Math 181 Fall 2018 Worksheet 6

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Math 181 Fall 2018 Worksheet 6 Name: ____________________________________ In the standard voting model, each voter provides a ranking of the candidates from the most to the least preferred. For instance, consider the table below: 33 voters 16 voters 3 voters 8 voters 18 voters 22 voters A B C C D E B D D E E C C C B B C B D E A D B D E A E A A A It shows that there are 5 candidates running in the election, namely A, B, C, D, and E. Out of 100 voters, 33 prefer A to B, B to C, C to D, and D to E; 16 voters prefer B to D, D to C, C to E, and E to A; etc. 1. Plurality vote: The winner is the candidate ranked first by the most voters. Which candidate is selected as the winner by the plurality vote? ___A_______ 2. Borda count: Each candidate is awarded a number of points equal to the number of candidates ranked lower than them on each ballot. (So the candidate ranked last gets 0 points, second to last—1 point, etc.) The points received by a candidate from each ballot are added up. The candidate with the most points wins. Which candidate is selected as the winner by the Borda count? ___B_______ Math 181 Fall 2018 Worksheet 6 For your convenience, the same table is copied again here. 33 voters 16 voters 3 voters 8 voters 18 voters 22 voters A B C C D E B D D E E C C C B B C B D E A D B D E A E A A A 3. Condorcet method: Candidate X beats candidate Y if more than half of the voters rank X higher than Y . The candidate who beats every other candidate wins. Which candidate is selected as the winner by the Condorcet method? ___C_______ 4. Instant-runoff voting (Hare system): The candidate who is ranked first by the fewest voters is eliminated (and completely removed from the ballots). This is repeated until only one candidate—the winner—remains. Which candidate is selected as the winner by the IRV? _____D_____ 5. Two-round plurality (plurality runoff): All but the two candidates ranked first by the most voters are eliminated. From the remaining two candidates, the winner is chosen based on who is ranked higher by more than half of the voters. Which candidate is selected as the winner by the two-round plurality vote? ____E______ .

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