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strategy and voting

Olympic Voting. Assumptions:Three IOC delegates: A, B and CThree cities: Athens, Beijing and SydneyPairwise votingPick two cities and voteThen vote on the winner and remaining city. Olympic Preferences. Condorcet Paradox. Cyclic votingIntransitive social preferencesOvercoming the paradoxCorrelated preferences (single crossing property)Smaller groups with smaller numbers of alternatives.

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strategy and voting

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    1. Strategy and Voting Can institutions that use voting as a means of decision-making be gamed?

    3. Olympic Preferences

    4. Condorcet Paradox Cyclic voting Intransitive social preferences Overcoming the paradox Correlated preferences (single crossing property) Smaller groups with smaller numbers of alternatives

    5. Agenda Paradox Suppose that A is the chair of the IOC committee How will A structure the rounds to get what it wants?

    6. Agenda Control Criminal court cases: Status Quo: determine guilt or innocence first and then the punishment. Roman Tradition: after hearing evidence, start with most severe punishment and work down the list. Mandatory Sentencing: specify the sentence for the crime and then decide if should be convicted.

    7. An Example

    8. Borda Count

    9. Reversal Paradox Suppose Warne is ineligible because he is not retired. Who wins? Violates independence of irrelevant alternatives Changes in the set of candidates should not affect the social ranking of the remaining set

    10. Methods of Voting Binary Methods Majority rule Pairwise voting Condorcet method Amendment procedure Copeland index (counting methods) Plurative Methods Plurality rule Borda count Approval voting (for more than one ‘winner’) Mixed Methods Majority runoff Proportional representation Single transferable vote or Hare procedure

    11. Method Determines Outcome 100 IOC delegates with preferences Outcomes under: Plurality rule, Borda count, majority runoff, plurality with elimination (as in Olympic voting)?

    12. Arrow’s Impossibility Theorem Does a reasonable and fair voting system exist? NO, never satisfies all of the following … (Completeness) Social ranking ranks all alternatives (Transitivity) If A pref B and B pref C than A pref C (Unanimity) If all pref A to B then rank A above B (Independence of Irrelevant Alternatives) If one outcome unavailable, then ranking over remaining outcomes should not change (No Dictatorship) No single voter should determine the social ranking

    13. Strategic Manipulation Gibbard and Satterthwaite have demonstrated that there is no voting mechanism that is immune from manipulation. That is, under every voting rule, some individuals will have an incentive not to vote according to their true preferences.

    14. Spoilers Plurality rules: seen as fair If there are two candidates (in say a Presidential race) then a third candidate can enter the race and spoil the chances of the leader. E.g., Perot in Clinton v. Bush (1992), Wallace in Humphrey v. Nixon, Bjelkie-Peterson in Hawke v. Howard.

    15. Pairwise Voting Common in committee decision-making over time: compare alternatives in pairs Exercise in strategic manipulation

    16. Borda Count Used to guarantee a particular outcome is not chosen Incentive to put top choice first and second choice last

    17. Voting as Commitments Charitable contributions by foundations (one in Melbourne and the other in Sydney) There are two foundations each with a budget of $250,000 Three grant applications: Help to poor Melbourne Business School AGSM Both prefer a $200,000 grant to homeless. If one foundation starts first it won’t do this so as to compel the other to do so. Pre-empt and limit choices of others.

    18. Median Voter Theorem Strategic analysis of candidate behaviour Suppose there are two candidates and a distribution of voter preferences. Then candidates will position their strategies to win the median voter

    19. Pivot Voter Pivot voters have the most power In US, the Vice-President holds the tie-breaking vote in the Senate. Often used on important issues – including John Adams, Richard Nixon and George Bush What are your chances of being a pivot voter?

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