b. For C to win the election outright, at least how many of the remaining 30 votes need to have C in first place? Explain. Use the plurality method to find the winner of the election. 3a. 3b. Tie-breaking rule: If there is more than one alternate with a plurality of the first-place votes, then the tie is broken by choosing the alternate with the fewest last place Who is the winner? votes. 3c. Tie-breaking rule: If there is more than one alternate with a plurality of the first-place votes, then the tie is broken by a head-to-head comparison Who is the winner? between the two candidates. 1.5 The Method of Pairwise Comparisons Pairwise Comparisons: # of 10 15 5 3 voters 1st A C A B A Head-To-Head comparison of candidates. choice 2nd B A C C Whoever is on the ballot gets all the votes “higher” choice for that ballot. The winner of a comparison gets 1 point, loser gets 0 points. 3rd C B B A In a tied comparison, both candidates earn ½ point. (Ties are common) choice A versus B A versus C A versus D B versus C B versus D C versus D A = B = C = D = Who wins by this method? How would you RANK the candidates? (1st, 2nd, etc.) FAIRNESS: The method of pairwise comparisons-- cannot violate the majority criterion cannot violate the Condorcet criterion So what’s the problem with Pairwise comparisons? Example: The table shows the voter preference for who a new NFL expansion team should make their number 1 draft pick. If we check pairwise comparisons we find: A = 3 points
b. For C to win the election outright, at least how many of the remaining 30 votes need to have C in first place? Explain. # of voters 10 15 5 3 1st choice A C A B 2nd choice B A C C 3rd choice C B B A 3a. Use the plurality method to find the winner of the election. 3b. Tie-breaking rule: If there is more than one alternate with a plurality of the first-place votes, then the tie is broken by choosing the alternate with the fewest last place votes. Who is the winner? 3c. Tie-breaking rule: If there is more than one alternate with a plurality of the first-place votes, then the tie is broken by a head-to-head comparison between the two candidates. Who is the winner? 1.5 The Method of Pairwise Comparisons Pairwise Comparisons: A Head-To-Head comparison of candidates. Whoever is “higher” on the ballot gets all the votes for that ballot. The winner of a comparison gets 1 point, loser gets 0 points. In a tied comparison, both candidates earn ½ point. (Ties are common) A versus B A versus C A versus D B versus C B versus D C versus D A = B = C = D = Who wins by this method? How would you RANK the candidates? (1st, 2nd, etc.) FAIRNESS: The method of pairwise comparisons-- cannot violate the majority criterion cannot violate the Condorcet criterion So what’s the problem with Pairwise comparisons? Example: The table shows the voter preference for who a new NFL expansion team should make their number 1 draft pick. If we check pairwise comparisons we find: A = 3 points
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