1. Suppose I have a state with a population 10,000,000 where 5,200,000 are Republicans and 4,800,000 are Democrats (so 52% Republican and 48% Democratic). Suppose I want to divide the state into h=10 equally sized (how large) House districts. For this problem, let's ignore the question of where people live (the geography) and assume that any person can be put into any district.Your job is to assign people to districts. In each question below, list 10 districts (District 1 through District 10), tell me how many Republicans and how many Democrats you put in each district, and tell me which party will "control" the district in an election (you can assume everybody votes, and they all vote along strict party lines). Finally, tell me in each case the number of Republican and Democratic seats that result. (a) One idea of naive idea equity is for each district to mirror the party affiliation of the state as a whole. What would happen in this case? Who would benefit? (b) Another idea is to get the proportion of Republican vs Democratic seats "as close as possible" to 52% and 48%. How would you do this? (c) If the Democrats were somehow given control of the redistricting process, what is the maximum number of seats they could control?

2. For each of the answers (a), (b) and (c) in problem 1, calculate the "efficiency". If a party wins a district, its wasted votes are any number over a simple majority. If a department loses a district, all of its votes are wasted. Compute the total wasted votes for Republicans and for Democrats over all 10 districts. The efficiency is the difference in wasted votes for the two parties (biggest waste minus smallest waste) divided by total votes.