Discrete Math A:Chapter 1 Test Review

Skills to help you prepare for the exam:

  • Interpret and construct preference schedules for elections involving preference ballots

(HW 1A and Exercises #1-10)

  • Determine the winner of an election using preference ballots using the
  • Plurality Method (HW 1B and Exercises #11,12)
  • Borda Count Method (HW 1D and Exercises #17-22)
  • Plurality-with-elimination Method (HW 1E and Exercises #27-34)
  • Method of Pairwise Comparison (HW 1C and Exercises #35-38)
  • Rank candidates using extended ranking methods (Exercises #41-44)
  • State the fairness criteria and identify when they are violated (Exercises #17-20,27,33-35,59,60)
  • Count the number of pairwise comparisons in a given election (Exercises 55,56), the number of votes needed to win an election (Exercises 13-16), and the Borda points given out (Exercises 23-26)
  • State Arrow’s Impossibility Theorem in your own words.

Practice Problems:

1. Your college radio station is holding auditions to find the next Campus Idol. There are four people competing in the auditions: Beth (B), Frank (F), Helen (H), and Sam (S). After all of the competitors have auditions, the audience members rank each contestant in order of preference and submit their ballots. The results are given below:

1A. How many preference ballots were cast in this election?

1B. Who would be the next Campus Idol if the Plurality method is used to calculate the winner?

1C. Who would be the next Campus Idol if the Method of Pairwise Comparisons is used to calculate the winner?

1D. Who would be the winner if the Borda Count method is used?

1E. Who would be the winner by the method of Plurality-with-elimination?

1F. Is there a Condorcet Candidate in this election?

2. What is the formula for finding the number of pairwise comparisons in an election with N-candidates?

3. The student union at your university has organized Chess-Stock, a round-robin Chess Tournament. Each participant will play every other participant once, and the winner will be chosen after all matches have been completed. If there are 12 people registered to play in the tournament, then how many matches will take place?

4.Five students: Joe, Sam, Peg, Lea, and Val are participating in a talent show. After the 5 students perform, the final preference schedule is below:

4A: Rank the candidates using extended Plurality.

4B: Rank the candidates using extended Borda Count.

4C: Rank the candidates using extended Pairwise Comparisons.

4D: Rank the candidates using extended Plurality-with-elimination

4E: Do any of A-D violate the Condorcet Criterion?

4F: Do any of A-D violate the Majority Criterion?

More Practice:

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