1. (18 pts) Huey, Dewey and Louie are three brothers. Their uncle left them $36 to share among themselves. So, they are trying to decide on an allocation of $36 as $h to Huey, $d to Dewey and $L to Louie, where h + d + L = 36. Particularly they are looking for an allocation proposal that would be a (weak or strong) Condorcet winner, i.e., the proposal should not be defeated against any other proposal in pairwise voting under majority rule. (i)Is the proposal (h, d, L) = (12, 12, 12) a (weak or strong) Condorcet winner? If Yes, clearly explain (in a few sentences) why no other proposal can defeat (12, 12, 12) in pairwise voting under majority rule. If No, provide another proposal (h', d', L') that defeats (12, 12, 12) in majority voting. (ii)Before they decide on an allocation, they discovered that their uncle had another restriction on the way they will distribute it: he wanted Dewey and Louie to receive the same share, d = L, Huey does not have to receive the same share. When you look only at the proposals that satisfy this additional restriction, is there a proposal that is a (weak or strong) Condorcet winner among all such proposals? If Yes, identify that proposal, clearly indicate whether it is a weak or strong Condorcet winner, and explain (in a few sentences) why this is the case. If No, clearly explain (in a few sentences) why