; CDR_003_Survey for Proposal on Prisoner's Dilemma.docx - Duke
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# CDR_003_Survey for Proposal on Prisoner's Dilemma.docx - Duke

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```									Christian Rogers
9/18/12
Homework #3
Game Theory and Democracy – MATH 89S
Survey on the Prisoner’s Dilemma
One night as you stumble back to your dorm from Shooters you see a delicious
dessert sitting in the common room. Another random person is also present, but the
two of you are too tired to speak so you can’t communicate. You are presented with
the following options, which do you choose? In other words, which choices have the
best risk to payoff ratio in your mind? (rank the options 1 to 5, 1 being the high and 5
being the low)

____ A. You take a large piece of the dessert without talking to the other person; the risk is that the
other person may tell on you and they are given the whole dessert as a reward (you also

____ B. You chance to see if the other person takes a large piece of the dessert; you then tell
on them and receive the whole dessert as a reward

____ C. You and the other person both take small pieces of the dessert and no one gets in
trouble

____ D. You and the other person simply leave the dessert alone and no gets in trouble or
gets any dessert

____ E. You try to cheat and collaborate/talk with the other person to get the whole cake to
share, the risk is that the other person might tell on you and they are given the
dessert

If the risks and payoffs were substantially greater would you still choose the same
options or would you change your order? For example instead of just dessert, the
two players would be two countries competing for increased power.

____ A. Yes

____ B. No
Question 1:

Plurality Winner: C (You and the other person both take small pieces of the dessert
and no one gets in trouble)

Instant Runoff Voting:
Round 1:
- Choices A and E are eliminated in the first round because they tie for last. 2 votes go
to C and 2 votes go to B

Round 2:
- Choice D is eliminated in the second round. All four votes go to C.

Round 3:
- In the final round, Choice C wins.
Winner by Instant Runoff Voting: Choice C (You and the other person both take small
pieces of the dessert and no one gets in trouble)

Borda Count/Margin of Victory Matrix:
A                B          C              D             E
A              0               1          -9             -5            -1
B             -1               0          -7             -3             1
C              9               7           0              7             5
D              5               3          -7              0             3
E              1              -1          -5             -3             0

Results:
 Choice A : -14
 Choice B: -10
 Choice C: 28
 Choice D: 4
 Choice E: -8
Total = 0

Winner of Borda Count/Margin of Victory Matrix: C (You and the other person both
take small pieces of the dessert and no one gets in trouble)

Sorted Margin of Victory Matrix:
C                D       E              B             A
C                0                7       5              7             9
D               -7                0       3              3             5
E               -5               -3       0             -1             1
B               -7               -3       1              0            -1
A               -9               -5      -1              1             0
Borda Instant Runoff/ Margin of Victory Matrix:

Round 1:
A           B            C         D          E          Total
A             0            1           -9        -5         -1          -14
B            -1            0           -7        -3          1          -10
C             9            7            0         7          5           28
D             5            3           -7         0          3            4
E             1           -1           -5        -3          0           -8
- choice A is eliminated

Round 2:
A             B           C         D          E          Total
A            0             1           -9        -5         -1          X
B           -1             0           -7        -3          1          -9
C            9             7            0         7          5          19
D            5             3           -7         0          3          -1
E            1            -1           -5        -3          0          -9
- choices B and E are eliminated

Round 3:
A             B            C         D          E          Total
A             0             1           -9        -5         -1          X
B            -1             0           -7        -3          1          X
C             9             7            0         7          5           7
D             5             3           -7         0          3          -7
E             1            -1           -5        -3          0          X

Winner by Instant Runoff Borda/ Margin of Victory Matrix: Choice C (You and the
other person both take small pieces of the dessert and no one gets in trouble)

Least Worst Defeat:
 Choice A (-9)
 Choice B (-7)
 Choice C (0)
 Choice D (-7)
 Choice E (-5)
Winner by Least Worst Defeat: Choice C (You and the other person both take small
pieces of the dessert and no one gets in trouble)
Ranked Pairs:
 9 (C > A)     
 7 (C > B)     
 7 (C > D)     
 5 (D > A)     
 5 (C >E)      
 3 (D > B)     
 3 (D > E)     
 1 (E > A)     
 1 (B> E)      

C>D>B>E>A

Winner by Ranked Pairs: Choice C (You and the other person both take small pieces
of the dessert and no one gets in trouble)

Question 2:

Since there were only two options and the “YES” votes received a majority, the “YES”
options wins for every case (Plurality, IRV, Borda, IR Borda, LWD, Ranked Pairs)

Discussion:
My proposal dealt with the concept of the Prisoner’s Dilemma as applied to
situations in international relations. Unfortunately, most people tend to be unfamiliar with
both the Prisoner’s Dilemma and the current situation in international politics. I tried to
create a situation that would give the Duke students I was surveying enough of an
understanding of the Prisoner’s Dilemma for them to complete the survey. I felt that a light
and relatable story would help produce the best results about what people think rather
than formally discussing some complex political issue. The presentation of the questions
was difficult because in the Prisoner’s Dilemma, each player has no idea what the other
player will do until it is decision time, but in order for the survey to work I had to include
the other player’s actions as well. In addition, I tried to spread the answers out in an
attempt to gain a variety of answer possibilities. Since the my main goal was to figure out
what course of action people might take in a serious situation such as one involving
multiple countries competing for power, I included a follow up question to see if people
would change the way they would play if the stakes of the game were higher. Although the
majority voted yes, it was an extremely close race, which demonstrated the many ways in
which people will act in a certain situation.
I also noticed that people had trends in their answers. For example, people would
rate all the safer choices higher while rating the risky choices lower or vice versa. People
would not typically flip back and forth between risky and safe strategies when ranking the
options. I was not surprised that most people took the safe route by choosing either choice
C or D. They offer some reward and no consequences. Many of the people I surveyed
tended to not be risk takers. These results could possibly change if I were to change the
group of people I surveyed.

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