Question

3. Assign three voters the weights 8? = frac{pi}{2} = 3.14159..., ?2 = 1, 83 = 0.500. a. If the voters are of the respective types one, three, five, find the weighted election outcome. b. Express the profile of part a as a normalized profile in Si(6). c. Show for these weights that whatever voter-one wants, voter-one gets. Namely, voter-one is a dictator. Show that if voter-one does not vote, then voter-two becomes a dictator. d. To extend a voting vector from strict preferences to all preferences, average the number of votes cast over all ways indifference can be broken. In this manner, a voter with ranking C1 ~ C3 > C2 would cast the ballot (frac{1}{2}, 0, frac{1}{2}) = frac{1}{2}([e1]2 + [e1]3). Show that the above weights define a sequential dictatorship. Namely, voter-one always gets his way - but when he is indifferent between two candidates, voter-two's preferences dominate. Voter-three's views are manifested only when the first two voters are indifferent.

          3. Assign three voters the weights 8? = frac{pi}{2} = 3.14159..., ?2 = 1, 83 = 0.500. 
a. If the voters are of the respective types one, three, five, find the weighted election outcome. 
b. Express the profile of part a as a normalized profile in Si(6). 
c. Show for these weights that whatever voter-one wants, voter-one gets. Namely, voter-one is 
a dictator. Show that if voter-one does not vote, then voter-two becomes a dictator. 
d. To extend a voting vector from strict preferences to all preferences, average the number 
of votes cast over all ways indifference can be broken. In this manner, a voter with ranking 
C1 ~ C3 > C2 would cast the ballot (frac{1}{2}, 0, frac{1}{2}) = frac{1}{2}([e1]2 + [e1]3). Show that the above weights 
define a sequential dictatorship. Namely, voter-one always gets his way - but when he is 
indifferent between two candidates, voter-two's preferences dominate. Voter-three's views are 
manifested only when the first two voters are indifferent.

$3. Assign three voters the weights 8? = fracpi2 = 3.14159..., ?2 = 1, 83 = 0.500. a. If the voters are of the respective types one, three, five, find the weighted election outcome. b. Express the profile of part a as a normalized profile in Si(6). c. Show for these weights that whatever voter-one wants, voter-one gets. Namely, voter-one is a dictator. Show that if voter-one does not vote, then voter-two becomes a dictator. d. To extend a voting vector from strict preferences to all preferences, average the number of votes cast over all ways indifference can be broken. In this manner, a voter with ranking C1 C3 > C2 would cast the ballot (frac12, 0, frac12) = frac12([e1]2 + [e1]3). Show that the above weights define a sequential dictatorship. Namely, voter-one always gets his way - but when he is indifferent between two candidates, voter-two's preferences dominate. Voter-three's views are manifested only when the first two voters are indifferent.$

Added by Derek W.

Question

Please give Ace some feedback