voter turnout. overview recap the “paradox” of voting incentives and voter turnout voter...

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

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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:

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


• 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


• 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


• 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


• 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:


Bill’sChoices

Hillary’s Choices

Vote for Obama Don’t Vote

Vote for Obama

Don’t Vote

50, 50 12.5, 62.5

62.5, 12.5 25, 25


• 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


• 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.


• 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

62.5, 37.5

75, 75 37.5, 62.5

25, 25

Hillary’s Choices

Bill’sChoices

• 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

62.5, 12.5

75, 75 12.5, 62.5

50, 50

Bill’sChoices

Hillary’s Choices

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 outcomeB = the difference in group benefits if the

preferred candidate winsc = 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 investment-movitated 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

Cooperate

Prisoners’ Dilemma

4 , 1

3 , 3 1 , 4

2 , 2


• 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 CooperatingPunishment > Sucker’s Payoff


• 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

Cooperate


4 , 1

3 , 3 1 , 4

2 , 2

back


• 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

Cooperate


4 , 1

3 , 3 1 , 4

2 , 2


• 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

Cooperate


4 , 1

3 , 3 1 , 4

2 , 2

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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voter turnout. overview recap the “paradox” of voting incentives and voter turnout voter...

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