Suppose Homer (i=1), Marge (i=2), Bart (i=3), Lisa (i=4), and Maggie (i=5) have to choose between two alternatives: Duff (x) and Butterfinger (y)....

1. Suppose Homer (i=1), Marge (i=2), Bart (i=3), Lisa (i=4), and Maggie (i=5) have to choose between two alternatives: Duff (x) and Butterfinger (y). Their preferences are as follows: Homer prefers Duff; Marge and Maggie are indifferent between the two alternatives; Bart and Lisa prefer Butterfinger.

a. Using the notation from the Kelly book:

(i) n = _____

(ii) (d1,...,dn) = ____________________________

(iii) The answer to (ii) is a ? ( set / list )

(iv) N+1= _______   N-1= ________

b. Use one of the equations for Simple Majority Voting that are described on pages 5-6 of the Kelly book to determine the outcome. Show your work.

c. Use the equation for Absolute Majority Voting on page 6 of the Kelly book to determine the outcome. Show your work.

2.  For the model that is on pages 5-6 of the Kelly book, give an example with n=4 where:

a. Simple Majority Voting assigns +1.

b. Simple Majority Voting assigns 0.

c. Absolute Majority Voting assigns -1.