to work on time, and the owner of the store has started giving her more responsibility. The problem is that he pays her very little - close to minimum wage - and he even complains about that. She would like to ask for a raise. When you ask her "Why not?", she says, "If I ask for a raise, he'll fire me for sure." What would you ask her to help her think about this problem?

5. Bob and Bill have televisions that work sometimes but not other times. Nobody knows why. Bob's works 50% of the time. Bill's works 60% of the time. Bob and Bill want to watch a game on TV. Whose TV should they try?

6. To decide who gets the last can of soda, Ben and Charlie decide to flip a coin nine times. Ben will call it - heads or tails - before each flip, and if he is right more often than he is wrong, he will get the soda. The first eight times, the coin comes up tails, and Ben calls it tails on four of those times, so he needs to be right the last time. (The coin is perfectly fair and Charlie is giving it a good spin shen he flips it.) What should Ben call, or does it matter?


1. You should not do the procedure. The patient has a better chance of escaping brain damage without it.

2. If you have a gun, the probability of getting killed is .003 + .002, or .005. (This is the sum of the probability of getting killed in an accident and the probability of getting killed by an intruder.) If you do not have a gun, the probability is .004. You are better off without a gun. These numbers are not accurate. They are for illustration only. However, the real numbers even more strongly favor not having a gun. Everyone thinks that they will not be the ones to have accidents. The people who have accidents think this just as strongly as everyone else.

3. You would ask which gives the lowest probability of getting polio. The cause of the polio does not matter. We should think about decisions like this in terms of the outcomes that we care about. If you get polio, you are about equally unhappy no matter what caused it.

4. She should think about how likely it is that her worse fear would be realized, and how likely it is that she will get the raise if she asks.

5. Bill's.

6. It doesn't matter. The coin has no memory of what it did the last eight flips. The probability of heads is still .5.

Problem: Two card games

Which of the following games is better to choose, or are they both the same?

A. A deck of cards will be shuffled and cut. A card will be drawn from the top of the deck. If the card is red, you win $1.

B. A deck of cards has been shuffled and cut. The top three cards have been drawn from the top and placed face down. (Any number of the three could be red.) The top card will be drawn from the three. If the card is red, you win $1.

Answer: The two games are equally good. In both games, you get $1 if the top card is red. The difference is just in the way the top card is drawn. In game B, it is drawn in two steps.

Some people think that game B is worse because they do not know what the probability is of the card being red when the three cards are in front of them. But the probability is .5 either way, becuas half the cards in the deck are red.

The feeling of now knowing the probability is called AMBIGUITY. People are inclined to be more cautios when they feel ambiguity. They have good reason to be cautious when the ambiguity is based on some missing information that they might get. For example, if they thought they could find out the number of red cards in the stack of three before they choose, they should certainly try to get that information before they decide. But when there is no way to get the information, it is best to go with your best estimate of the probability.

Probability and expected utility

Problem: Uncertainty in decisions

Some decisions are best to think of as having uncertain outcomes, so that the have to think about probabilities (tht P in GOOP). Other decisions are easiest to think about as if the outcomes were certain. Classify the following decisions into those in which uncertainty is important vs. those in which it is not:

1. doing homework;
2. practicing an instrument;
3. health habits (smoking, eating saturated fat, drinking, taking
drugs, exercise);
4. using birth control;
5. protective measures (checking for indoor radon);
6. the government deciding whether or not to raise taxes;
7. the government deciding how to spend its money;

Answer: There is no absolute right answer. Uncertainty is always present. In some cases we ignore the uncertainty because we find it easy to think about an outcome as something we know or understand. In this list, however, uncertainty is most clearly present in 3, 4, and 5. All of these have uncertain outcomes. For example, if you are careful to eat a diet low in saturated fat, exercise regularly, and not smoke, you greatly reduce you chance of having a heart attack. But some people who do all these things still have heart attacks, and many people who do none of them do not have heart attacks.

Problem: The shoulder operation

Bill is a baseball player. He has trouble with his shoulder. It keeps him from playing his best, but he can still play most of the time. He has to stay out once in a while to give his shoulder a rest. His doctor says there is an operation that can cure him completely if it works, but there is some chance that the operation will fail. If the operation fails, Bill will have to quit playing. Bill figures he has five years left in his baseball career. How should Bill think about his decision?

Answer: He needs to ask about his options, the possible outcomes of each option, the probability of each outcome, and how much each outcome will help achieve his goals. (We don't need exact figures here. The point is to get something reasonable.)

We could illustrate this decision in the form of a tree:

Options Possible outcomes Utility

no operation ----------- stay the same 0

------------ get better 20 /.9 operation \.1 ------------ get worse -60

Notice that we have put some numbers in this diagram. First, the doctor has said that the operation has a .9 chance of succeeding and a .1 chance of failing. But that isn't everything Bill needs to think about. He needs to htink about how important the outcomes are to him, how much he values them. He needs to think about them with respect to his goals. The numbers at the right are called utilities. The utility of an outcome is a measure of how much it achieves the decision-maker's goals. Bill has judged that he is not too unhappy with the way things are, so it will hurt his goals three times as much if he gets worse than it will help his goals if he gets better. That's why he gave getting worse a -60, which is three times as far from 0 as the 20 he gave to getting better.

A good way to decide is to multiply probability times the utility of each outcome and add up these numbers for the option of having the operation. If we do this, the expected utility of the operation is .9(20) + .1(-60), which is 18-6, or 12. This is better than the 0 from staying the same, so Bill should have the operation.

Why is this a good way to decide? If 100 people went through the same decision, we could get the total utility they would get from each option. How would we do this? Multiply the percent probability times the utility. Each percentage point is a person. If they all had the operation, 90 people would get a utiity of 20, and 10 people would get a utility of -60. The total utility for all 100 would be 90(20) + 10(-60), which is 1800-600, or 1200. The average utility per person is then 1200/100, or 12. "Expected utility" means average utility over many decisions of the same kind.

Utility measures how much an outcome achieves our goals. We have discussed total utility in multiattribute tables. This is the idea we are discussing. When probability is the same, or when we think of outcomes as certain, we ignore probability. We pick the option with the higher total utility.

Problem: Different probability

What if the probability of success of the operation were .60 instead of .90?

Answer: The expected utility of the operation for Bill would then be .6(20) + .4(-60), which is 12 - 24, or -12. (The probability of failure has to be .4.) Bill should not have the operation, even though it is more likely to succeed than to fail. He is more worried about failure.

If he had the same utilities for success and failure (60 and -60), then he should have the operation: the expected utility would be .6(60) + .4(-60), or 36 - 24, or 12. So it matters what a person's utilities are. The best decision for one person might not be the same as the best decision for another in the same situation, because their goals might be different.

Problem: The better bet, 100 times

You can have A or B 100 times? Which should you pick?

A. I give you $10.

B. I flip a fair coin. If it lands heads, I pay you $22. If it lands tails, I pay you nothing.

Answer: B is the better bet. If you play B over and over, you will win $22 half of the time and $0 the other half of the time. On the average, you will win $22 every two times you play, so you will win, on the average, $11 every time you play. If you play 100 times, you can expected to win 100 times $11, or $1100. $11 is called the expected value of this bet.

If you play A over and over, of course, the expected value is $10, because that is exactly what you get every time. If you play A 100 times, you can expect to get $1000. The expected value of A is therefore less than the expected value of B.

Problem: The better bet, once

You can have A or B once? Which should you pick?

A. I give you $10.

B. I flip a fair coin. If it lands heads, I pay you $22. If it lands tails, I pay you nothing.

Answer: B is still the better bet. You may have exactly this choice ever again, but you will have many choices like it. If you always choose the bet with the higher expected value, you will have more money in the end.

Problem: Big bucks

You can have A or B once? Which should you pick?

A. I give you $10,000,000.

B. I flip a fair coin. If it lands heads, I pay you $22,000,000. If it lands tails, I pay you nothing.

Answer: A is now almost certainly the better bet. Choices involving such large amounts of money do not come up more than once in a lifetime for most of us. You will not have another chance. For most people, the value to you of having $22,000,000 is not much greater than the value to you of having $10,000,000. Both amounts of money would allow you to retire in comfort and pursue your interests as you please. If you choose B, you might wind up losing this fantastic opportunity.

To express this idea, we say that the utility of $22,000,000 is less than twice the utility of $10,000,000. Utility is a number that we assign to an outcome in order to indicate how much the outcome achieves our goals. If we assign a utility of 0 to $0 and a utility of 10 to $10,000,000, we might assign a utility of 14 to $22,000,000. The expected utlity of B is 7, which is less than the expected utility of A, which is 10.

Why is this different from the last problem? The utility of small amounts of money is roughly proportional to the amount of money. If the utility of $0 is 0 and the utility of $10 is 10, then the utility of $22 might be 21 or 22. This is because small amounts of money add up over a few years.

Problem: A lottery

100 tickets are sold to a lottery. Each ticket has a different number, from 1 to 100. A set of tickets just like the ones that were sold will be placed in a container. The container will be shaken up, and a blindfolded person will pick out a number. The person holding the ticket with that number will win $100.

Would it be a mistake to play this lottery?

Answer: No. The expected value of the lottery is exactly $1. You have a .01 probability of winning $100. To calculate the expected value, you can multiply the probability of winning times the amount you will win: .01 x $100 = $1. If you play the lottery 100 times, you can expecte to win once. You will spend $100 in tickets and you will get $100 back from winning once. The average winning is $1 per play, which is equal to the average cost. So this is not a bad lottery to play.

Problem: Another lottery

100 tickets are sold to a lottery. Each ticket has a different number, from 1 to 100. A set of tickets just like the ones that were sold will be placed in a container. The container will be shaken up, and a blindfolded person will pick out a number. The person holding the ticket with that number will win $60.

Would it be a mistake to play this lottery?

Answer: Yes. The expected value of this lottery is only $0.60: .01 x $60 = $0.60. You can expect to pay $1 and get back $0.60 on the average.

Notice that in the second lottery, the person who puts on the lottery will pocket $40. He will get $100 by selling all the tickets, and he will pay out $60 for the prize, so he will have $40 left. Whenever people make money from a lottery, the expected value of the lottery is less than the price of the ticket. State lotteries make money for the state. The expected value of state lottery tickets is less than the cost of the ticket.

Problem: Maintenance contract

You are the proud owner of a new washing machine. The store asks you if you want to buy a maintenance contract. An average repair costs $200. Repairs are needed, on the average, once every four years. You expect to use the machine about an average amount - no more and no less than most other people who have washing machines. The contract costs $75 per year. If you buy the contract, repairs will be free. If you do not buy the contract, you will get the repairs just as quickly, but you will have to pay. Should you buy the contract?

Answer: No. The expected value of the contract is, of course, -$75 per year. The expected value of not having the contract is $200/4, or $50 per year. (If repairs cost $200 once every four years, that is an average of $50 per year. Another way to look at it is to multiply the probability of the repair, .25, times the cost, $200: .25 x $200 = $50.)

Stores that sell maintenance contracts usually make money on them. They are like states that run lotteries. They are usually a bad deal unless you get something else with them, for example, a promise of faster service. If you think you will have more trouble than most people, however, they might be worthwhile.

Problem: Fire insurance

You are the proud owner of a new house. An insurance salesperson asks if you want to buy fire insurance. If your house burned down, you would lose $50,000, practically all your savings. It would be years before you could save up enough to buy another house. You know that houses have a .001 probability of burning down. The insurance costs $75 per year. If you buy the insurance and your house burns down, the insurance company will pay for a new house. Should you buy the insurance?

Answer: Yes. A loss of $50,000 would be terrible. Remember "Big bucks?" The same principle operates here.

Notice that the insurance company still makes money. If you calculate the expected value, the insurance is not worth it. The expected value of the insurance is -$75. The expected value of not having insurance is .001 x -$50,000 = -$50. (In other worse, if a thousand people have insurance in one year, we can expect one of them to lose a house in a fire. The total loss would be $50,000, and the average loss would be $50,000/1000 = $50.)

So why buy the insurance? Because the disutility (negative utility) of losing $50,000 is much more than 1000 times the disutility of losing $50. It is even more than 1000 times the disutility of losing $75. With large amounts of money, it is a good idea to think in terms of the utility of the money - its value to you in achieving your goals - rather than the money itself.

Insurance companies perform a service when they insure large losses. But they take advantage of their customers when they offer insurance for small losses that the customers could easily pay themselves. For example, auto insurance against the loss of a car, or against large medical bills that might result from an accident, is worth buying. But insruance that pays for fixing a dent in the fender (at a cost of $200) is not worth it. Over several years, the insurance will cost you more than if you paid yourself for the dents.

Insurance policies have a "deductable" amount. The insurance pays the cost after subtracting the deductable amount. If you have a car accident that costs $1000, and you have a $200 deductable policy, the insurance will pay $800. It is a good idea to get deductables as large as possible.

But it is not a good idea to try to save money on insurance by limiting the maximum amount that a policy will pay off. It is the large losses that you want insurance for.

Problem: Investments

Imagine you have $10,000 and you want to save it. You can put it in a bank and get 5% interest, you can buy a U.S. Government bond and get 7% interest, or you can by a bond issued by the Mexican Government, which pays 15% interest. The government bonds come due in 10 years; that means that the governments promise to pay back your $10,000 in ten years. In the meantime, you get just the interest. What should you do?

Answer: It is not clear what ou should do. If you put your money in the bank, it is almost certain that you will be able to take out exactly what you put in, plus the interest you have earned.

If you buy the U.S. bond, you can sell it if you need the money before the ten years are up, but the price you get for it could be higher or lower than what you paid. The price of bonds depends on how many people want to buy them. The more people who want them, the higher the price. It is practically certain that you can sell the bond to someone, and if you wait until the bond "comes due," you could get exactly what you paid. But you do take a risk. The outcome is less certain here, compared to putting your money in a bank. If you don't mind taking the risk, then you should get the bond.

What about the Mexican bond? Here, the interest is higher, because many people are not sure that Mexico will be able to keep its promise to pay back the full $10,000. So the risk you would take here is even greater. In general, the more risk you are willing to take, the more interest you will get.

Stocks are usually riskier than bonds (except for Mexican bonds), but people who buy stocks expect to make more money than the intereste they would get from bonds. Of course, they could lose too. The price of stocks sometimes falls very quickly.

Problem: The waitress

Jane, single, age 30, was living from hand to mouth as an actress and waitress when her father died and left her his life savings. The money was tied up in stock, which he had held for years because of the capital gains tax he would have had to pay if he sold it. Jane, of course, could sell it without paying the tax, but she did not plan to do so, as the value of the stock had just gone down, and she hoped it would go back up. What would you advise her to do?

Answer: We need to think about her options. One is to sell the stock and invest in something else, perhaps something safer like U.S. government bonds. Another is to keep the stock. If she buys bonds, she will have some steady income that she can depend on. This sounds like the better option for her. Her life seems to have enough risk as it is.

Problem: Status quo

Jane was thinking of keeping the stock. A friend asked Jane, "If you had the money in cash instead of the stock, would you buy the stock at its current price?" "Of course not," she replied. "I want a safe and steady income to supplement what I earn, and the stock could just as easily go down some more." "So, if you had a choice between the stock and the cash, you'd choose the cash, right?" Does it matter whether she already has the stock or whether she is going to buy it?

Answer: No. We call something the status quo when it is the present state, the way things are now (literally "state in which"). In general, what matters is the future consequences. If the future is better with one choice than with another, all things considered, take the better one. It does not matter what the status quo is.

Problem: Reasons to stay with the status quo

Are there ever reasons to stay with the status quo just because it is the status quo? In general, what are the reasons not to change, to stock with the status quo? Consider other cases, like changing your behavior - starting to do your homework, renting an apartment, getting a job, being nice to your little brother, moving away from home.

Answer: Here are some reasons not to change:

1. The status quo is sometimes less risky than changing. Can you afford the apartment? Will you be able to keep the job? But at other times, such as Jane's decision, the status quo is more risky. It is the risk that matters, not whether something is the status quo or not.

2. Change often has its own costs. (Economists call these "transaction costs.") A new paratment involves moving. Selling stock involves paying a broker. Changing the way you act involves learning new things. Moving involves making new friends. Most of these are short-term costs only. You need to think about the long run. These costs may well be worth paying.

3. Sometimes you have made promises to other people. WHen you change, you break a promise. But if you have promised to change, you break a promise when you don't change. What matters is breaking the promise, not whether you change or not.

4. People also make promises to themselves. They promise to do their homework, to stop picking on their little sister, to be nicer to their parents, and so on. If you break one of these promises, you are less likely to trust yourself in the future to carry out other promises of the same sort. But, again, it does not matter whether a promise is to change or not to change. What matters is whether it is a promise.

5. There might be some value in being predictable. If you are a person of habit, other people know what you will do, and it is easier for them to take your needs into account. But people are allowed to change. We do not expect our friends to put up with intolerable situations just so that we can predict what they will do.

Notice that all the good reasons to stick with the status quo involve the future. It is the future that matters when we make decisions. As much as we would sometimes like to undo the past, we cannot. The future is all we can affect through our decisions.

Problem: The TV dinners

On your way home you buy a tv dinner on sale for $3 at the local grocery store . . . Then you get an idea. You call up your friend to ask if he would like to come over for a quick tv dinner and then watch a good movie on TV. Your friend says "Sure." So you go out to buy a second tv dinner. However, all the on-sale tv dinners are gone. You therefore have to spend $5 (the regular price) for a tv dinner identical to the one you just bought for $3. You go home and put both dinners in the oven. When the two dinners are fully cooked, you get a phone call. Your friend is ill and cannot come. You are not hungry enough to eat both dinners. You can not freeze one. You must eat one and discard the other. Which one do you eat? Or does it matter?

Answer: It doesn`t matter. The money was spent in the past. It cannot be undone. You have spent $8 for one dinner eaten, and there is absolutely nothing you can do about it.

Problem (without answer): The ring

You are planning to give your mother a ring for Mother's Day. It costs $200 and you are buying it by paying $20 a week from the money you earn at a part-time job. You have paid $100 already, so you have five payments left. One day, you see in the paper that a new jewelry store is selling the same ring for only $90 as a special sale. You can pay for it the same way, except that you will have to pay only $10 in the last week instead of $20. The new store is across the street from the old one. If you decide to get the ring from the new store, you will not be able to get your money back from the old store, but you would save $10 overall. How would you think about this? (Follow up: What if you not paid anything yet and one store charged $100 and the other 90$. Which would you buy from?)

Problem (without answer): The drawing

There is going to be a school exhibit of students' drawings. You have spent the last three art classes working on a drawing for the exhibit. At the end of the last session, you had an idea for a new kind of drawing that was much easier to do. You tried it, and, in a few minutes, you produced a new drawing. You liked it better than the one you had worked on for three classes. Which drawing would you hand in for the exhibit? Why?

Problem: The salad dressing

You are a tennis player. In the final game of a tennis tournament, you were to play Ivan. Ivan was a much better player than you, but you really wanted to win. You went out to dinner with Ivan the night before you played your match. You knew that Ivan would get a stomach ache if he ate cayenne pepper, and you also knew that the regular salad dressing in the restaurant had cayenne pepper in it. You decided to get Ivan to eat the regular dressing. You were about to tell Ivan that he should try the regular dressing, when Ivan ordered it himself. Of course, you did not tell Ivan that the dressing had cayenne pepper. Ivan got a stomach ache the next day, and you won the match. Was your behavior just as bad as if you had told Ivan to try the regular dressing?

Answer: Yes. What matters is what outcome you intended to bring about and why. You intended that Ivan would get sick so that you could beat him. It does not matter whether you bring this about through acting or not acting. We must evaluate decisions according to the intended outcomes. The outcome is the same.

Problem: The witness

You saw an accident. A friend of yours ran into someone else's car. You hoped that the accident would not be blamed on your friend. You decided to lie to the police about whose fault the accident was, if they asked you. The police came. You expected that they would blame it on the other person, even though it was your friend's fault. They didn't ask you. You did not speak up and tell the truth. Is this just as bad as if you had lied?

Answer: Yes. The reason is the same as in "The salad dressing."

Problem: The conductor

You are the conductor on a train. A woman gets on the train without a ticket. You tell her that the fare is $2, plus $1 for not buying a ticket at the station. The woman refuses to pay the extra dollar, although she has the money. She says that she didn't know the rule. You do not believe her. You have seen her many times riding the train, and you know that there is a sign posted in the station where she got on. The rules say that passengers must be made to pay or they must be put off the train, if necessary by calling the police. Calling the police would delay the train and make all the other passengers late. All the other passengers are listening to your conversation with the woman. How would you think about what to do in this case?

Answer: There are many considerations here on both sides. But one that people sometimes miss is the precedent set by each option. If you make the woman pay or get off the train, you set a precedent for yourself, if this happens again, and you show her and the other passengers that the rule will be enforced. If you let her ride, you encourage her and the other passengers to try to cheat. You also set a precedent for yourself. If the same decision comes up again, you will have no reason to act any differently than you acted here.

Problem (without answer): The threat

You want to watch a TV program on Saturday, but your parents won't allow you to watch it because they think it is too violent. You get into a furious argument about it. In the end, you tell them that if they won't let you watch the program, you won't do your homework on Monday. They still won't let you watch it. On Monday, when you come home from school, you realize that you will get in trouble if you don't do your homework. Besides, there is very little of it, and you think the work you have would be fun. You wish you hadn't made the threat. How would you think about what to do?

Final problem for class discussion:

Karen and Alisha were in the 10th grade. They lived across the street from each other, and they had been close friends ever since grade school. In the last few weeks Alisha had become withdrawn. She wasn't her usual self. One day, Karen went to the bathroom and found Alisha sitting and crying. Alisha wouldn't say what was the matter. Finally, one day, Alisha told Karen that her life was a mess, that she (Alisha) was a terrible person and would never amount to anything. Boys didn't like her. She wasn't a good student. Her parents fought all the time and blamed everything on her. Alisha said she was thinking about killing herself. She had been reading about drugs, and she thought she could do it by taking an overdose of some drugs in the house.

After Alisha had told Karen all this, she wished that she hadn't. She was afraid that Karen would tell someone, who would come and take Alisha away somewhere. Alisha made Karen promise not to tell anyone ever. Alisha said she would never be Karen's friend again if Karen told anyone. Alisha said that she wasn't really serious anyway.

Karen was terrified. She was afraid that Alisha was serious. She had promised not to tell anyone, but she thought that she ought to tell their teacher, the principal, the guidance counselor, or someone else. How would you help her decide what to do?