Math 0824/0924 Quiz III
Show all your work on the paper you hand in.
1. and 2. Imagine that there are 27 delegates (voters) to a political party's
convention at which four people Ann, Bob, Claire, and Dave have been nominated as
the party's candidates for governor. Assume the delegates' preference schedules are
as follows.
Number of Delegates 8 6 13
First Choice A B D
Second Choice B A C
Third Choice C C B
Fourth Choice D D A
1a). What nominee would win if the party uses the plurality method?
D with 13 first place votes.
1b). What nominee would win and by what margin if the party has a runoff between
top two candidates?
A wins. A would beat D in a runoff, 14 to 13.
1c.) What nominee would win if the party uses a Borda count which assigns 4, 3, 2,
and 1 point(s) for a first, second, third, and fourth choice, respectively. Show
calculations.
A: 8*4 + 6*3 + 13*1 = 63.
B: 8*3 + 6*4 + 13*2 = 74
C: 8*2 + 6*2 + 13*3 = 67
D: 8*1 + 6*1 + 13*4 = 66.
So B wins in a Borda Count.
2a). If the candidates in the big bold font are approved of by the number of delegates
indicated, what nominee wins and by what margin if approval voting is used?
A-14; B-6; C-19; D-13. C wins.
2b). What if the 6 voters who approve of B, A, and C decide that they don't approve
of C after all. Now who wins by approval voting?
C loses 6 approvals, so C has only 13, the same as D, so C and D are tied, and A wins
with 14 approvals.
2c.) Who, if anyone, is the Condorcet winner?
B versus A, B wins; B versus C, B wins; B versus D, B wins, so B is the Condorcet
winner.
3a.) You prefer Mexican to Italian to Chinese food, but your two friends hate
Mexican food. One prefers Italian, the other Chinese. You're all deciding where to
eat. How might you be tempted to tell your friends about your preferences, and
what does this have to do with insincere or strategic voting?
You vote insincerely and pretend you prefer Italian to Mexican to Chinese. By doing
so you can at least get your second choice of Italian instead of your last choice of
Chinese.
3b.) If you're is 6 blocks west and 5 blocks south of the restaurant you've decided
