# solve math problems

1. Dr. Kaus has her students vote on the time slot for the final exam. The choices are 8am (E), 9am (N), or 10am (T). The outcome of the election is shown in the preference schedule below:
Number of Votes 8 14 8 2
First choice E T N E
Second choice T E E N
Third choice N N T T
a) How many students voted?
b) What is a majority?
c) Which time slot won using the plurality method? Explain.
d) Does this election violate the Condorcet criterion?
Make sure to show all work.

2. A committee is trying to award a scholarship to one of four students, Assad (A), Brian (B), Chee (C), and Debby (D). The preference table is shown below.
5 5 6 4
1st choice D A C B
2nd choice A C B D
3rd choice C B D A
4th choice B D A C
a) Perform a pairwise comparison to determine the winner of this election. Show all work.
b) Suppose it is found out afterwards that Debby was ineligible for the scholarship and must be removed from the ballot. The committee decides to remove Debby from consideration. Write out a new preference table with Debby removed and perform another pairwise comparison to determine the winner. Show all work.
c) Does the outcome of part b) violate irrelevant alternatives criterion? Explain.

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