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  3. 3 three people named x y and z are trying...

Question: 3 three people named x y and z are trying...

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3. Three people, named X, Y, and Z, are trying to decide which equally-priced pitcher of soda to purchase and share: Coke (C), Root Beer (RB), or Dr. Pepper (DP). The following table depicts each persons preference ordering: RankP 15 Person X Person Y Person Z st DP RB DP nd RB DP 37 RB Arrows Impossibility Theorem states that with at least 3 voters and 3 alternatives no rank-type voting systems can covert everyones preferences into a social rankinjg unless we use some form of a dictatorship. Lets try some rank-type voting systems a) (5 pts) Majority rule - each person votes for their first choice. Which soda gets the most first choice votes? b) (5 pts) Condorcet method - the winner is who would win the most pairwise runoffs In other words, who has the most wins when DP vs. C, C vs. RB, and then RB vs. DP? c) (5 pts) Plurality with runoff- restrict the soda candidates to just two; see who wins and the winner has a runoff with the third soda. For example, suppose they first vote between Coke and Root Beer, then the winner is pitted against Dr. Pepper. Which pitcher do they purchase? Now suppose they first vote between Coke and Dr. Pepper, then the winner is pitted against Root Beer. Which pitcher do they purchase? Finally, they first vote between Root Beer and Dr. Pepper with the winner pitted against Coke. Which pitcher do they purchase? d) (5 pts) Given your findings above, how would you decide which soda should be purchased for the table of three?

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