Strategic Voting Voting decision conditioning on pivotal event

Example: Plurality rule election with 3 candidates• a voter has preference a≻b≻c over candidates• a sincere voter votes for a• a strategic voter makes decision conditioning on the

event of tying, that is, how strategic voter behaves depends on her belief on pivot prob T={Tab,Tbc,Tca} Δ³∈ , 1. if her belief is T={1,0,0}, she vote for a2. if her belief is T={0,0,1}, she vote for a3. if her belief is T={0,1,0}, she vote for b Note:

she would never vote for c

• Strategic voting is important in many models of politics• Strategic voting plays an important role in actual elections.• However, how important strategic voting is is an

empirical question.

What we do1. propose an estimable model of strategic voting• added sincere voters to Myerson and

Weber(1993)

2. study (partial) identification of the model• not straightforward due to multiplicity of

equilibria3. estimation using inequality based estimator4. use only aggregate data from a Japanese election5. counterfactual experiment: i) proportional

representation, ii) sincere voting under plurality

Model Estimation

Inferring Strategic VotingKei Kawai Yasutora Watanabe

Northwestern University Northwestern University

In each election d {1,...,D}, there are ∈ K≥3 candidates, Md municipalities m₁,m₂,..., mMd, and Nm voters in municipality m• Voter n's utility of having candidate k in office is

unk= - (θIDxn - θPOSzkPOS)2 +θQLTYzkm

QLTY+ξkm+εnkwhere xn : voter characteristics

zk : candidate characteristics ξkm : candidate-municipality shock

εnk : voter idiosyncratic shock

• Sincere voter votes according to preference:vote for candidate k ⇔ unk≥unl,∀l

• Strategic voter takes into consideration tie probabilities.

vote for candidate k ⇔ ūnk(Tn)≥ūnl (Tn),∀l • Expected utility from voting for k:

ūnk (Tn)=(1/2)∑l∈{1,..,K}Tn,kl ×(unk-unl)

• Voter types: αnm=0 is sincere and αnm=1 is strategic• Probability that voter n in municipality m is strategic:

Pr(αnm=1|αm)=αm

where αm: municipality level random shock, which is assumed to follow a Beta distribution in estimation.

Equilibrium(C1) votes cast votes to maximize utility given T, i.e.,

As Nm→∞, the vote share outcome is approximated asvkm(T) ≡ (1-αm) vkm

SIN + αm vkmSTR(T)

where (g and fm are dist. of ε and characteristics x)

vkmSIN : vote share by sincere voters to candidate k,

i.e., vkmSIN ≡ 1{∬ unk≥unl,

∀l}g(ε)dεfm(x)dx

vkmSTR(T): vote share by strategic voters to cand k,

i.e.,vkm

STR ≡ 1{∬ unk(T)≥unl(T), ∀l}g(ε)dεfm(x)dx

(C2) consistency in belief, i.e., T ∈T(v) vk>vl ⇒Tkj≥Tlj ∀k,l,j∈{1,...,K}

Pivot prob. involving cand. with high vote shares are larger than those with low vote shares: v₁>v₂>v₃ T₁₂ ≥T₁₃ ⇒≥T₂₃

• Set of outcome W={T,{v}} is non-empty, and not a singleton• Restriction: no voter votes for his least preferred candidate. • However, beyond this restriction, the model leaves

considerable freedom in how vkmSTR(T) is linked to voter

preferences. - This is because solution concept requires T ∈T(v), and we do not observe T.

(Partial) Identification of Preference• Use restriction that no one votes for his least preferred candidate.• Partial b/c T is not observable, and (C2) is the only restriction.

Example: magnitude of age parameter depends on T

(Partial) Identification of the Extent of Strategic Voting• Given preference, sincere voting outcome is computed as

Δm(0)• An observation can be always be written as convex combination of Δm(0) and vm

STR(T).

• If Md→∞ (Many observations within same district), observations should be on line segment L, but edge could be either L’ or L

• If D→∞ (Many observations of districts), observations should be on the same line segment within district.

Corresponding to partial identification, we used moment inequality estimator (Pakes, Porter, Ho, and Ishii, 2006)

We constructed our moment inequality as: 1. Fix some θ and T. For any random shocks ξ and α, model

predicts outcome vPRED(T,θ)

2. In each district d, regress vPRED(T,θ) on demographic and candidate characteristics and obtain βd(T,θ) for each district. Do the same with vDATA to obtain βd

DATA.• Note that this regression is just an auxiliary model as in

Indirect Inference.

3. Find βsupd (θ)=sup βd(T,θ) and βinf

d (θ)=inf βd(T,θ) by varying Td∈T(vd

data) and integrate them over distribution of shocks ξ and α.

4. Construct moments as E[βinfk,d(θ₀)-βk,d

DATA] ≤ 0, and E[βsup

k,d(θ₀)-βk,dDATA] ≥ 0.

Introduction (Partial) Identification

Distinguishing Strategic and Misaligned Voting• misaligned voting: voting for a candidate other

than the one the voter most prefers• strategic voting: decision making conditioning on

pivotal event• misaligned voting is subset of strategic voting (strategic voter may not necessarily engage in

misaligned voting)

Existing empirical studies measures misaligned voting (and not the extent of strategic voting!)

• distinction is critical• extent of strategic voting is model primitive• extent of misaligned voting is only an

equilibrium object

Strategic vs. Misaligned Voting

Data• 2005 Japanese General Election Data• We use the particular structure that

• there are many elections (D→∞)• there are breakdowns of votes available at

sub-district (municipality) level

• We find large fraction [75.3%, 80.3%] of strategic voters

• Utility goes down as the distance between the voter’s municipality and the candidate’s hometown increases.• New candidates was more preferred than the incumbents and the

candidates who had some experience.• Ideological positions are LDP=0, DPJ=[-3.00, -2.99], JCP=[-3.47, -3.45], YUS=[-0.068,-0.065]

Based on the estimated parameters, we can calculate the fraction of misaligned voting.• We find small fraction [2.4%, 5.5%] of misaligned voting

• This is close to the existing estimates of "strategic voting" (3% to 15%)

Based on the estimated parameters, we can also conduct counterfactual policy experiment. We did i) hypothetical “sincere voting” experiment, and ii) proportional representation.

Results

  Counterfactual Experiment: Sincere Voting Outcome   JCP DPJ LDP YUSActual  Vote Share (%) 7.7 38.4 49.7 35  Number of Seats 0 35 131 9Counterfactual  Vote Share (%) [8.4, 10.2] [40.6, 43.8] [42.6, 45.7] [33.9, 38.8]  Number of Seats [0, 0] [52, 75] [86, 111] [11, 18]