Juan, Amy, and Ivan were the candidates running for president of a college science club. The...

  

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Juan, Amy, and Ivan were the candidates running for president of a college science club. The members of the club selected the winner by vote. Each member ranked the candidates in order of preference. The ballots are summarized below. 13. Number of votes First choice Second choice Third choice Amy Ivan Juan 8 Ivan Juan Amy Amy Juan Ivan 11 Juan (a) Which candidate has a majority of the first-choice votes? Ivan Amy 17 The members plan to use the Borda count method to determine the winner and want to make sure the results seem fair. For this purpose, they will rely on a set of criteria to verify the fairness of the results. One of these criteria is known as the majority criterion. The Majority Criterion If a candidate has a majority of the first-choice votes, then that candidate should be the winner. It turns out that the Borda count method can sometimes violate this criterion. Answer the parts below to determine if the majority criterion is violated. X S (b) Use the Borda count method to determine the winner. (c) Would using the results of the Borda count method violate the majority criterion? Juan, Amy, and Ivan were the candidates running for president of a college science club. The members of the club selected the winner by vote. Each member ranked the candidates in order of preference. The ballots are summarized below. 13. Number of votes First choice Second choice Third choice Amy Ivan Juan 8 Ivan Juan Amy Amy Juan Ivan 11 Juan (a) Which candidate has a majority of the first-choice votes? Ivan Amy 17 The members plan to use the Borda count method to determine the winner and want to make sure the results seem fair. For this purpose, they will rely on a set of criteria to verify the fairness of the results. One of these criteria is known as the majority criterion. The Majority Criterion If a candidate has a majority of the first-choice votes, then that candidate should be the winner. It turns out that the Borda count method can sometimes violate this criterion. Answer the parts below to determine if the majority criterion is violated. X S (b) Use the Borda count method to determine the winner. (c) Would using the results of the Borda count method violate the majority criterion?