Inferring Strategic Voting

Transcription

1 nerring Strategic Voting Kei Kawai Northwestern Yasutora Watanabe Northwestern Jan 2011 Kawai and Watanabe (): nerring Strategic Voting

2 Strategic Voting This paper addresses the extent to which voters vote sincerely or strategically Sincere Voting Voting naively according to preerences Strategic Voting Voting knowing that one should take into account the tie probabilities. Kawai and Watanabe (): nerring Strategic Voting

3 Strategic Voting Strategic voting is important in political economy Di erent models make di erent assumptions models o strategic voting comparing perormance o di erent electoral rules (e.g. Myerson and Weber [1993]) inormation aggregation (e.g. Feddersen and Pesendorer) models o sincere voting Multi-party competition (e.g.palrey 1984, Osborne [2000], allander [2005]) itizen andidate: Osborne and Slivinski [1996] To what extent do voters vote strategically is an empirical question Strategic voting is important in practice The extent to which voters vote strategically a ects election outcomes: e.g., 2000 U.S. Presidential Election Kawai and Watanabe (): nerring Strategic Voting

4 iterature Previous empirical studies o strategic voting lvarez and Nagler (2000), lais et al (2001) denti es misaligned voting, which is a subset o the set o strategic voting. Distinction between misaligned voting and strategic voting is important: equilibrium object v.s. primitive Other recent work: deological voting: Myatt (2007), Degan and Merlo (2009) Kawai and Watanabe (): nerring Strategic Voting

5 Setting 2005 Japanese House o Representatives Election 3 or more candidates. 175 plurality rule elections. Variation in the district is important or identi cation. Model: daptation o Myerson and Weber (1993) with sincere voters. Kawai and Watanabe (): nerring Strategic Voting

6 What we do First, identiy and estimate the preerences o voters in a setting where Voting o strategic voters depend on (unknown) tie probabilities The extent o strategic voting is unknown. Second, identiy and estimate the extent o strategic voting Set identi cation and bounds estimation. Kawai and Watanabe (): nerring Strategic Voting

7 This paper we nd large raction [75.3%, 80.3%] o strategic voters on average. we nd small raction [2.4%, 5.5%] o misaligned voting on average. this is close to the existing estimates o strategic voting (3% to 15%) n our counteractual experiment we nd that absent any strategic voting, one party would gain [17,40] seats and another would lose [20,45] seats (out o 175). arge change due to the act that oten races are close. Kawai and Watanabe (): nerring Strategic Voting

8 Outline ntroduction rie ntuition o denti cation Model Data denti cation Estimation Results and ounteractual Kawai and Watanabe (): nerring Strategic Voting

9 denti cation: Preerence Discrete choice setup: utility o voters as unction o demographic and candidate characteristics Problem: No one-to-one correspondence between choice and preerence or strategic voters: Depends on belies. c. utomobile choice or consumers Use the act that it is a (weakly) dominated strategy to vote or least preerred candidate: partial identi cation Kawai and Watanabe (): nerring Strategic Voting

10 denti cation: Extent o Strategic Voters Once preerence is identi ed, possible to predict outcome i all voters vote according to preerences No strategic voters =) match predicted outcome apart rom random shocks With strategic voters, not necessarily the case Strategic Voters =) Systematic Deviation Then di erence between predicted outcome and actual outcome identi es strategic voting. Source o identi cation in the data liberal municipality in a liberal district (both sincere and strategic are likely to vote according to preerences) liberal municipality in a conservative district (strategic voters likely to change their votes) Kawai and Watanabe (): nerring Strategic Voting

11 denti cation: Extent o Strategic Voters Kawai and Watanabe (): nerring Strategic Voting

12 Model: Voter Preerence n each election d 2 1,..., Dg, K 3 candidates M municipalities m 1, m 2,..., m M N m voters in municipality m Voter n s utility o having candidate k in o ce is u nk = u(x n, z k ) + ξ km + ε nk where x n : voter characteristics z k : candidate characteristics ξ km : candidate-municipality shock ε nk : voter idiosyncratic shock Kawai and Watanabe (): nerring Strategic Voting

13 Kawai and Watanabe (): nerring Strategic Voting

14 Model: Voter Preerence Sincere voter votes according to preerence: vote or candidate k, u nk u nl, 8l Strategic voter takes into consideration tie probabilities. vote or candidate k, ū nk (T n ) ū nl (T n ), 8l T n = T n,kl g kl voter n s belies that k and l are going to be tied or 1st place Expected utility rom voting or k: ū nk (T n ) = 1 2 T n,kl (u nk u nl ) l21,..,k g,l6=k Note that depending on the value o T n, possible that voter votes or any candidate except the candidate k with the lowest u nk. ssume that or some k, lg, T n,kl > 0. Then can normalize k l>k T n,kl = 1, or T n 2 K. Kawai and Watanabe (): nerring Strategic Voting

15 Model: Voter Type Voter type: r.v. α nm 2 0, 1g α nm = 0 is sincere and α nm = 1 is strategic α nm drawn rom a binomial. Municipal speci c prob. o success: α m. Probability that voter n in municipality m is strategic: Pr(α nm = 1jα m ) = α m Probability that voter n in municipality m is sincere: where Pr(α nm = 0jα m ) = 1 α m : r.v. drawn rom a eta distribution α m Kawai and Watanabe (): nerring Strategic Voting

16 ommon elie ssumption ssumption elies T n = T n,kl g kl are common across voters in the same electoral district: T n,kl g = T n 0,kl g or 8n, n 0 Kawai and Watanabe (): nerring Strategic Voting

17 Vote Share Outcome Vk,m SN : Fraction o votes cast by sincere voters to candidate k. (T ): Fraction o votes cast by strategic voters to candidate k. V STR k,m Vk,m SN = Nm n=1 (1 α nm) 1u nk u nl, 8lg N m n=1 (1 α, nm) Vk,m STR (T ) = Nm n=1 α nm 1u nk (T ) u nl (T ), 8lg N m n=1 α. nm Total vote share or candidate k: V k,m (T ) = N m n=1 (1 α nm) N m ZZ Vk,m SN + Nm n=1 α nm N m V STR k,m (T ) t (1 α m ) 1u nk u nl, 8lg]g(ε)dε m (x)dx ZZ + α m 1u nk (T ) u nl (T ), 8lgg(ε)dε m (x)dx Kawai and Watanabe (): nerring Strategic Voting

18 Solution oncept 1 : V k > V l ) T kj T lj 8k, l, j 2 1,..., K g Pivot probabilities involving candidates with high vote shares are larger than those with low vote shares: e.g.,v 1 > V 2 > V 3 ) T 12 T 13 T 23 weaker version o Myerson and Weber (1993) voting equilibrium (1 α nm) n=1 N m Vk,m SN + Nm α nm n=1 N m Given belies T, voters vote optimally 2 : V k,m = Nm V STR k,m (T ) embodies the restriction that no voter votes or his least preerred candidate De nition set o solution outcomes n W is all pairs o belies (T ) and vote shares, ( V km g km ), W = T, o V k,m g K M k=1 such that 1 and m=1 2 are satis ed. W is non-empty, not a singleton Kawai and Watanabe (): nerring Strategic Voting

19 Data Vote share data 2005 Japanese House o Representatives Election 175 plurality rule elections reakdown o votes or 1830 Municipalities Demographics data Municipality level data on income distribution, years o schooling, population above 65. andidate data Party a liation, hometown, previous political experience Kawai and Watanabe (): nerring Strategic Voting

20 Data Structure n each electoral district, municipality-level breakdown is available. District Municipality cand 1 cand 2 cand 3 cand 4 Narumiya Kitagami Nakagawa Tanaka (JP) (DPJ) (DP) (YUS) Kyoto 4 Ukyo-ku 16,929 30,967 31,021 17,945 Sakyo-ku 10,571 26,743 26,518 13,341 Kameoka 4,613 10,732 8,629 27,573 Miyama ,554 Sonobe ,961 4, TOT 35,705 73,550 75,192 75,036 Kawai and Watanabe (): nerring Strategic Voting

21 Data: Descriptive Statistics mean st.d. min max # obs # o municipalities per district winner s vote share (%) 3 candidate district candidate district winning margin (%) 3 candidate district candidate district margin between 2nd and 3rd (%) 3 candidate district candidate district Kawai and Watanabe (): nerring Strategic Voting

22 denti cation: Overview Our identi cation argument ollows two steps 1. set-identiy preerence 2. set-identiy extent o strategic voting Kawai and Watanabe (): nerring Strategic Voting

23 denti cation: Preerence Use the restriction that weakly-dominated to vote or the least preerred candidate Fix a preerence parameter θ. Ordering Pr( Ordering θ ) 1/ 6 1/ 6 1/ 6 1/ 6 1/ 6 1/ 6 V V V [0,2 [0,2 [0,2 3] 3] 3] No restriction on T. Kawai and Watanabe (): nerring Strategic Voting

24 denti cation: Preerences ommon elies within a municipality 6 1/ 6 1/ 6 1/ 6 1/ 6 1/ 6 1/ [0,1 2] [0,1 2] [0,1 2] V V V Kawai and Watanabe (): nerring Strategic Voting

25 denti cation: Preerences ommon elies within a district 6 1/ 6 1/ 6 1/ 6 1/ 6 1/ 6 1/ [0,1 2] [0,1 2] [0,1 2] V V V 4 1/ 4 1/ 4 1/ 4 1/ 0 0 4] [0,3 4] [0,3 [0,1 4] V V V (V 1, V 1, V 1 ) = (0, 1/2, 1/2) and (V 2, V 2, V 2 ) = (1/4, 3/4, 0) are individually not rejected. (V 1, V 1, V 1 ) = (0, 1/2, 1/2) requires T t 1. (V 2, V 2, V 2 ) = (1/4, 3/4, 0) requires T t 1. Jointly rejected Kawai and Watanabe (): nerring Strategic Voting

26 denti cation Extent o Strategic Voting ssume (or now) that we have identi ed the preerence parameters. Recall that i we knew T, and or given preerence parameters, then we could predict outcome as a unction o α m (and ξ m ) as: V k,m (T, α m ) t (1 α m )vk,m SN + α m vk,m STR (T ) ZZ where vk,m SN 1u nk u nl, 8lg]g(ε)dε m (x)dx ZZ vk,m STR (T ) 1u nk (T ) u nl (T ), 8lgg(ε)dε m (x)dx g and m are dist. o ε and characteristics x u nk = u(x n, z k ) + ξ km + ε nk ū nk (T n ) = 1 2 l21,..,k g,l6=k T n,kl (u nk u nl ) V k,m (T, α m ) is the point which divides vk,m SN and v STR k,m (T ) with ratio (1 α m ) and α m. However, we do not know T [T V m (T, α m ) is the predicted set o vote shares Kawai and Watanabe (): nerring Strategic Voting

27 denti cation: Extent o Strategic Voting Vote share can be expressed as a point in the simplex v 1m + v 2m + v 3m = 1. De ne m (α m ) as the possible set o vote shares when the raction o strategic voters is α m : m (α m ) = [ T V m (T, α m ) m (0) is the vote share corresponding to the what the sincere voters vote: m (0) = v SN k,m Kawai and Watanabe (): nerring Strategic Voting

28 First: gnore randomness rom ξ (ξ t 0) n nite # o municipalities within district i.e. One election and many municipalities. Fix demographic characteristics. Then V m line up along a line segment between vk,m SN v SN and v STR k,m (T ) and v STR k,m (T ) same or all m: Di erences among V m arise rom k,m di erences in α m. observed vote share map di erently into di erent values o α depending on the position o vm STR (T ), e.g, it can be or 0 ase corresponds to U, and ase to. Kawai and Watanabe (): nerring Strategic Voting

29 Second: No randomness, in nite # o districts, nite # o municipalities within district Position o vm STR (T ) changes across districts because T are di erent. Still, a vote share realization can be mapped to a value o α. ase 0 : the upper bound, and ase 0 : the lower bound. ntuitively, having liberal municipalities in conservative districts make 0 and close: necessary to make tight prediction on lower bound o the distribution o α. Kawai and Watanabe (): nerring Strategic Voting

30 denti cation: Extent o Strategic Voting 1. n the actual data, the vote shares would not lie on the same line segment So ar, our identi cation argument has ignored randomness in ξ m ξ m is the municipality level shock that would account or dispersion. the distribution o ξ m were completely unrestricted! may be hard to separately identiy the distribution o α m and ξ m. ut as long as ξ m is nicely behaved: uni-modal and mean zero, the same intuition carries through. We assume ξ ollows Normal! can parametrically account or the dispersion around the line segment. 2. Preerence parameters are only partially identi ed For each preerence parameter in the identi ed set, we recover the distribution o α. Take the union. Kawai and Watanabe (): nerring Strategic Voting

31 Estimation: Overview we knew T, the model predicts unique outcome given parameters =) we can estimate with ME or GMM. Unobserved T, which results in partial identi cation o parameters, makes inequality based estimation appropriate. Operationalize our identi cation argument Need to exploit variation in demographic characteristics and votes. Need to exploit the structure (district-municipality) Use Pakes, Porter, Ho, shii (2007) Kawai and Watanabe (): nerring Strategic Voting

32 Estimation: Speci cation o Utility Function Recall utility o voter n in municipality m, electing candidate k: u nmk = u(x n, z km ; θ PREF ) + ξ km + ε nk We allow both ideological ( spacial component) and non-ideological component in utility u(x n, z km ; θ PREF ) = (θ D x n θ POS z POS k ) 2 + θ QTY z QTY km θ D x n : ideological position o voter n x n : income, education, age (over 65 or not) θ POS z POS k : ideological position o candidate k z POS k : political party a liation o candidate k θ QTY z QTY km : quality o candidate k z QTY km : hometown, political experience (e.g., incumbent) o candidate k Kawai and Watanabe (): nerring Strategic Voting

33 Estimation: onstructing Moment nequalities onstruct moment inequalities based on our identi cation argument. dea similar to ndirect nerence 1. Fix some θ and T 2. For any random shocks ξ and α, model predicts outcome v PRED (T, θ) 3. n each district d, regress v PRED (T, θ) on demographic and candidate characteristics and obtain β d (T, θ) or each district. 4. Vary T to nd β d (θ) = supβ(t, θ) and β d (θ) = inβ(t, θ) and integrate them over distribution o shocks ξ and α. T 5. Regress actual vote share v DT on demographic and candidate characteristics and obtain β DT d. 6. onstruct moments as T E [β k,d (θ 0 ) β DT k,d ] 0, and E [β k,d (θ 0 ) β DT k,d ] 0. Kawai and Watanabe (): nerring Strategic Voting

34 Extensions: 1. The raction o strategic voting (α) may depend on T. people become aware o the possibility to vote strategically when T is close. one way to test this is compare variance o α within districts: var 1 (α) overall variance o α across districts: var 2 (α) var 1 (α) < var 2 (α), then evidence o dependence o α on T. 2. nclude voter turn-out. nclude a cost (or consumption value) o voting: outside option. Key di erence is that the absolute value o T n matter or turnout Scale matters: cannot normalize k l>k T n,kl = 1 Use level o turnout to pin down k l>k T n,kl. Standard pivotal-voting models are sensitive to very small changes in T. Found computational burden to be quite high. Kawai and Watanabe (): nerring Strategic Voting

35 Results: Parameter Estimates The utility unction we estimate is u(x, z km ; θ PREF ) = n [θ const, θ income, θ educ, θ >65 ]x n [θ DP, θ JP, θ DPJ, θ YUS ]z POS k +[θ incumb, θ prev, θ no_exp, θ htown1, θ htown2, θ htown3, θ htown4 ]z QTY km +ξ km + ε kn,.... θ const [ 1.420, 1.418] θ incumbent 0 θ income [ 0.164, 0.162] θ previous [ 0.204, 0.199] θ education [0.177, 0.179] θ no_experiecne [0.080, 0.083] θ above65 [ 0.003, 0.001] θ hometown1 [0.437, 0.444] θ JP [ 3.467, 3.448] θ hometown2 [0.180, 0.187] θ DPJ [ 2.998, 2.990] θ hometown3 [0.038, 0.041] θ YUS [ 0.068, 0.065] θ hometown4 0 θ DP 0 θ ξ [0.373, 0.385] Kawai and Watanabe (): nerring Strategic Voting o 2

36 Results Two parameters o the beta distribution θ α1 :[5.210, 6.005] and θ α2 :[1.473, 1.706] verage extent o strategic voting is [75.3%, 80.3%] Using the estimated model, we can recover the extent o misaligned voting. verage extent o misaligned voting is [2.4%, 5.5%] This number is comparable to the estimate o "strategic voting" in the existing studies, which varies rom 3% to 15%. Kawai and Watanabe (): nerring Strategic Voting

37 ounteractual Experiment: Sincere Voting JP DPJ DP YUS ctual Vote Share (%) Number o Seats ounteractual Vote Share (%) [8.4, 10.2] [40.6, 43.8] [42.6, 45.7] [33.9, 38.8] Number o Seats [0, 0] [52, 75] [86, 111] [11, 18] DPJ adds [17, 40] seats and DP would lose [20, 45] seats. The impact is large because the winning margin is oten small. JP and DPJ vote shares increase, and DP vote shares decrease. DP candidates are strong while DPJ and JP candidates were not. Sincere-voting e ect or YUS is small. Kawai and Watanabe (): nerring Strategic Voting

38 onclusion This paper proposes an estimable model o strategic voting study identi cation in discrete choice setting estimation using inequality based estimator (Pakes et. al. (2006)) results show a large raction [75.3%, 80.3%] o strategic voters, and a small raction [2.4%, 5.5%] o misaligned voting. counteractual experiment: sincere voting under plurality Kawai and Watanabe (): nerring Strategic Voting