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The Mathematics of Voting: The...
Quiz #1

Questions 1 through 5 refer to an election with 4 candidates (A, B, C, and D), 71 voters and preference schedule given by the following table.

1 .       Using the plurality method the winner of the election is 



2 .       Using the method of pairwise comparisons the winner of the election is 



3 .       Using the extended plurality ranking method, which candidate comes in last? 



4 .       Using the extended Borda count ranking method, which candidate comes in last? 



5 .       The candidate that comes in third place using the recursive plurality with elimination ranking method is 



6 .       How many people voted in this election?
 



7 .       What is the total number of pairwise comparisons in an election among 21 candidates? 



8 .       2 + 4 + 6 + . . . + 198 + 200 = 



9 .       "If there is a choice that has a majority of the first-place votes in an election, then that choice should be the winner of the election." This fairness criterion is called the 



10 .       "If in an election there is a Condorcet candidate, then such a candidate should be the winner of the election." This statement is another way to phrase the 



11 .       An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. Due to an irregularity in the original vote count a recount is required. Before the recount takes place, candidate B drops out of the race. In the recount, still using voting method X, candidate D wins the election. Based on this information, we can say that voting method X violates the 



12 .       An election is held among six candidates (A, B, C, D, E, and F) Using the method of pairwise comparisons A gets 6 points; B gets 3 points; C gets points; D gets points, and E gets 1 point. How many points does F get? 



13 .       An election involving 5 candidates and 30 voters is held and the results of the election are to be determined using the Borda count method. The maximum number of points a candidate can receive is 



14 .       An election is held for president of the United States. Three candidates are running, a Democrat, a Republican, and an Independent. A certain voter prefers the Independent candidate over the other two, but realizing (because of all the pre-election polls) the race is going to be a close race between the Democrat and the Republican and that the Independent doesn't have a chance, he votes instead for his second choice (his preference between the Democrat and the Republican). This is an example of 



15 .       The method of pairwise comparisons violates 



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