Q1) If 71 people vote in an election which involves 3 candidates, what is the fe
ID: 3143784 • Letter: Q
Question
Q1) If 71 people vote in an election which involves 3 candidates, what is the fewest number of votes a majority candidate can receive?
Q2) Now construct an election with 63 voters according to these clues:
Watch out: the clues can be randomly ordered!
1) 2 voters turned in ballots that help Barclay win with the Plurality method of voting. These ballots had Corinna at the bottom.
2) 10 voters turned in ballots that help Corinna win with the Plurality method of voting. These ballots only give Annie 1 Borda point per vote.
3) 3 voters turned in ballots that give 3 Borda points per vote to Corinna and 2 Borda points per vote to Annie.
4) 11 voters turned in ballots that give 2 Borda points per vote to Corinna and only 1 Borda point per vote to Barclay.
5) 19 voters turned in ballots that really help Barclay beat Annie if the Borda count method is used to determine the winner, because they give the maximum amount of points per vote to Barclay and the minimum amount of points per vote to Annie. These ballots give far more Borda points to Barclay per vote than they do to Annie.
10 2 19 18 Corinna Annie Barclay Annie Corinna Barclay Corinna Barclay Annio Annie Barclay Corinna Barclay Corinna Annie Barclay Annie CorinnaExplanation / Answer
Q1.
Total people voting =V= 71
Total candidates = C = 3
Now if it was a draw between all candidates the vote distribution will be V/C
V/C =71/3 =23.67
Above implies that if total people voting would have been 69 then their was a posibility of draw(23 to each candidate) among all three.
However we have 71 Candidates so their are 2 extra votes and as we have been said that their is majority candidate so this implies these extra 2 votes must be with majority candidate.
So fewest no. Of votes with majority candidate becomes 23+2 =25 votes.
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