Voter Turnout
Overview
• Recap the “Paradox” of Voting
• Incentives and Voter Turnout
• Voter Mobilization
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 x’s vote will either break a tie leading to her
preferred candidate’s 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
Paradox of Voting
• We formalized this insight this way:
ΔP * B > c
ΔP = 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
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:
ΔP * B + D > c
D = extra consumption benefits of voting not
connected to the result of the vote
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 can’t 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
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
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 group’s support in
order to win
Incentives and Voter Turnout
• Further suppose the following conditions:
• Assume the group’s 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 it’s a tie
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 it’s 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
Incentives and Voter Turnout
• But remember, we
need to include the
costs of voting, c,
which we’ll set at 50
utils
• We can now contstruct
a payoff matrix to help
us determine what Bill
and Hillary should do:
Incentives and Voter Turnout
Hillary’s Choices
Don’t Vote
Vote for Obama
Vote for
Obama
50, 50
12.5, 62.5
Don’t
Vote
62.5, 12.5
25, 25
Bill’s
Choices
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
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.
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
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
Mobilization
• Assume that the
turkey is worth 25
utils to each, then the
new payoff for Bill
and Hillary would
look like
Hillary’s Choices
75, 75
37.5, 62.5
Bill’s
Choices
62.5, 37.5
25, 25
• 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?
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 that’s the case, we’re right back in
the prisoner’s dilemma situation
• What to do?
Mobilization
• Social Selective
Incentives (SSI)
defined as the utility
that Bill and Hillary
receive from acting
together as a group in
a social situation
Hillary’s Choices
75, 75
Bill’s
Choices
62.5, 12.5
12.5, 62.5
50, 50
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
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
Mobilization
• Formalizing this dynamic we get:
∆Pg * Bg > 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
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
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
Mobilization
•
•
But what happens if the group mobilizing
voters and the voter’s investmentmovitated choice differ?
We have 2 types of mobilization forces:
1. mobilization of benefit seeking groups
2. mobilization of officer seeking groups
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.
Mobilization
• Office seeking groups mobilize in voters
committed to the idea of electing members
of the group and act accordingly
– examples: political parties
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.
Next Week
• Candidates, Primaries, and Divergence
• How did we end up with Obama and
McCain as the nominees?
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
Prisoners’ Dilemma
• Symbolic Form:
• We’re in a Prisoner’s Dilemma situation
whenever:
T>R>P>S
Temptation to defect > Rewards of
Cooperation
Rewards > Punishment for Not Cooperating
Punishment > Sucker’s Payoff
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
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
back
Prisoners’ Dilemma
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
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
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
Don’t
Cooperate
Don’t
Cooperate
Cooperate
3,3
1,4
4,1
2,2
Cooperate
Prisoners’ Dilemma
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 that’s the case, then no one will do the work
and the collective benefit won’t be delivered
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