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: N A , N B ◮ Two types of voters: active partisans, passive partisans ◮ Large size of the base partisans: R AL , R BL ◮ Small size of the base partisans: R AS , R BS ◮ Chance of having large size: π A , π B ◮ Campaigns and Polls ◮ Voting cost: c i , independently drawn from a uniform distribution f ( c ) ◮ Rewards: H and L
A Quasi-Symmetric Voter Turnout Equilibrium Notation ◮ ( p A , p B ): voting probabilities ◮ ( c A , c B ): critical cost levels ◮ ( q A , q B ): pivotal probabilities Z c A p A = f ( c ) dc = F ( c A ) 0 Z c B p B = f ( c ) dc = F ( c B ) 0 c A = H − L q A 2 c B = H − L q B 2 ◮ P p ( 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: P p ( k − r L | p , n ) or P p ( k − r S | p , n ) Polls: P N ( k | p , n , π, r L , r S ) = π · P p ( k − r L | p , n − r L ) + (1 − π ) · P p ( k − r S | p , n − r S )
Three Types of Situations: 1. Both conduct Campaigns ( q ∗ ); 2. One Campaigns, One Polls ( q ∗∗ ); 3. Both Polls (˜ q ) min { N A − 1 , N B } ˘ P p ( k − R A | p ∗ q ∗ X A , N A − R A − 1) · P p ( k − R B | p ∗ B , N B − R B ) ¯ A = k =max { R A , R B } min { N A − 1 , N B − 1 } ˘ P p ( k − R A | p ∗ X A , N A − R A − 1) · P p ( k + 1 − R B | p ∗ B , N B − R B ) ¯ + k = r A min { N A − 1 , N B } ˘ P p ( k − R A | p ∗∗ q ∗∗ X A , N A − R A − 1) · P N ( k | p ∗∗ B , N B , π B , R BL , R BS ) ¯ = A k = R A min { N A − 1 , N B − 1 } ˘ P p ( k − R A | p ∗∗ X A , N A − R A − 1) · P N ( k + 1 | p ∗∗ + B , N B , π B , R BL , R BS ) ¯ k = R A min { N A − 1 , N B } ˘ P N ( k | ˜ X p B , N B , π B , R BL , R BS ) ¯ ˜ q A = p A , N A − 1 , π A , R AL , R AS ) · P N ( k | ˜ k =0 min { N A − 1 , N B − 1 } ˘ P N ( k | ˜ X p B , N B , π B , R BL , R BS ) ¯ + p A , N A − 1 , π A , R AL , R AS ) · P N ( k + 1 | ˜ k =0
Experimental Design ◮ N A = N B = 4, R AL = R BL = 3, R AS = R BS = 1, π A = 0 . 6, and π B = 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 R A ; π A R B ; π B p ∗ p ∗ N A N B A B 4 4 1 1 0.573 0.573 CC 4 4 3 1 0.407 0.465 4 4 1 3 0.465 0.407 4 4 3 3 0.909 0.909 4 4 1 0.4 0.525 0.537 CP 4 4 3 0.4 0.762 0.659 4 4 0.6 1 0.500 0.500 PC 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 ∗ r ) and p ∗ s ( r , r ) > p ∗ s ( r , ˆ 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 N A N B R A ; π A R B ; π B p ∗ p ∗ A 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 outcome than polls, resulting in a higher or lower propensity to cast a vote: ◮ p ∗ s ( r , r ) > p ∗ s ( π A , r ) and p ∗ s ( r , r ) > p ∗ s ( r , π B ), where s ∈ { A , B } and r ∈ { 1 , 3 } . ◮ p ∗ r ) < p ∗ r ), and p ∗ r ) < p ∗ s ( r , ˆ s ( π A , ˆ s ( r , ˆ s ( r , π B ), 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 p ), and Theory with Subjective Belief (ˆ Table: Turnout Rates: Theory ( p ∗ ), Data (ˆ ˆ p ) No. of ˆ ˆ Subjects R A ; π A R B ; π B p ∗ ˆ p A p A ˆ p ∗ ˆ p B ˆ p B A B 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 p , ˆ p ) and Test of Pivotality Belief (ˆ p , p ∗ ) Table: Test of Appropriate Behavior (ˆ ˆ ˆ CCMajority CCMinority CCTie1 CCTie3 Data & NE p > p ∗ ˆ - - - p > ˆ p > ˆ Appropriate behavior ˆ ˆ p - - ˆ p ˆ Pivotality belief - - - - CPMajority CPMinority CPFaceMajority CPFaceMinority Data & NE - - p < p ∗ ˆ ˆ p > p ∗ p > ˆ Appropriate behavior ˆ ˆ p - - - ˆ ˆ ˆ Pivotality belief p < p ∗ ˆ - p < p ∗ ˆ ˆ p > p ∗ PCMajority PCMinority PCFaceMajority PCFaceMinority Data & NE - p > p ∗ ˆ p < p ∗ ˆ ˆ p > p ∗ Appropriate behavior - - - - ˆ ˆ ˆ ˆ Pivotality belief p < p ∗ ˆ p > p ∗ 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) -0.0049 ∗ -0.0054 ∗∗ -0.0018 0.0019 Period (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) -0.33 ∗∗∗ -0.34 ∗∗∗ -0.17 ∗ -0.16 ∗ Belief of being Pivotal (0.13) (0.13) (0.095) (0.093) 0.16 ∗∗ 0.11 ∗ lead = 0 or -1 ( dummy ) (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
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