Final Exammgf

# Final Exammgf - 22:38 Final Exam Material from Exams 1-3...

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22:38 Final Exam: Material from Exam’s 1-3 Independence of irrelevant alternatives) , Arrow’s Theorems, Two alternate systems Syste m CWC Paret o Condi tion IIA M o n o ti ci t y Is sys ma ble Plura lity No Yes No Y e s No Bord a Coun t No Yes No Y e s No can s. Y mo 3 can s Seq. PW. Yes No No Y e yes

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Votin g s Hare Syste m No Yes No N o yes Plura lity Runo ff No Yes No N o yes Appr oval Votin g No No No Y e s yes
Desirable Properties (know which systems satisfy or do not satisfy the different properties) Pareto Condition - IIA - 3) Condorcet Winner Criterion (CWC) -  The  Condorcet candidate  or  Condorcet winner  of an  election  is the candidate who, when compared with every  other candidate, is preferred by more voters. Informally, the  Condorcet winner is the person who would win a two- candidate election against each of the other candidates. A  Condorcet winner will not always exist in a given set of votes,  which is known as Condorcet's  voting paradox . voting system  satisfies the  Condorcet criterion  if it  chooses the Condorcet winner when one exists. Monotonicity - A candidate  x  should not be harmed  [i.e., change from being a winner to a loser]  if  x  is raised on  some ballots without changing the orders of the other  candidates. 5) Manipulability - Know the yes/no chart

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Monotone – If a voter switches their vote from a losing candidate to the winning candidate and everyone votes the same the outcome of the election will be the same. Plurality Voting Borda Count - Sequential PairWise voting (w/ given agenda) Hare System Plurality Runoffs Approval Voting every voter is treated equally both candidates treated equally system is monotone Majority rule satisfies all 3. Dictatorship does not satisfy 1. Minority rule does not satisfy 3. Imposed rule does not satisfy 2. Arrow’s Impossibility Theorems Strong b/c it applies to any number of voters (even or odd), satisfies IIA and Pareto
Weak applies to an odd amount of voters, always a winner when it comes to IIA and CWC. Three alternate systems Given matrix Find Winner Using 2 3 5 3 Plurality Voting - In single winner plurality voting, each voter is  allowed to vote for only one candidate, and the winner of the election is  whichever candidate represents a  plurality  of voters, that is, whoever received the  largest number of votes. This makes the plurality voting system among the  simplest of all voting systems for voters and vote counting officials (it is however  very contentious to draw district boundary lines in this system). Borda Count -

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Final Exammgf - 22:38 Final Exam Material from Exams 1-3...

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