Question

1.

The homeowner’s association is deciding a new set of neighborhood standards for architecture, yard maintenance, etc.  Four options have been proposed.  The votes are:

	8	9	11	7	7	5
1st	B	A	D	A	B	C
2nd	C	D	B	B	A	D
3rd	A	C	C	D	C	A
4th	D	B	A	C	D	B

a) How many voters voted in this election?

b) How many votes are needed for a majority?

Find the winner under the indicated method.

c) Plurality                                                     d) Borda Count

e) Copeland’s method                                  f) Instant Runoff

Answer 1

a)

the number of voters voted in this election = 8+ 9+11+7+7+5 = 47

b)

Votes needed for majority = 47/2 = 23.5 = 24

c)

Plurality

A=9+7= 16, B= 8+7= 15, C=5, D=11

A is the winner under plurality method

d)

Borda count

A =1*11 + 2*13 + 3 * 7 + 4 *16 = 122

B =1*14 + 2*0 + 3 * 18 + 4 *15 = 128

C =1*7+ 2*27 + 3 * 8 + 4 *5 = 105

D =1*15 + 2*7 + 3 * 14 + 4 *11 = 115

B is the winner under Borda count method

e)

Copeland’s method  

A 21, B 26

B 33, C 14

C 20, D 27

A 23, C 24

B 22, D 25

A 31, D 16

B has 2 wins and so does D.

So, B and D are winners

f)

Instant Runoff

A = 16+8+7 = 31

D = 11+5 = 16

A is the winner