Voter Turnout

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Voter Turnout
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Overview

• Recap the Paradox of Voting
• Incentives and Voter Turnout
• Voter Mobilization

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The Paradox of Voting

• Given standard assumptions on Expected Utility,
  voting is rarely a rational action.
• For any individual, x, voting is rational if and
  only if xs vote will either break a tie leading
  to her preferred candidates winning or creating
  a tie so her preferred candidate does not lose
• As the pool of potential voters increases, the
  probablility of either of these situations
  decreases dramatically

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Paradox of Voting

• We formalized this insight this way
• ?P B gt c
• ?P the change my vote makes in the prospects
  of victory for my prefered candidate
• B the difference in the benefits I receive
  when my preferred candidate wins or loses
• c costs of voting

back
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Paradox of Voting

• We ended class by noting that people do in fact
  vote, so either there are millions of irrational
  people out there, or we need to refine the model
• That is, there must be some extra benefit to
  voting such that
• ?P B D gt c
• D extra consumption benefits of voting not
  connected to the result of the vote

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Pardox of Voting

• And we further noted, that that explanation is
  not terribly helpful until or unless we can
  provide some content for D.
• That is, we cant simply say people vote because
  they like to vote.
• We need to uncover why they like to vote even
  when the prospects of making a difference are
  slim to zero

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Incentives and Voter Turnout

• One possible understanding of D is that we
  omitted to include the group benefits of voting
• That is, if my vote helps advance the interests
  of a group that I support, then maybe I should
  vote

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Incentives and Voter Turnout

• Suppose we have two members of group, Bill and
  Hillary, and the group supports a particular
  candidate (e.g, Obama over McCain)
• Further suppose that the preferred candidate
  needs the groups support in order to win

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Incentives and Voter Turnout

• Further suppose the following conditions
• Assume the groups preferred candidate, Obama,
  will lose by a single vote if neither of our two
  voters votes
• That means that if both vote, then Obama wins and
  if one votes its a tie

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Incentives and Voter Turnout

• Drawing on the Expected Utility idea we discussed
  earlier, we can put some numbers on the various
  scenarios
• If Obama wins, each will receive 100 utils
• If McCain wins, each will recieve 25 utils
• The utility difference (the B term above) would
  then be 100 - 25 75
• If its a tie, then they would expect to get 100
  util half the time, and 25 the other half, or
  100 (.5) 25 (.5) 62.5 utils

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Incentives and Voter Turnout

• But remember, we need to include the costs of
  voting, c, which well set at 50 utils
• We can now contstruct a payoff matrix to help us
  determine what Bill and Hillary should do

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Incentives and Voter Turnout
Hillarys Choices
Dont Vote
Vote for Obama


Vote for Obama
50, 50
12.5, 62.5
Bills Choices
62.5, 12.5
25, 25
Dont Vote
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Incentives and Voter Turnout

• Note that this is a classic prisoners dilemma
• Neither Bill nor Hillary has incentive to vote
• The two will have difficulty acting collectively
  to elect Obama

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Incentives and Voter Turnout

• Even though as a group they have the chance to
  influence the election to their preferred outcome
  (Obama), each individual voter has strong
  incentive to free ride on the actions of others
• Upshot would be McCain elected.

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Incentives and Voter Turnout

• Which means in order to get voters to vote we
  need to transform the payoff matrix so that we
  are no longer in the prisoners dilemma
• We need to provide other incentives for people to
  vote beyond the possibility of affecting the
  outcome

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Mobilization

• One way is to provide private selective
  incentives (PSI)
• PSI is an extra benefit, privately defined, that
  is received by the individual voter
• For instance, suppose the local organizers
  provide a free turkey to Bill and Hillary if they
  vote

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Mobilization

• Assume that the turkey is worth 25 utils to each,
  then the new payoff for Bill and Hillary would
  look like

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Hillarys Choices


75, 75
37.5, 62.5
Bills Choices
62.5, 37.5
25, 25
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• Note that in this case, the Nash equilibrium is
  for both Bill and Hillary to vote
• So, is PSI the means to achieve higher voter
  turnout?

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Mobilization

• Not really, since we need to be wary of bribery
  and vote selling
• PSI are legal only if the goods in question are
  available independent or regardless of the vote
• And if thats the case, were right back in the
  prisoners dilemma situation
• What to do?

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Mobilization

• Social Selective Incentives (SSI) defined as the
  utility that Bill and Hillary receive from acting
  together as a group in a social situation

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Hillarys Choices


75, 75
12.5, 62.5
Bills Choices
62.5, 12.5
50, 50
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Mobilization

• Note that this is not a prisoners dilemma, but
  it is different from the last game we had
• Here, we have not one but two Nash equilibria
  (both vote or neither vote)
• The issue here, then, is to coordinate the group
  of voters on the voting equilibrium rather than
  the nonvoting one

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Mobilization

• Factors that contribute family and peer groups
• Purposive Benefits
• Incentives that identify the benefits to the
  individual of the benefits of the group
• That is,individuals come to equate the group
  benefits with their individual benefits

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Mobilization

• Formalizing this dynamic we get
• ?Pg Bg gt cg
• Where
• ?P the effect of mobilizing groups of voters on
  the election outcome
• B the difference in group benefits if the
  preferred candidate wins
• c is the cost to the group of mobilization

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Mobilization

• Note that, for the group, the effect of
  mobilizing on the election can be as large as the
  benefits can be
• That means benefits may outweigh the costs of
  mobilizing

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Mobilization

• Notice, too, that as the costs of voting for
  individuals increases, turnout decreases
  (mobilization becomes more difficult as costs
  rise)
• Likewise, if voters are mobilized by groups whose
  preferences are the same as theirs, we find a
  positive relationship between turnout and both
  the investments of voting and the probability
  that an election is close

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Mobilization

• But what happens if the group mobilizing voters
  and the voters investment-movitated choice
  differ?
• We have 2 types of mobilization forces
• mobilization of benefit seeking groups
• mobilization of officer seeking groups

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Mobilization

• The first (benefit seeking groups) use the
  ability to mobilize its memberships to deliver
  votes for benefit seeking groups
• examples NOW, Focus on the Family, labor
  organizations, NAACP, etc.
• Expectation is that this electoral help will
  translate into policies favored by the group
• Mobilization based on selective incentives of
  group benefits.

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Mobilization

• Office seeking groups mobilize in voters
  committed to the idea of electing members of the
  group and act accordingly
• examples political parties

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Mobilization

• Note as Morton points out If voters are not
  mobilized by groups seeking policy or benefit
  motivations...but are instead motivated by
  private consumptive benefits doled out by office
  seeking groups then office-seeking groups have
  less reason to respond to them.
• In other words, the group, although mobilized to
  vote, will have little tangible rewards to show
  as a group for their effort.

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Next Week

• Candidates, Primaries, and Divergence
• How did we end up with Obama and McCain as the
  nominees?

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Dont Cooperate
Cooperate


3 , 3
1 , 4
Dont Cooperate
Cooperate
4 , 1
2 , 2
Prisoners Dilemma
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Prisoners Dilemma

• Symbolic Form
• Were in a Prisoners Dilemma situation whenever
• T gt R gt P gt S
• Temptation to defect gt Rewards of Cooperation
• Rewards gt Punishment for Not Cooperating
• Punishment gt Suckers Payoff

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Prisoners Dilemma

• Note that even if we start at the cooperative
  outcome, that outcome is not stable
• Each player can improve his/her position by
  adopting a different strategy

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Dont Cooperate
Cooperate


3 , 3
1 , 4
Dont Cooperate
Cooperate
4 , 1
2 , 2
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Prisoners Dilemma
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Prisoners Dilemma

• But since both players have changed strategy we
  end up at the non-cooperative outcome, where both
  players are worse off than if they had chosen to
  cooperate

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Dont Cooperate
Cooperate


3 , 3
1 , 4
Dont Cooperate
Cooperate
4 , 1
2 , 2
Prisoners Dilemma
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Prisoners Dilemma

• And, as we noted, this non-cooperative outcome is
  also a Nash equilibrium outcome
• Neither player has any incentive to change
  strategy since whoever changes will do
  immediately worse by making the move

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Dont Cooperate
Cooperate


3 , 3
1 , 4
Dont Cooperate
Cooperate
4 , 1
2 , 2
Prisoners Dilemma
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PD Interest Group

• If a collective good is involved, individuals
  have little incentive to work towards achieving
  that good.
• Makes sense for others to do the work and sit
  back and reap the benefits of their labor
• But if thats the case, then no one will do the
  work and the collective benefit wont be
  delivered
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