Philosophy 666: Rational Choice Theory

Ben Eggleston—eggleston@ku.edu

with responses and comments

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 document the answers to these questions that occur to you at the start of this course.

- 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., your investment is lost). How would you compare these two investments, and which one would you end up choosing?

- “Compare the risk and reward; is a 1/5 chance of failure worth the extra
$450? My choice would depend on how important my $1,000 is to me. As a college
student, I would take the safe road. Three years ago, when I was making more
money, I would have went with the risk.”
- Makes sense to me.

- “Gambling is fun and 80% is a big nod in my favor, so I might go that
route and have the fun of checking its performance regularly. However, a
guaranteed 50 bucks is also attractive, but not very well worth the wait. If I
had more initial capital, a guaranteed 5% could be very beneficial but I
don’t, so I will gamble.”
- Makes sense, and an interesting contrast from the previous answer. It was more risk-averse, this one more risk-seeking.

- “To compare them I would find our the equation that would make them
equivalent and then choose. But on the face of it I would choose the (wrong)
decision of gambling.”
- Well, I don’t know if there’s anything wrong about that. And I like the idea of trying to find a common metric that they can be fitted to so that you can compare them objectively.

- “The junk bond seems more favorable to me because it has a high payout,
and the success rate also seems high enough to warrant the risk. I would pick
the junk bond.”
- Fair enough.

- “One investment is low-risk but is also low gain. The other option is
high-risk, but high gain. My decision is merely to determine whether the risk
is worth it. At this stage in my life, I can gamble with investments more
freely than if retirement were impending, and 4/5 odds aren’t all that bad.
I’d buy the junk bond.”
- Makes sense, and well said.

- [no response]
- “With an 80% chance of success, I would risk the $1,000 to get the $1,500
payout.”
- Fair enough.

- “I would take the junk bond because 80% is pretty good odds, especially
when there’s a $450 difference between it and the CD.”
- Fair enough.

- “CD—the risk/reward of the bond is too great (up $500 or down $1,000),
while the CD is a purely profitable option.”
- Fair enough.

- “I would probably choose the assured bond [the CD] and get $1,050 but
that’s just because I hate losing money and I live in Kansas where we don’t
take chances often. Although I believe if I would have lived somewhere else
where I think people take greater risks more often then the other one would be
better.”
- Makes sense—interesting perspective on attitudes toward risk.

- “$1,050 guaranteed or 4/5 chance of $1,500 vs. 1/5 chance of $0? What one
would end up choosing depends on one’s psychology—is one a risk-taker or not?”
- Yes, that is what it comes down to.

- “Weigh the risk of importance of $1,000. If loss is even slightly
acceptable, risk it. If not, don’t. I’m a gambler, so [I would take the]
bond.”
- O.k., fair enough.

- “The expected value of the bond is (0.80)($1,500) + (0.20)($0) = $1,200,
compared to $1,050 for the CD. The natural log of $1,200 is greater than that
of $1,050, so the utility of the bond is greater than that of the CD.”
- I’m with you on the expected-value stuff, and with using the natural log
as your utility function for money. But taking the natural log of the expected values
of the investment options seems like an unnecessary step, since if one
investment has a
greater expected value, then it’s going to have a greater natural log,
too—taking the natural log will never change what you choose. It seems like
maybe you want to take the natural log of $1,500 and $0, in computing the
expected
*utility*of the bond (rather than compute the expected*value*of the bond and then take the natural log of that).

- I’m with you on the expected-value stuff, and with using the natural log
as your utility function for money. But taking the natural log of the expected values
of the investment options seems like an unnecessary step, since if one
investment has a
greater expected value, then it’s going to have a greater natural log,
too—taking the natural log will never change what you choose. It seems like
maybe you want to take the natural log of $1,500 and $0, in computing the
expected
- “Not sure if this is the kind of answer you had in mind, but . . . : Two
background factors would determine my decision, the first being how much my
financial outlook depended on it. For example, if I had multiple other
investments, some junk bonds, the 80% chance of a $1,500 return is nice. But
only if that chance is surrounded by other investments, some of which will
probably succeed and some probably won’t. The other factor is the “How screwed
would I be?” test. If the investor were the sole bread-winner of a family with
a net income of $3,000, having a 20% chance of losing 1/3 of it is
ridiculously unwise. If, however, the lost money may not even be missed, the
chance of a large return would be a rational chance to take, based on the fact
that there is an over 50% chance.”
- Makes sense—some intelligent and nicely put thoughts here on attitudes towards risk.

- 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 have virtually no revenue at all. So, your possible outcomes are as follows. The best outcome for you is if 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 if 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 if 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 and antagonism between you and your rival, 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?

- “Two of the three best outcomes are with me advertising high. The risk of
advertising low is not worth potentially saving a couple of bucks.”
- O.k.—makes sense.

- “I hate marketing but in this society you can’t let your brand be
forgotten (plus Pay-Less seems to be doing well) so I’d advertise a lot.“
- O.k., but in general we’re going to want to stick more to the facts given (about preferences and outcomes and so forth) rather than appeal to business theories about the need for advertising and so forth.

- “You must advertise a lot under these circumstances without any
communication or previous agreement.”
- O.k., but I’d be interested in knowing how you arrived at this result.

- “It would be in my best interest always to choose to invest a lot, to
minimize my potential of losing the market.”
- Fair enough—avoiding the worst outcome.

- “Advertising a little leaves me with either #2 or #4 on my preference
list. Advertising a lot leaves me either with #1 or or #3. The preference is
clear; I advertise a lot. In any case, advertising a lot doesn’t allow me to
lose market share, while advertising a little at best is a draw, at worst a
loss.”
- Well analyzed, and well stated.

- [no response]
- “This is basically the prisoner’s dilemma. I would advertise a lot because
this would get me the 1
^{st}or 3^{rd}best outcome.”- Quite right about the kind of problem, and your answer is certainly fine!

- “I would advertise a lot in the hope that my partner would play it safe
and only advertise a little thinking I would do the same, in which case I come
out ahead. But even if he also chooses to advertise a lot as well, I’m still
better off than the worst scenario. And choosing to advertise a little just
isn’t worth the risk.”
- Well analyzed, and well stated.

- “I have no choice, I must advertise a lot to avoid having no revenue,
although I risk the third best option. 1 and 3 are better than 2 and 4.”
- Right—makes sense.

- “Option 3 is the only option. Assuming the other guy wants the same as
me.”
- Well, remember that you have only two
*options*—advertise a lot or advertise a little. I take it that you mean that you would choose to advertise a lot, and the other guy would as well, resulting in the third-best*outcome*for each of you. If so, fair enough.

- Well, remember that you have only two
- “If I advertise a lot, then there’s a 50% chance that I get
__all__the market, and a 50% chance that my rival and I split the market. The odds are better for me to turn a profit by advertising a lot than by advertising a little, because the__worst__that could happen if I advertise a lot is that I split the market with my rival, whereas the__worst__that could happen if I advertise a little is that my rival gets__all__the market. If I advertise a little, it would be unlikely that my rival also advertises a little. So, betting on my rival to advertise regardless, I should, too.”- I'm not sure I’m with you at the start, with the 50-50 stuff, because it’s not clear that your rival will flip a coin or do anything else that makes it equally likely that he or she will do one thing versus the other. But then what you say about the worst outcomes makes sense. Then, however, I’m not sure why, if you advertise a little, it is unlikely that your rival also advertises a little. But I see how, if you do bet that your rival will advertise a lot, it makes more sense for you to advertise a lot as well.

- “Revenue is out of the question. Advertise a lot. At least you will have
options.”
- Hmm—not really sure where this comes from.

- [There’s a table showing the following information: “With a lot and a lot, you have 2, 2. With a lot and a little, you have 5,
0. With a little and a lot, you have 0, 5. With a little and a little, 3, 3.”
Then all except the last one are circled.”]
- I think the way you’ve scored the outcomes can be interpreted as correct, and I take it that you are indicating something about the last one. Otherwise, I’m not sure what’s going on.

- “Your clear choice should be to advertise a lot. This rationale is shown
in this complicated chart. [Then there’s a chart, nicely done, and not too complicated.] There
are four possible events: if you advertise a lot, your opponent can either
advertise a little or a lot, and vice versa. If you advertise a lot, the
outcome will be either very favorable or somewhat favorable to you. If you
advertise a little, the outcome will be either somewhat favorable or
non-favorable to you.”
- I see what you mean; my only quarrel would be with your representing both of the two middle outcomes as somewhat favorable. The one where you and your rival both advertise a little is better than the one where you and your rival both advertise a lot. It is not quite right to collapse them both into the category of “somewhat favorable,” because that implies that the worst outcome that can result from your advertising a lot is at least as good, for you, than the best outcome that can result from your advertising a little. But this is not so.

- 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?

- “Assign 3 points to favorite, 2 to next, and 1 to least. Add them up.
Wendy’s is the lowest preferred so scratch it. McDonald’s and Burger King both
have 1 person that dislikes, so it is a push. Burger King has 2 middle and
1 high to McDonald's 2 high and 1 middle so McDonald's is the higher
rated. Most good for most people.”
- You started out with the principle of what is known as the Borda-count method, but you didn’t say what the totals ended up being. It looks like McDonald's gets 9 points, Wendy's gets 7 points, and Burger King gets 8. So maybe that is how you concluded that Wendy’s is the least preferred. But then it seems that if you are using the Borda-count method, you don’t need all that other stuff you said—McDonald’s just has the highest score.

- “McDonald’s has two 1
^{st}s , a 2^{nd}, and a 3^{rd}choice.

Burger King has one 1^{st}, two 2^{nd}s, and a 3^{rd}choice.

Wendy’s has one 1^{st}, one 2^{nd}, and two 3^{rd}choices.

Since all kids will eat any fast food (especially if their friends are eating it) I’d pick McDonald’s since it is the mode 1st choice and only one kid’s least preferred option. (I would eat nothing there, however, except some fries.)”- Makes sense.

- “McDonald’s, highest average ranking between kids.”
- Fair enough—essentially the Borda-count method.

- “I would assign values to their preferences and see if one is valued
overall more so than the others. [A table follows.] Lowest # should be most
liked overall. M = 7, W = 9, BK = 8.”
- Fair enough—the Borda-count method, but with the numbers reversed (so lowest score wins rather than highest).

- “The preferential balloting system used in student congress (high school
speech & debate competition format) would award preference to McDonald’s
because it received the highest number of first place votes. This seems
reasonable because then half of the children receive their top choice, while
only one receives their lowest choice.”
- Makes sense.

- [no response]
- “Taco Bell. Not Wendy’s, because two children wrote it as 3
^{rd}preference and not Burger King, because it was 2^{nd}twice. McDonald’s seems to be the highest ranked in general (and they have happy meals).”- Fair enough.

- “I would pick McDonald’s because if you rank the preferences by giving a 3
to all 1
^{st}choice rankings, a 2 for 2^{nd}, and a 1 for 3^{rd}, McDonald’s gets a total of 9, Burger King gets an 8 and Wendy’s gets a 7.”- Sure, it’s our old friend the Borda-count method!

- “McDonald’s, then Burger King, then Wendy’s.”
- O.k., but I also asked how you would arrive at your result. . . .

- “I have no idea, take them to Taco Bell.”
- What is it with Taco Bell?

- “Go to Burger King, because 2 out of 4 children make it their 2
^{nd}choice, and one makes it their first, so 3 out of 4 children would at least have it as their 2^{nd}choice, and only one lists it as their third choice.”- O.k., but can’t the same be said for McDonald’s?

- “100 for first, 50 for second, 0 for third. McDonald’s—250, Wendy’s—150,
Burger King—200.”
- The Borda-count method, in disguise! (Start with the basic method, but modify the numbers by subtracting 1 and multiplying by 50.)

- “Ask them to associate their preference with a number, like from 10 to
–10, with 10 being love it and –10 hate it. The restaurant with the highest
score wins.”
- Interesting—you want the kids to give you
*cardinal*information, not just*ordinal*information. Good idea.

- Interesting—you want the kids to give you
- “Give a point value for each restaurant for each child, with preference 1
receiving 10 points, P2 gets 5 points, and P3 gets only 1 point.”
- Interesting. This is like the Borda-count method, but with extra spacing inserted between 1 and 2, compared to 2 and 3—as if being someone’s first choice, compared to second, should count a little more than being someone’s second choice, compared to third.

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

- “Enjoyed. I have
__never__approached any of the situations from a logical perspective. So it is opening a new vein of thought.”- Great!

- “It’s fun to solve problems.”
- Great!

- “Fun, frustrating.”
- Well, I’m glad it was fun, and I'm sorry it was frustrating. Hopefully the things this course covers will help make these things less frustrating to think about.

- “I liked thinking about these problems. Question 2 recalled previous ideas
I had heard of before (Prisoner’s Dilemma type problem) and Question 3 seemed
like a question of election methods as I’ve had in a Political Science class.”
- Right—they are exactly those kinds of problems.

- “I have enjoyed these examples, but wonder at whether or not the methods
we will learn later fall prey to the same limitations as Bentham’s Hedonic
Calculus.”
- A reasonable concern—at least in regard to some aspects of the course.

- “Excellent questions; but how are they philosophical
enterprises/questions, I am not sure.”
- Thank you—I think—but if you don’t like this sort of thing, and won’t answer any questions like these when asked, you might want to think about whether you really want to be in this class.

- “That was enjoyable but admittedly difficult.”
- Sure—I did ask you some hard stuff for the first day.

- “It wasn’t too unpleasant.”
- Good.

- “Yes, I did enjoy answering said questions. :-)”
- Good!

- “I think the questions were interesting although obviously I don’t know
how to answer them.”
- That’s fine—and I should mention that there is not just one right way of answering any of these.

- “a little of both”
- O.k., well, we’ll try to ratchet up the liking and ratchet down the unpleasantness.

- “I liked it very much!”
- Great!

- [no response]
- That natural-log stuff you did for question 1? You must like it. :-)

- “I liked it.”
- That’s good.