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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={T ab,T bc,T ca } ∈ Δ³, 1.if her belief is T={1,0,0}, she vote for a 2.if her belief is T={0,0,1}, she vote for a 3.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 do 1.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 equilibria 3.estimation using inequality based estimator 4.use only aggregate data from a Japanese election 5.counterfactual experiment: i) proportional representation, ii) sincere voting under plurality Model Estimation Inferring Strategic Voting Kei Kawai Yasutora Watanabe Northwestern University Northwestern University In each election d ∈ {1,...,D}, there are K≥3 candidates, M d municipalities m ₁,m ₂,..., m Md, and N m voters in municipality m Voter n's utility of having candidate k in office is u nk = - (θ ID x n - θ POS z k POS ) 2 +θ QLTY z km QLTY +ξ km +ε nk where x n : voter characteristics z k : candidate characteristics ξ km : candidate-municipality shock ε nk : voter idiosyncratic shock Sincere voter votes according to preference: vote for candidate k ⇔ u nk ≥u nl, ∀ l Strategic voter takes into consideration tie probabilities. vote for candidate k ⇔ ū nk (T n )≥ū nl (T n ), ∀ l Expected utility from voting for k: ū nk (T n )=(1/2)∑ l ∈ {1,..,K} T n,kl ×(u nk -u nl ) Voter types: α nm =0 is sincere and α nm =1 is strategic Probability that voter n in municipality m is strategic: Pr(α nm =1|α m )=α m where α m : 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 N m →∞, the vote share outcome is approximated as v km (T) ≡ (1-α m ) v km SIN + α m v km STR (T) where (g and f m are dist. of ε and characteristics x) v km SIN : vote share by sincere voters to candidate k, i.e., v km SIN ≡ ∬ 1{u nk ≥u nl, ∀ l}g(ε)dεf m (x)dx v km STR (T): vote share by strategic voters to cand k, i.e., v km STR ≡ ∬ 1{u nk (T)≥u nl (T), ∀ l}g(ε)dεf m (x)dx (C2) consistency in belief, i.e., T ∈ T (v) v k >v l ⇒ T kj ≥T lj ∀ k,l,j ∈ {1,...,K} Pivot prob. involving cand. with high vote shares are larger than those with low vote shares: v ₁ >v ₂ >v ₃ ⇒ T ₁₂ ≥T ₁₃ ≥T ₂₃ 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 v km STR (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 Δ m (0) An observation can be always be written as convex combination of Δ m (0) and v m STR (T). If M d →∞ (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 v PRED (T,θ) 2.In each district d, regress v PRED (T,θ) on demographic and candidate characteristics and obtain β d (T,θ) for each district. Do the same with v DATA to obtain β d DATA. Note that this regression is just an auxiliary model as in Indirect Inference. 3.Find β sup d (θ)=sup β d (T,θ) and β inf d (θ)=inf β d (T,θ) by varying T d ∈ T(v d data ) and integrate them over distribution of shocks ξ and α. 4.Construct moments as E[β inf k,d (θ ₀ )-β k,d DATA ] ≤ 0, and E[β sup k,d (θ ₀ )-β k,d DATA ] ≥ 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 JCPDPJLDPYUS Actual Vote Share (%)7.738.449.735 Number of Seats0351319 Counterfactual 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]

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