Question

Table 22-13 A high school Spanish class and their teacher are planning to take a Spring Break trip abroad but they have to decide where to go. They have narrowed the options to: Spain, Mexico, Ecuador, and Costa Rica. The voters’ preferences are shown in the table below. Voter First Choice Second Choice Third Choice Fourth Choice 1 Spain Mexico Ecuador Costa Rica 2 Costa Rica Mexico Ecuador Spain 3 Spain Mexico Ecuador Costa Rica 4 Ecuador Costa Rica Mexico Spain 5 Costa Rica Mexico Ecuador Spain 6 Spain Costa Rica Ecuador Mexico 7 Spain Mexico Ecuador Costa Rica 8 Costa Rica Mexico Ecuador Spain 9 Mexico Ecuador Spain Costa Rica 10 Spain Mexico Ecuador Costa Rica 11 Spain Mexico Ecuador Costa Rica 12 Ecuador Mexico Costa Rica Spain 13 Costa Rica Mexico Ecuador Spain 14 Costa Rica Ecuador Mexico Spain 15 Mexico Spain Costa Rica Ecuador 16 Ecuador Costa Rica Spain Mexico 17 Mexico Spain Ecuador Costa Rica 18 Costa Rica Ecuador Mexico Spain 19 Spain Mexico Costa Rica Ecuador 20 Mexico Ecuador Spain Costa Rica 21 Costa Rica Ecuador Mexico Spain

Refer to Table 22-13. In a pairwise election between Mexico and Ecuador and then a second election between the winner and Costa Rica, which countries are chosen?

a. Ecuador is chosen in the in the first and second elections.

b. Ecuador is chosen in the first election and Costa Rica is chosen in the second.

c. Mexico is chosen in the first and second elections.

d. Mexico is chosen in the first election and Costa Rica is chosen in the second.

Answer 1

For the pairwise elections, we shall compute the total votes for both parties and then choose the winner.

We have the following table, where each voter is followed by their choice of the candidate based on their preferred position. For example, for the first voter, Mexico is preferred over Ecuador, then the preferred choice of Mexico is written in the next column. Following the same for all voters and summing up the preferences would give us the winner in the first election.

Voter	Preferred choice
1	Mexico
2	Mexico
3	Mexico
4	Ecuador
5	Mexico
6	Ecuador
7	Mexico
8	Mexico
9	Mexico
10	Mexico
11	Mexico
12	Ecuador
13	Mexico
14	Ecuador
15	Mexico
16	Ecuador
17	Mexico
18	Ecuador
19	Mexico
20	Mexico
21	Ecuador
Mexico=	14
Ecuador=	7

So, in the first election, Mexico wins. Now for the next election, we shall compare Mexico and Costa Rica, which give us the following tables:

Voter	Preferred choice
1	Mexico
2	Costa Rica
3	Mexico
4	Costa Rica
5	Costa Rica
6	Costa Rica
7	Mexico
8	Costa Rica
9	Mexico
10	Mexico
11	Mexico
12	Mexico
13	Costa Rica
14	Costa Rica
15	Mexico
16	Costa Rica
17	Mexico
18	Costa Rica
19	Mexico
20	Mexico
21	Costa Rica
Mexico=	11
Costa Rica=	10

So, in teh second game also, Mexico wins and hence we van say that c is teh correct answewr.