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.
- \(9+19+11+8 = 47\)
- 24 for majority; 16 for plurality (though a choice would need a minimum of 17 votes to actually win under the Plurality method)
- Atlanta, with 19 first-choice votes
- Atlanta 94, Buffalo 111, Chicago 77. Winner: Buffalo
- Chicago eliminated, 11 votes go to Buffalo. Winner: Buffalo
- A vs B: B. A vs C: A. B vs C: B. B gets 2 pts, A 1 pt. Buffalo wins.
5.
- \(120+50+40+90+60+100 = 460\)
- 231 for majority; 116 for plurality
- A with 150 first choice votes
- A 1140, B 1060, C 1160, D 1240. Winner: D
- B eliminated, votes to C. D eliminated, votes to A. Winner: A
- 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.
- 33
- 17
9. Yes, B
11. B, with 17 approvals
13. Independence of Irrelevant Alternatives Criterion
15. Condorcet Criterion