Inferring Strategic Voting Model

Inferring Strategic Voting
Kei Kawai
Yasutora Watanabe
Northwestern University
Introduction
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 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
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
Model
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
Northwestern University
(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
4.  Construct moments as E[βinfk,d(θ₀)-βk,dDATA] ≤ 0, and
E[βsupk,d(θ₀)-βk,dDATA] ≥ 0.
(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).
vkmSTR(T):
vote share by strategic voters to cand k, i.e.,
vkmSTR ≡∬1{unk(T)≥unl(T), ∀l}g(ε)dεfm(x)dx
•  Utility goes down as the distance between the voter’s
•  If Md→∞ (Many observations within same district), observations
should be on line segment L, but edge could be either L’ or L
(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.
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
Results
•  We find large fraction [75.3%, 80.3%] of
strategic voters
(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 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
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)
3.  Find βsupd (θ)=sup βd(T,θ) and βinfd (θ)=inf βd(T,θ) by varying
Td∈T(vddata) and integrate them over distribution of shocks ξ
and α.
•  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)
Equilibrium
Corresponding to partial identification, we used moment inequality
estimator (Pakes, Porter, Ho, and Ishii, 2006)
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 βdDATA.
•  Note that this regression is just an auxiliary model as in
Indirect Inference.
•  Sincere voter votes according to preference:
vote for candidate k ⇔ unk≥unl,∀l
•  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.
Estimation
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%)
•  If D→∞ (Many observations of districts), observations should be
on the same line segment within district.
Based on the estimated parameters, we can also conduct
counterfactual policy experiment. We did i) hypothetical “sincere
voting” experiment, and ii) proportional representation.
Counterfactual Experiment: Sincere Vo5ng Outcome JCP DPJ LDP YUS Actual Vote Share (%) 7.7 38.4 49.7 35 Number of Seats 0 35 131 9 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]