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# Review Sheet for MATH 105 at KU

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
Math 105 Test 3 Review You will want to bring something to write with a pencil would be a good plan and a calculator No notesbooksfriends will be allowed on the test Chapter 1 The Mathematics of Voting vocabulary candidate or choice majority insincere voting preference ballot plurality ranking preference schedule Condorcet candidate recursive voting methods plurality method Borda count method pluralitywithelimination method instant runoff voting pairwise comparison method Copeland s method be able to use each one and recognize when one is unfair fairness criteria Majority Criterion If a choice receives a majority of the firstplace votes in an election then that choice should be the winner of the election Condorcet Criterion If there is a choice that in a headtohead comparison is preferred by the voters over each of the other choices then that choice should be the winner of the election Monotonicity Criterion If choice X is a winner of an election and in a reelection the only changes in the ballots are changes that only favor X then X should remain a winner of the election Independence of Irrelevant Alternatives Criterion If choice X is a winner of an election and one or more of the other choices is disqualified and the ballots recounted then X should still be a winner of the election ranking methods extended plurality method extended Borda count method extended pluralitywithelimination method extended method of pairwise comparisons Arrow s Impossibility Theorem It is mathematically impossible for a democratic voting method to satisfy all of the fairness criteria Chapter 2 Weighted Voting Systems vocabulary motion dictator losing coalition player dummy grand coalition weight veto power critical player quota coalition sequential coalition power winning coalition pivotal player be able to describe weighted voting systems use notation be able to work out the way votes should be distributed according to a description the number of possible coalitions in a system with N players 2N 7 1 nd the Banzhaf Power Index of a voting system the number of possible sequential coalitions with N players N nd the ShapleyShubik Power Index for a voting system

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