Getting Out the Vote: Information and Voting Behavior Yi-Yi Chen - - PowerPoint PPT Presentation

Getting Out the Vote: Information and Voting Behavior

Yi-Yi Chen Washington University in St. Louis October 19, 2013

228, One Million People Hand-In-Hand to Protect Taiwan

Figure: Two million Taiwanese formed a 500-kilometer long human chain

Getting Out the Vote: Information and Voting Behavior

Two Information Revealing Mechanisms

Mechanism 1

◮ Active supporters show their support without paying costs ◮ Polls (Grober and Schram 2010; Agranov et al. 2012) ◮ Cheap talk

Mechanism 2

◮ Active supporters have to pay to support their candidates ◮ Campaigns ◮ Provide more certainty than Mechanism 1

Outline

◮ Pivotal Voter Model (Downs 1957; Palfrey and Rosenthal 1985) ◮ Two Mechanisms

◮ Polls ◮ Campaigns

◮ Experiments ◮ Results ◮ Conclusion

The Two-Party Races

Setting

◮ Two parties: A and B ◮ Party size: NA, NB ◮ Two types of voters: active partisans, passive partisans ◮ Large size of the base partisans: RAL, RBL ◮ Small size of the base partisans: RAS, RBS ◮ Chance of having large size: πA, πB ◮ Campaigns and Polls ◮ Voting cost: ci, independently drawn from a uniform distribution f (c) ◮ Rewards: H and L

A Quasi-Symmetric Voter Turnout Equilibrium

Notation

◮ (pA, pB): voting probabilities ◮ (cA, cB): critical cost levels ◮ (qA, qB): pivotal probabilities

pA = Z cA f (c)dc = F(cA) pB = Z cB f (c)dc = F(cB) cA = H − L 2 qA cB = H − L 2 qB

◮ Pp(k|p, n): probability that k passive partisans turn out to vote when there are n

passive partisans and each passive partisan has a voting probability p. Campaigns: Pp(k − rL|p, n) or Pp(k − rS|p, n) Polls: PN(k|p, n, π, rL, rS) = π · Pp(k − rL|p, n − rL) + (1 − π) · Pp(k − rS|p, n − rS)

Three Types of Situations:

• 1. Both conduct Campaigns (q∗); 2. One Campaigns, One Polls (q∗∗); 3. Both Polls (˜

q)

q∗

A = min{NA−1,NB }

X

k=max{RA,RB }

˘ Pp(k − RA|p∗

A, NA − RA − 1) · Pp(k − RB|p∗ B, NB − RB) ¯

+

min{NA−1,NB −1}

X

k=rA

˘ Pp(k − RA|p∗

A, NA − RA − 1) · Pp(k + 1 − RB|p∗ B, NB − RB) ¯

q∗∗

A

=

min{NA−1,NB }

X

k=RA

˘ Pp(k − RA|p∗∗

A , NA − RA − 1) · PN(k|p∗∗ B , NB, πB, RBL, RBS) ¯

+

min{NA−1,NB −1}

X

k=RA

˘ Pp(k − RA|p∗∗

A , NA − RA − 1) · PN(k + 1|p∗∗ B , NB, πB, RBL, RBS) ¯

˜ qA =

min{NA−1,NB }

X

k=0

˘ PN(k|˜ pA, NA − 1, πA, RAL, RAS) · PN(k|˜ pB, NB, πB, RBL, RBS) ¯ +

min{NA−1,NB −1}

X

k=0

˘ PN(k|˜ pA, NA − 1, πA, RAL, RAS) · PN(k + 1|˜ pB, NB, πB, RBL, RBS) ¯

Experimental Design

◮ NA = NB = 4, RAL = RBL = 3, RAS = RBS = 1, πA = 0.6, and

πB = 0.4

• 1. Voters are more likely to guess correctly
• 2. Compare differences between campaigns and polls

◮ Costs and Benefits (Levine and Palfrey 2007)

◮ Voting costs: uniform distribution ranging from 0 to 11 ◮ Rewards: L = 1, H = 21, Tie = 11

◮ Four treatments

◮ CC: Both parties conduct campaign activities ◮ CP: Party A conducts campaign activities; Party B only has polls ◮ PC: Party A only has polls; Party B conducts campaign activities ◮ PP: Neither party conducts campaign activities; both have polls only

Hypotheses 1-3

Table: Experimental Design and Predictions

Treatment NA NB RA;πA RB;πB p∗

A

p∗

B

CC 4 4 1 1 0.573 0.573 4 4 3 1 0.407 0.465 4 4 1 3 0.465 0.407 4 4 3 3 0.909 0.909 CP 4 4 1 0.4 0.525 0.537 4 4 3 0.4 0.762 0.659 PC 4 4 0.6 1 0.500 0.500 4 4 0.6 3 0.787 0.867 PP 4 4 0.6 0.4 0.694 0.661

H1: The Size Effect: p∗

A(1, 1) < p∗ A(3, 3) and p∗ B(1, 1) < p∗ B(3, 3).

H2: The Underdog Effect: p∗

A(1, 3) > p∗ B(1, 3) and p∗ B(3, 1) > p∗ A(3, 1).

H3: The Competition Effect: p∗

s (r, r) > p∗ s (r, ˆ

r) and p∗

s (r, r) > p∗ s (ˆ

r, r), where s ∈ {A, B}, r ∈ {1, 3}, ˆ r ∈ {1, 3}, and r = ˆ r.

Hypothesis 4: Information-Revealing Effect

Table: Experimental Design and Predictions

Treatment NA NB RA;πA RB;πB p∗

A

p∗

B

CC 4 4 1 1 0.573 0.573 4 4 3 1 0.407 0.465 4 4 1 3 0.465 0.407 4 4 3 3 0.909 0.909 CP 4 4 1 0.4 0.525 0.537 4 4 3 0.4 0.762 0.659 PC 4 4 0.6 1 0.500 0.500 4 4 0.6 3 0.787 0.867 PP 4 4 0.6 0.4 0.694 0.661

Compared with polls, campaign activities provide greater certainty of an election

• utcome than polls, resulting in a higher or lower propensity to cast a vote:

◮ p∗

s (r, r) > p∗ s (πA, r) and p∗ s (r, r) > p∗ s (r, πB), where s ∈ {A, B} and r ∈ {1, 3}.

◮ p∗

s (r, ˆ

r) < p∗

s (πA, ˆ

r), and p∗

s (r, ˆ

r) < p∗

s (r, πB), where s ∈ {A, B}, r ∈ {1, 3},

ˆ r ∈ {1, 3}, and r = ˆ r.

Experimental Protocol

◮ An A group was randomly paired with a B group ◮ Four Phases

• 1. Participants decided whether to vote or not
• 2. Participants stated their subjective belief as to the probability that

their decision would be pivotal

• 3. Participants stated their guesses about the final outcome
• 4. The result of the round was revealed

◮ In each pair, the group receiving the majority of votes won ◮ Participants were also paid for their guesses being correct ◮ Neutral language was used to write the experimental instructions

Turnout Rates: Comparison of Theory and Data

Table: Turnout Rates: Theory (p∗), Data (ˆ

p), and Theory with Subjective Belief (ˆ ˆ p)

• No. of

Subjects RA;πA RB;πB p∗

A

ˆ pA ˆ ˆ pA p∗

B

ˆ pB ˆ ˆ pB CC 26 1 1 0.573 0.635 0.647

• 3

1 0.407 0.659 0.473 0.465 0.402 0.420 1 3 0.465 0.402 0.420 0.407 0.659 0.473 3 3 0.909 0.870 0.802

• CP

28 1 0.4 0.525 0.554 0.569 0.537 0.677 0.618 3 0.4 0.762 0.794 0.606 0.659 0.533 0.529 PC 30 0.6 1 0.500 0.661 0.625 0.500 0.634 0.612 0.6 3 0.787 0.609 0.662 0.867 0.746 0.716 PP 28 0.6 0.4 0.694 0.735 0.680 0.661 0.692 0.665 ◮ Unpredictably high turnout in CCMajority → failure of support for the

competition effect and the underdog effect.

◮ Unpredictably high turnout in CPFaceMinority and PCFaceMinority →

failure of support for the information-revealing effect.

Tset: Behavior and Pivotality Belief

Table: Test of Appropriate Behavior (ˆ p, ˆ ˆ p) and Test of Pivotality Belief (ˆ ˆ p, p∗)

CCMajority CCMinority CCTie1 CCTie3 Data & NE ˆ p > p∗

• Appropriate behavior

ˆ p > ˆ ˆ p

• ˆ

p > ˆ ˆ p Pivotality belief

• CPMajority

CPMinority CPFaceMajority CPFaceMinority Data & NE

• ˆ

p < p∗ ˆ p > p∗ Appropriate behavior ˆ p > ˆ ˆ p

• Pivotality belief

ˆ ˆ p < p∗

• ˆ

ˆ p < p∗ ˆ ˆ p > p∗ PCMajority PCMinority PCFaceMajority PCFaceMinority Data & NE

• ˆ

p > p∗ ˆ p < p∗ ˆ p > p∗ Appropriate behavior

• Pivotality belief

ˆ ˆ p < p∗ ˆ ˆ p > p∗ ˆ ˆ p < p∗ ˆ ˆ p > p∗ PPMajority PPMinority Data & NE

• Appropriate behavior
• Pivotality belief
• “-” represents that the two values are not significantly different at the 0.01 critical level.

Probit Regressions Explaining Turnout

Table: Probit Regressions: CCMajority and CPMajority (Marginal Effects Reported)

Dependent variable: Vote CCMajority CCMajority CPMajority CP Majority Voting Cost

• 0.084∗∗∗
• 0.087∗∗∗
• 0.050∗∗∗
• 0.051∗∗∗

(0.027) (0.028) (0.015) (0.014) Period

• 0.0049∗
• 0.0054∗∗
• 0.0018

0.0019 (0.0028) (0.0027) (0.0014) (0.0014) Voted at t-1 0.71∗∗ 0.73∗∗∗ 0.45∗∗ 0.45∗∗ (0.304) (0.279) (0.228) (0.221) Won at t-1

• 0.0065
• 0.0066
• 0.0021
• 0.0016

(0.0077) (0.0075) (0.0043) (0.0043) Voted and Won at t-1

• 0.0057
• 0.0069
• 0.00047
• 0.00073

(0.010) (0.010) (0.0050) (0.0050) lead of the majority if in majority

• 0.13∗∗
• 0.078∗∗

(0.062) (0.035) Belief of being Pivotal

• 0.33∗∗∗
• 0.34∗∗∗
• 0.17∗
• 0.16∗

(0.13) (0.13) (0.095) (0.093) lead = 0 or -1 (dummy) 0.16∗∗ 0.11∗ (0.066) (0.064) # of obs. 188 188 263 263

Why Negative? Not Bandwagon!

Figure: Frequency Distribution of Stated Leads: CCMajority

Let x denote each participant’s stated pivotality probability blue line: 0 x < 0.2 red line: 0.2 x < 0.4 yellow line: 0.4 x < 0.6 green line: 0.6 x < 0.8 purple line: 0.8 x 1

Psychological Effect

Leading in interim stages has a psychological impact on performance in tournament.

◮ Theoretical work: Alex Krumer (2013) ◮ Empirical work: Gonzalez-D´

ıazy and Ignacio Palacios-Huerta (2010)

◮ Experiment work: Duffy, John and Margit Tavits (2008)

Conclusion

There are three main findings.

• 1. Subjects followed the ideas of the pivotal voter model in most of the

situations

• 2. When subjects were informed of being in an advantageous situation

by campaigns

◮ turnout became significantly higher ◮ effect of leading in an interim stage

• 3. Compared with campaigns, it is more difficult for polls to cause the

same effect