QuestionIs it possible for a candidate with a majority of votes to lose an election using plurality-with-elimination? Explain.
Studdy Solution
STEP 1
Assumptions1. The candidate initially has a majority of the vote.
. The election is using the plurality-with-elimination method.
3. The statement is asking if it's possible for a candidate with a majority of the vote to lose the election.
STEP 2
We need to understand what the plurality-with-elimination method is. In this method, voters rank candidates in order of preference. The candidate with the least first-place votes is eliminated, and their votes are redistributed to the remaining candidates based on the second preferences of the eliminated candidate's voters. This process continues until a candidate has a majority of the votes.
STEP 3
Now, let's analyze each of the given options.
Option A "The statement does not make sense. The candidate with the majority of first-place votes wins the election before any eliminations and recounts are carried out."
This option suggests that if a candidate has a majority of first-place votes, they win the election immediately, without any need for eliminations or recounts. This is true in a simple majority vote system, but not in the plurality-with-elimination method.
STEP 4
Option B "The statement does not make sense. If the candidate has the majority of first-place votes, they will win each pairwise comparison with the other candidates in the election."
This option suggests that a candidate with a majority of first-place votes would win in any pairwise comparison, which is not necessarily true in the plurality-with-elimination method.
STEP 5
Option C "The statement makes sense. The candidate could lose the majority if another candidate is eliminated and the counts are updated."
This option suggests that a candidate with a majority of first-place votes could lose their majority if another candidate is eliminated and their votes are redistributed. This is possible in the plurality-with-elimination method.
STEP 6
Option D "The statement makes sense. It is possible for the candidate with the majority of first-place votes to receive fewer points than another candidate depending on the number of times they are listed as second place, third place, etc. in the election."
This option suggests that a candidate with a majority of first-place votes could end up with fewer points than another candidate if they are not listed as a second or third choice as often. This is also possible in the plurality-with-elimination method.
STEP 7
Based on our analysis, the statement does make sense. A candidate could have a majority of first-place votes but still lose the election in the plurality-with-elimination method if they are not listed as a second or third choice as often, or if another candidate's votes are redistributed in a way that gives another candidate a majority. Therefore, the correct answer is either option C or D.
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