Strategic Voting Voting decision conditioning on pivotal event

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Inferring Strategic Voting Kei Kawai Yasutora Watanabe Northwestern University Northwestern University Introduction Model Estimation (Partial) Identification • (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 vmSTR(T). • If Md→∞ (Many observations within same district), observations should be on line segment L,butedgecould 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: • Fix some θand T. For any random shocks ξ and α, model predicts outcome vPRED(T,θ) • 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 vDATAto obtain βdDATA. • Note that this regression is just an auxiliary model as in Indirect Inference. • Find βsupd (θ)=sup βd(T,θ)and βinfd (θ)=inf βd(T,θ)by varyingTd∈T(vddata)and integrate them over distribution of shocks ξ and α. • Construct moments as E[βinfk,d(θ₀)-βk,dDATA] ≤ 0, and • E[βsupk,d(θ₀)-βk,dDATA] ≥ 0. • 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 probT={Tab,Tbc,Tca}∈Δ³, • if her belief is T={1,0,0}, she vote for a • if her belief is T={0,0,1}, she vote for a • 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 isan empirical question. • What we do • propose an estimable model of strategic voting • added sincere voters to Myerson and Weber(1993) • study (partial) identification of the model • not straightforward due to multiplicity of equilibria • estimation using inequality based estimator • use only aggregate data from a Japanese election • counterfactual experiment: i) proportional representation, ii) sincere voting under plurality • 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 +θQLTYzkmQLTY+ξkm+εnk • where 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 as • vkm(T) ≡ (1-αm) vkmSIN + αm vkmSTR(T) • where (g and fm are dist. of εand 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 candk, i.e., • vkmSTR≡∬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. Results • 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. Strategic vs. Misaligned Voting • 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 • 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