Q1: Samantha, April, and Jane want pizza and are trying to decide between Pizza Hut, Domino's, Papa John's, and Pegasus Pizza (a place in Eugene). Since Samantha knows how to compute Borda counts, she suggests that the three of them write down their preference orders for pizza places, and then she will use the Borda method to determine where they will eat. Use the following preference orders and the Borda method to determine the "societal" preference order between the three of them. If they do indeed use this method, where will they be eating?

Samantha: Pizza HutPegasus PizzaPapa John'sDomino's

April: Domino'sPizza HutPegasus PizzaPapa John's

Jane: Pegasus PizzaDomino'sPapa John'sPizza Hut

Q2: 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, 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

please answer with clear explanation