Mat 102

Quiz 1

Answer Key to Part 1

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

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

c)

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

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

C got 4 x 3 + 5 x 4 +3 x 1 +1 x 4= 39

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

C wins the election using the Borda-Count method.

d) D beat A 9:4, D beat B 9:4, and D beat C 7:6. D 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 (D) did not win.