Chapter 6.1, Problem 14E

Five candidates, Fino (F), Gempler (G), Holloway (H), Isho (I), and James (J), are running for president of the Polar Bear Swim Club. After the polls close, ranked ballots are tallied, and the results are summarized in Figure $6.34$.

	Number of Ballots cast
	$12$	$18$	$29$	$11$	$21$	$19$	$18$
$1\text{st}$ choice	F	F	G	H	I	J	J
$2\text{nd}$ choice	G	I	F	G	J	H	F
$3\text{rd}$ choice	I	G	H	F	G	I	G
$4\text{th}$ choice	J	H	J	I	F	G	I
$5\text{th}$ choice	H	J	I	J	H	F	H

Figure $6.34$ Voter preference table for Exercise $14$.

a. How many votes were cast?

b. Use the plurality method of voting to determine the winner.

c. What percent of the votes did the winner in part (b) receive?

d. Use the instant runoff method to determine the winner.

e. What percent of the votes did the winner in part (d) receive?

f. Use the Borda count method to determine the winner.

g. How many points did the winner in part (f) receive?

h. Use the pairwise comparison method to determine the winner.

i. How many points did the winner in part (h) receive?