Strategy and Voting

1
Strategy and Voting

• Can institutions that use voting as a means of
  decision-making be gamed?

2
Olympic Voting

• Assumptions
• Three IOC delegates A, B and C
• Three cities Athens, Beijing and Sydney
• Pairwise voting
• Pick two cities and vote
• Then vote on the winner and remaining city

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
Arrows 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 wont 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?