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Problem 4 In the voters' problem, assume that we start by wanting the following: - 1 to beat 2 pairwise by two votes - 1 to beat 3 pairwise by two votes - 2 to beat 3 pairwise by four votes - 3 to beat 2 in a plurality election by three votes - 2 to beat 1 in the same plurality election by three votes - the total number of voters to be sixty a) Set up your system of equations and unknowns. Explain carefully any additions you make to the model as covered in class. b) Find the solution (N, N2, N3, N4, N, N) (Hint: this is not very difficult if you remember your matrix algebra and you use Excel) c) Take your solution and check what happens in pairwise confrontations between 1 and 2, 1 and 3, and 2 and 3. Also check what happens in a plurality election. How are your results related to the given? Problem 4 In the voters' problem, assume that we start by wanting the following: - 1 to beat 2 pairwise by two votes - 1 to beat 3 pairwise by two votes - 2 to beat 3 pairwise by four votes - 3 to beat 2 in a plurality election by three votes - 2 to beat 1 in the same plurality election by three votes - the total number of voters to be sixty a) Set up your system of equations and unknowns. Explain carefully any additions you make to the model as covered in class. b) Find the solution (N, N2, N3, N4, N, N) (Hint: this is not very difficult if you remember your matrix algebra and you use Excel) c) Take your solution and check what happens in pairwise confrontations between 1 and 2, 1 and 3, and 2 and 3. Also check what happens in a plurality election. How are your results related to the given