1. You are forming a new UO chapter of the national group Math Fans Anonymous. The presidency of this group is down to a vote between you and your arch-nemesis, Regina. The one who will become president is determined by four members of a committee (you can call these members A, B, C, and D).

a. Construct a voting system (by showing votes and results of at least three elections) that illustrates a quota system with q = 3. Construct one of your elections so that no winner is produced.

b. Write the results of the elections you used from part (a), assuming q = 2.