a) For which vectors v is ? Explain your answer. For which vectors v is ? Explain youranswer.(c) For which vectors v is ? Explainyour answer.

Math 103: Week B Notes (01/17) Monotonicity Criterion: If Candidate X wins a first election, and before a second election all voters who change their votes put an X first, then X should win again. - Always satisfied by lurality Independence on Irrelevant Alternatives: If X wins a first election, and before a second election one of the losers drops, then X should still win. - None of the Voting Theory Methods always satisfy Arrow’s Theorem: There is no “perfect fairness” in counting/collecting votes...no method is 100% fair. Weighted Voting: Accomplished by persons with a hold of power over or agreement with the the counter/ collector of votes (e.g. US security council, Legislature, business partnerships) - When working with weighted voting the components includes payers/ voters (P1, P2...Pn), the weight of each player (W1, W2...Wn), and the Quota (number of votes needed to pass a notation). - Weighted Voting ALWAYS searches to satisfy an explicit “yes” or “no” HW: pg. 28, #53 & 56