<em class="emphasis">Try it Now</em>Solutions

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Section 1.9 Try it NowSolutions

Try it Now 1.2.4Using plurality method:
- G gets 44+14+20 = 78 first-choice votes
- M gets 70+22 = 92 first-choice votes
- B gets 80+39 = 119 first-choice votes
Bunney (B) wins under plurality method.
Try it Now 1.2.10Determining the Condorcet Winner:
- G vs M: 44+14+20 = 78 prefer G, 70+22+80=172 prefer M: M preferred
- G vs B: 44+14+20+70=148 prefer G, 22+80+39 = 141 prefer B: G preferred
- M vs B: 44+70+22=136 prefer M, 14+80+39=133 prefer B: M preferred
M is the Condorcet winner, based on the information we have.
Try it Now 1.4.4Using IRV: G has the fewest first-choice votes, so is eliminated first. The 20 voters who did not list a second choice do not get transferred - they simply get eliminated

136 133

1 st choice M B

2 nd choice B M

McCarthy (M) now has a majority, and is declared the winner.

Try it Now 1.5.4Using Borda Count:

We give 1 point for 3 rd place, 2 points for 2 nd place, and 3 points for 1 st place.

	44	14	20	70	22	80	39
1st choice	G	G	G	M	M	B	B
	132 pt	42 pt	60 pt	210 pt	66 pt	240 pt	117 pt
2nd choice	M	B		G	B	M
	88 pt	28 pt		140 pt	44 pt	160 pt
3rd choice	B	M	M 20 pt	B	G	G	M 39 pt
	44 pt	14 pt	B 20 pt	70 pt	22 pt	80 pt	G 39 pt

G: 132+42+60+140+22+80+39 = 515 pts M: 88+14+20+210+66+160+39 = 597 pts B: 44+28+20+70+44+240+117 = 563 pts

McCarthy (M) would be the winner using Borda Count.

Try it Now 1.3.6Using Copeland’s Method:

Looking back at our work from Try it Now 2, we see

G vs M: 44+14+20 = 78 prefer G, 70+22+80=172 prefer M: M preferred – 1 point

G vs B: 44+14+20+70=148 prefer G, 22+80+39 = 141 prefer B: G preferred – 1 point

M vs B: 44+70+22=136 prefer M, 14+80+39=133 prefer B: M preferred – 1 point

M earns 2 points; G earns 1 point. M wins under Copeland’s method.
Try it Now 1.7.3Using Approval voting:
- Seattle has 30+10+15+5 = 60 approval votes
- Tacoma has 30+15+20+15+5 = 85 approval votes
- Puyallup has 10+20+25+5 = 50 approval votes
- Olympia has 15+15+5 = 35 approval votes
Tacoma wins under this approval voting