18.2: Voting Theory

1.

\(\begin{array}{|l|l|l|l|l|l|}
\hline \text { Number of voters } & 3 & 3 & 1 & 3 & 2 \\
\hline 1^{\text {st }} \text { choice } & \mathrm{A} & \mathrm{A} & \mathrm{B} & \mathrm{B} & \mathrm{C} \\
\hline 2^{\text {nd }} \text { choice } & \mathrm{B} & \mathrm{C} & \mathrm{A} & \mathrm{C} & \mathrm{A} \\
\hline 3^{\text {rd }} \text { choice } & \mathrm{C} & \mathrm{B} & \mathrm{C} & \mathrm{A} & \mathrm{B} \\
\hline
\end{array}\)

3.

1. \(9+19+11+8 = 47\)
2. 24 for majority; 16 for plurality (though a choice would need a minimum of 17 votes to actually win under the Plurality method)
3. Atlanta, with 19 first-choice votes
4. Atlanta 94, Buffalo 111, Chicago 77. Winner: Buffalo
5. Chicago eliminated, 11 votes go to Buffalo. Winner: Buffalo
6. A vs B: B. A vs C: A. B vs C: B. B gets 2 pts, A 1 pt. Buffalo wins.

5.

1. \(120+50+40+90+60+100 = 460\)
2. 231 for majority; 116 for plurality
3. A with 150 first choice votes
4. A 1140, B 1060, C 1160, D 1240. Winner: D
5. B eliminated, votes to C. D eliminated, votes to A. Winner: A
6. A vs B: B. A vs C: A. A vs D: D. B vs C: C. B vs D: D. C vs D: C. A 1pt, B 1pt, C 2pt, D 2pt. Tie between C and D.

Winner would probably be C since C was preferred over D

7.

1. 33
2. 17

9. Yes, B

11. B, with 17 approvals

13. Independence of Irrelevant Alternatives Criterion

15. Condorcet Criterion

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