QuestionEvaluate if the approval voting method meets fairness criteria and choose the correct explanation from options A-D.
Studdy Solution
STEP 1
Assumptions1. The statement is about a voting method called approval voting.
. In this method, voters approve or disapprove of each candidate.
3. The candidate with the most approval votes wins.
4. The statement claims that this method satisfies all four fairness criteria.
5. The four fairness criteria are majority criterion, monotonicity criterion, head-to-head criterion, and the independence of irrelevant alternatives criterion.
STEP 2
Let's analyze each option one by one.Option A suggests that the monotonicity criterion could be violated. The monotonicity criterion states that if a candidate wins an election, and in a re-election the candidate only receives more votes, then the candidate should still win. If candidate A has more approval votes than both candidates B and C in one election, and candidate A wins in a re-election where only candidate B's approval changes by going up, this does not violate the monotonicity criterion because candidate A's votes did not decrease.
STEP 3
Option B suggests that the head-to-head criterion could be violated. The head-to-head criterion states that if a candidate would win a head-to-head competition against each other candidate, then that candidate should win the election. If candidate A has greater approval when compared to candidate B, candidate A has greater approval when compared to candidate C, but candidate C has the highest approval overall, this does violate the head-to-head criterion because candidate A should win according to this criterion.
STEP 4
Option C suggests that the statement makes sense because the approval voting method satisfies all four of the fairness criteria. However, as we saw in the analysis of option B, this is not necessarily true.
STEP 5
Option D suggests that the majority criterion could be violated. The majority criterion states that if a candidate is the first choice of more than half of the voters, then that candidate should win the election. If candidate A is the first choice of51% of voters and is approved by60% of voters, yet candidate B is the first choice of49% of voters and is approved by70% of voters, this does violate the majority criterion because candidate A should win according to this criterion.
STEP 6
Based on the analysis of all options, the correct answer is that the statement does not make sense. The approval voting method could violate the head-to-head criterion and the majority criterion.So, the correct answer is a combination of options B and D.
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