University of Kansas, Fall 2007
Philosophy 666: Rational Choice Theory
Ben Eggleston—eggleston@ku.edu

Survey of initial responses—
with summaries of responses

Please write your answers to the following questions in the space below the questions and on the back of this sheet. These questions may seem strange to you, and it is not expected that you can answer these questions with depth and rigor (though maybe you can). The purpose of this survey is simply to elicit the answers to these questions that occur to you at the start of this course.

question:

1. Suppose you have $1,000 to invest and you have two options, each resulting in a payout of some amount or other at the end of one year. One option is to buy a CD paying 5 percent interest, resulting in a guaranteed payout to you, at the end of one year, of $1,050. The other option is to buy a junk bond paying 50 percent interest. But the bond might be worthless at the end of the year—that’s why they have to offer such high interest rates to get people to buy them. You estimate that the bond has a 80-percent chance of a payout of $1,500 at the end of one year, and a 20-percent chance of a payout of $0 (i.e., a 20-percent chance of being worthless). How would you compare these two investments, and which one would you end up choosing?

summary of responses:

1. Three students focused on the relative safety and riskiness of the two options. Two of the three said that because of the riskiness of the junk bond, they would choose the CD. The third student said that while the CD risk is “none,” the bond risk is still “low”, so that the risk levels are comparable, and that the higher potential payout of the bond would cause him or her to choose the bond.
2. Four students gave a lot of weight to whether the investor has only a little bit of money, or a lot. They said, quite sensibly, that an investor having only a little bit of money might be well-advised to play it safe with $1,000, while an investor with a lot of money might be well-advised to go for the higher payoff. Implicated in these students’ comments was what we call the diminishing marginal utility of money, which we’ll get into later.
3. Three students got a little more mathematical.
   1. One said that since the CD has a 100-percent chance of paying out, with a profit of 5 percent, and the junk bond has an 80-percent chance of paying out, with a profit of 50 percent, the junk bond “has a higher ratio of profit.”
   2. The other two students who got a little more mathematical both thought about making the same choice ten straight times. One student focused on total savings and the other focused on profits, but (converting talk of profit to talk of total savings) both pointed out that choosing the CD all ten times would leave one with $10,500. Concerning the junk bond, one student pointed out that one could expect to end up with $12,000, while the other said, “For the junk bond, I would get $12,000 – $3,000 which equals $9,000.” This latter calculation isn’t quite right, however. If you chose the junk bond ten times, you could expect it to end up being worth $1,500 eight times, for a total payout of $12,000. And you could expect it to end up being worthless twice, for a total payout of $0. You shouldn’t count those latter two events (when the junk bond is worthless) as two events of losing $1,500 (for a total loss of $3,000); you should just count them as events in which you get $0. So, you have $12,000 (not $12,000 – $3,000). Anyway, both of these students, who thought about what it would be like to make this choice multiple times rather than just once, are hot on the trail of what we call “expected value,” which is another concept we’ll get into later.

question:

2. Suppose you own one of two discount furniture stores in a college town. You and the owner of the other store can each advertise a lot or advertise a little. If you each advertise the same amount (whether a lot or a little), then you will split the market approximately evenly. If one of you advertises a lot and the other advertises a little, then the one who advertises a lot will gain enough market share to more than offset the extra expense of advertising a lot, while the other will have virtually no revenue at all. So, your possible outcomes are as follows. The best outcome for you is that you advertise a lot, and your rival advertises a little. Then you have the whole market and make a lot of money. The second-best outcome for you is that you and your rival both advertise a little—if the two of you are going to split the market, you might as well not spend too much money on advertising. The third-best outcome for you is that you and your rival both advertise a lot—the two of you split the market, and pay a lot to do so. But this is still better (for you) than the worst outcome for you, in which you advertise a little and your rival advertises a lot—for then you have virtually no revenue at all. You know that your rival is in the same situation as you. Due to antitrust laws, the two of you must make your decisions independently of each other. How would you decide what to so, and which strategy (advertise a lot or advertise a little) would you end up choosing?

summary of responses:

1. One student said he or she would advertise a little, both to minimize costs and to “play defense.”
2. Five students said they would advertise a lot, to avoid the worst outcome (advertising a little while rival advertises a lot) and/or to create the possibility of the best outcome (advertising a lot while rival advertises a little).
3. Four students mentioned that this problem is a case of the prisoner’s dilemma, which we’ll get into in the game theory part of the course.
   1. Three said that they would advertise a lot.
   2. One regarded the situation as what we’ll call an “iterated” prisoner’s dilemma. He or she said it would make sense to start by advertising a little, to see whether the other player would, too, and then be ready to advertise a lot if necessary to avoid being taken advantage of. This is a tried-and-true strategy for playing the prisoner’s dilemma.

question:

3. Suppose you are in charge of taking four children out for lunch one Saturday. You can take them to McDonald’s, Wendy’s, or Burger King, but unfortunately they do not all have the same preferences. Specifically, one prefers McDonald’s, then Wendy’s, then Burger King; the second prefers McDonald’s, then Burger King, then Wendy’s; the third prefers Wendy’s, then Burger King, then McDonald’s, and the fourth prefers Burger King, then McDonald’s, then Wendy’s. Assuming you want to take them where they collectively most want to go, how would you go about aggregating their preferences into one collective preference, and which option (McDonald’s, Wendy’s, or Burger King) would you end you regarding as the children’s collectively most-preferred place to have lunch?

summary of responses:

1. Three students said they would pick McDonald’s, and cited facts about its being first on two kids’ lists, facts about Wendy’s being easy to eliminate, and other facts.
2. Seven students used some version of a method known as the Borda count. This method involves giving each option 1 point for being ranked in last place, 2 points for being ranked in 2nd-to-last place, 3 points for being ranked in 3rd-to-last place, and so on. Since there are just three options, the point values are 3, 2, and 1. Burger King gets 8 points (1 + 2 + 2 + 3 points), McDonald’s gets 9 points (3 + 3 + 1 + 2), and Wendy’s gets 7 points (2 + 1 + 3 + 1). So, using this method, McDonald’s wins. We’ll revisit this method in the social choice theory part of the course.

question:

4. Have you liked thinking about the foregoing questions, or has it been rather unpleasant?

summary of responses:

• Most responses were quite positive, though there were a couple that were lukewarm or qualified.