Chapter 1: The Mathematics of Voting: The Paradoxes of Democracy
Quiz


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

Note: answer choices in this exercise are randomized.

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