Application of the Political Mathematics Discussion Questions

Question Description

I’m working on a political science writing question and need an explanation and answer to help me learn.

1. [From the textbook] We say that a social choice system satisfies the criterion of unanimity if an alternativeis the unique social choice whenever every ballot has that alternative ranked highest. Prove that if a socialchoice procedure satisfies Pareto, then it must also satisfy unanimity.

2. [From the textbook] We saw that sequential pairwise voting does not satisfy Pareto. Does it satisfyunanimity? Explain.

3. [From the textbook] A board of directors for a small corporation consists of three members: Derek with 5votes as the largest shareholder, Christina with 4 votes as the next largest shareholder, and Isabelle with 3votes as the smallest shareholder. The quota for passage of any issue is 7 votes. Prove that although eachof the three directors has a different number of votes, each has equal power in the sense that no onevoter can single-handedly pass a motion and any two voter scan pass any motion.

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