Question

A travel agent is booking a trip to England, Scotland, Ireland, and France for a group of senior citizens. The agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (E = England, I = Ireland, S = Scotland, F = France). Which country is the Condorcet winner?

number of votes 15 12 16 19


1st F E E I


2nd E S I S


3rd S I S E


4th I F F F



1. Scotland




2. England




3. France




4.Ireland

Answer 1

Answer: 1

Scotland

Explanation:

In the first vote, points are:

France = 15

England = 12 + 16 = 28

Ireland = 19

2nd vote

England = 15

Scotland = 12 + 19 = 31

Ireland = 16

3rd vote

Scotland = 15 + 16 = 31

Ireland = 12

England = 19

4th vote

Ireland = 15

France = 12 + 16 + 19 = 47

At the end of everything

England = 19 + 15 + 28 = 62

France = 15 + 47 = 62

Scotland = 31 + 31 = 62

Ireland = 19 + 16 + 12 + 15 = 62

To find the Condorcet winner, the number of votes for runner over opponent (runner,opponent) is compared with the number of votes for opponent over runner (opponent,runner)

Only Scotland has the highest (31) points twice.