Mat 102

Quiz 1

Answer Key to Part 1

a) No. The total number of voters is 5+4+3+1=13, so at least 7 votes are required for a majority.

b) A got 6 1^st place votes, B got 4 and D got 3, so A wins using the Plurality method.

c)

A got 5 x 4 +4 x 3 +3 x 1 + 1 x 4 = 39 points

B got 5 x 3 +4 x 4+ 3 x 2 +1 x 1 = 38

C got 5 x 2 + 4 x 2 +3 x 3 +1 x 3= 30

D got 5 x 1+ 4 x 1 + 3 x 4 + 1 x 2 = 23

A wins the election using the Borda-Count method.

d) B beats A 7:6, B beats C 9:4, and B beats D 9:4. B is the Condorcet candidate.

e)

No one got a majority, so the majority criterion is not violated.

The Condorcet criterion was violated using the Borda Count method, because the Condorcet candidate (B) did not win.