On the Extent of Strategic Voting Tables

Figure 1: Theoretical Predictions under Sincere and Strategic Voting A. Sincere Voters B. Strategic Voters share of precinct’s candidate votes I. Non-Contender 100% 100% 100% (1! ! ) 50% 50% 50% ! share of precinct’s list votes 45° 0% 0% 50% share of precinct’s list votes 0° 100% 50% 100% 100% 100% 50% 50% 50% share of precinct’s list votes share of precinct’s list votes 0% 0% 50% 100% 100% share of precinct’s candidate votes 100% 45° share of precinct’s list votes < 45° 0% 50% share of precinct’s candidate votes share of precinct’s candidate votes II. Contender C. Mixture of Sincere and Strategic Voters share of precinct’s candidate votes share of precinct’s candidate votes share of precinct’s list votes 0% 50% 100% 50% 100% Figure 2: Empirical Example, 2009 Federal Election in Electoral District 207 Dr. Ludwig Tauscher, CDU (36.0%) Manuel Höferlin, FDP (9.7%) Pia Schellhammer, Green Party (7.3%) Michael Post, The Left (7.1%) Others (2.3%) II. Non-Contenders I. Contenders Klaus Hagemann, SPD (37.6%) Notes: Figure depicts the relationship between list votes and candidate votes for contenders (upper two panels) as well as non-contenders (lower four panels) in District 207 during the 2009 federal election. Each dot corresponds to one electoral precinct. Figure 4: Distribution of Direct Mandates in the 2005 and 2009 Federal Elections A. 2005 B. 2009 Notes: Figure depicts majority of the candidate vote by electoral district and candidates' party affiliation in the 2005 (left) and 2009 (right) federal elections. In the 2005 (2009) election, candidates running for the CDU/CSU won the plurality of votes in 150 (218) out of 299 electoral districts. SPD candidates gained 145 (64) direct mandates. Candidates of the The Left won 3 (16) districts, and the Green Party achieved 1 (1) direct mandate. No FDP contestant won a district race. Sources: Based on Bundeswahlleiter (2005a, 2005b, 2008, 2009a). Figure 5: Relationship between List and Candidate Votes for Non-Contenders Notes: Figure shows a semi-parametric estimate of the relationship between list and candidate votes for non-contenders and the associated 95%-confidence interval. Estimates are obtained by the differencing procedure in Yatchew (1998) and local-mean smoothing using an Epanechnikov kernel with a bandwidth of .55%. Figure 6: Difference in the Share of Strategic Voters between East and West Germany, 1990–2009 20% 10% 0% -10% -20% -30% -40% 1990 1994 1998 2002 2005 2009 Notes: Figure shows the percentage point difference in the share of strategic voters between East and West Germany for each federal election from 1990 to 2009 as well as the associated 95%-confidence intervals. Negative values indicate fewer strategic voters among residents of the former GDR. The null hypothesis of a constant difference across all years can be rejected at the 1%-confidence level, and that of an equal difference in 1990 and 2009 is rejected at the 5%-level. Figure 7: Observed vs Predicted Distribution of Votes, 2009 Federal Elections A. Marginal Distribution of Candidate Votes 45% 40% Observed Predicted Share of Candidate Votes 35% 30% 25% 20% 15% 10% 5% 0% CDU SPD FDP The Left Green Party Party B. Marginal Distribution of List Votes 40% 35% Observed Predicted Share of List Votes 30% 25% 20% 15% 10% 5% 0% CDU SPD FDP The Left Green Party Party C. Joint Distribution of Candidate and List Votes 35% Candidate Vote 30% CDU Observed Share of Vote Combinations Predicted 25% SPD 20% 15% FDP CDU 10% Left SPD 5% Greens Greens SPD CDU SPD Left FDP Left Greens FDP CDU CDU SPD Left Greens FDP Greens FDP Left 0% CDU/CSU SPD FDP The Left Green Party List Vote Notes: Figure depicts actual and predicted vote shares in the 2009 federal election. Panel A shows the marginal distribution of candidate votes, and panel B that of list votes. Panel C depicts the frequency of valid list and candidate vote combinations, i.e. their joint distribution. Dark columns are based on official statistics by the Federal Returning Officer (Bundeswahlleiter 2009a, 2010). Light columns corresponds to the predictions of the structural model in Section 7. Figure 8: Counterfactual Seat Distributions in the 17th Bundestag B. Proportional Representation Based on Actual List Votes A. Status Quo Green Party 10.9% The Left 12.2% Green Party 11.4% The Left 12.7% CDU/CSU 38.4% FDP 15.0% CDU/CSU 36.0% FDP 15.5% SPD 23.5% SPD 24.5% C. Plurality Rule Sincere and Strategic Voters Green Party 0.7% D. Plurality Rule Sincere Voters Only Green Party 0.7% The Left 2.0% The Left 3.1% SPD 18.7% CDU/CSU 77.6% SPD 23.5% CDU/CSU 73.8% Notes: Figure depicts counterfactual seat distributions in the Bundestag following the 2009 federal election. See the main text for a description of the assumptions underlying each panel. Table 1: Distribution of List and Candidate Votes in the 2009 Federal Election Party Share of List Vote Share of Number of Candidate Vote Direct Mandates CDU/CSU SPD Candidate Vote as Fraction of Party's List Vote FDP The Left Green Party Others Invalid CDU/CSU 33.3% 38.7% 218 .876 .042 .048 .007 .017 .005 .006 SPD 22.7% 27.5% 64 .045 .858 .011 .024 .052 .004 .006 FDP 14.4% 9.3% 0 .458 .048 .448 .011 .021 .009 .005 The Left 11.7% 10.9% 16 .031 .128 .017 .757 .048 .014 .005 Green Party 10.6% 9.0% 1 .061 .333 .021 .036 .536 .008 .004 Others 5.9% 2.9% 0 .133 .130 .090 .114 .125 .378 .030 Invalid 1.4% 1.7% -- .117 .079 .021 .025 .013 .013 .732 Notes: Entries denote each party's number of direct mandates, share of the list and candidate vote, as well as the frequency of different list and candidate vote combinations (calculated as fraction of a party's list vote) in the 2009 federal election. Due to rounding entries may not add up to unity. Source: Author's calculations based on Bundeswahlleiter (2009a, 2010). Table 2A: Summary Statistics for Electoral Precincts Variable Number of Eligible Voters Turnout Share of Candidate Vote (in %): CDU/CSU SPD FDP The Left Green Party Others Share of List Vote (in %): CDU/CSU SPD FDP The Left Green Party Others Absentee Precinct West Germany 2005 2009 821.5 834.2 (385.4) (387.6) .789 .727 (.071) (.083) East Germany 2005 2009 782.9 802.5 (460.3) (487.7) .751 .658 (.069) (.084) 41.07 (13.02) 32.23 (12.61) 7.04 (3.93) 9.66 (9.67) 6.87 (5.29) 3.08 (2.88) 44.81 (13.33) 38.73 (12.66) 4.59 (2.25) 3.95 (3.06) 5.46 (3.78) 2.38 (2.75) 41.94 (11.49) 28.80 (10.71) 9.66 (3.74) 7.35 (4.01) 9.32 (5.23) 2.88 (2.59) 29.65 (9.93) 31.35 (8.28) 5.16 (2.85) 24.86 (7.37) 3.76 (5.80) 5.22 (3.10) 32.94 (10.32) 20.03 (7.54) 8.17 (3.73) 28.61 (8.46) 5.53 (6.08) 4.72 (2.70) 35.47 (11.60) 27.98 (10.91) 12.01 (4.83) 10.43 (9.23) 8.83 (5.38) 5.23 (2.85) 38.67 (12.48) 34.22 (10.84) 10.10 (3.56) 4.83 (3.09) 8.38 (4.87) 3.71 (2.03) 35.59 (10.25) 23.62 (8.63) 15.18 (4.61) 8.40 (4.26) 10.93 (5.25) 6.23 (2.76) 26.21 (8.59) 29.96 (7.16) 8.00 (3.25) 25.05 (6.26) 4.78 (4.13) 6.01 (3.03) 30.65 (8.92) 17.95 (5.94) 10.57 (3.76) 28.27 (7.56) 5.90 (4.93) 6.66 (3.03) Full Sample 820.7 (406.1) .747 (.087) .148 .155 .166 .090 .098 (.355) (.362) (.372) (.286) (.297) 177,425 71,614 72,056 17,110 16,645 Notes: Entries are means and standard deviations for all precinct level variables used in the analysis, differentiating between East and West Germany as well as election year. See the Data Appendix for a precise definition of each variable. Table 2B: Characteristics of Direct Candidates Variable Party Affiliation FDP The Left Full Sample CDU/CSU SPD Age 47.16 (11.97) 49.14 (9.72) 48.87 (9.83) 44.96 (11.29) Female .226 (.418) .191 (.393) .353 (.478) Doctorate .109 (.312) .204 (.403) Currently Member of Parliament .231 (.422) Holds Direct Mandate Also on Party List Position on Party List | Also List Candidate Green Party Others 49.29 (10.48) 44.01 (10.97) 46.94 (14.45) .169 (.375) .259 (.438) .344 (.475) .139 (.346) .134 (.341) .161 (.367) .090 (.287) .105 (.306) .041 (.199) .652 (.477) .602 (.490) .161 (.367) .083 (.277) .148 (.356) .002 (.039) .111 (.315) .376 (.485) .403 (.491) .000 (.000) .009 (.092) .003 (.058) .001 (.028) .626 (.484) .759 (.428) .950 (.218) .888 (.316) .434 (.496) .546 (.498) .414 (.493) 12.89 13.26 17.36 17.47 9.40 8.89 7.32 (12.86) (12.79) (15.46) (15.32) (8.19) (6.94) (7.02) 4,257 598 598 598 587 593 1,283 Notes: Entries are means and standard deviations of characteristics of direct candidates running in the 2005 or 2009 federal elections, by party affiliation. See the Data Appendix for the precise definition and source of each variable. Table 3: Ranking of Candidates in the 2005 & 2009 Federal Elections Rank Based on Candidate Vote 1 2 Rank Based on List Vote 3 4 1 557 38 3 2 39 502 3 2 4 5 6 0 0 0 54 3 0 0 44 369 139 39 5 0 14 131 306 138 9 5 0 0 39 139 332 87 6 0 0 2 11 88 474 Total 598 598 598 598 597 575 First or Runner-Up 99.7% 90.3% 9.5% 0.5% 0.0% 0.0% Notes: Entries denote the number of candidates for each combination of own rank based on received candidate votes (left column) and the within district ranking of the associated party based on the list vote in the same year (top row). For instance, out of the 598 candidates whose party received the most list votes within a particular district, 557 won the direct mandate for that district, 39 candidates finished in second place, and 2 ended up third. The rank order correlation within districts is .93. Table 4: Preference Based Rank and the Candidate-List-Vote Gradient Share of Candidate Vote Independent Variable (1) (2) (3) (4) (5) Share of List Vote × Ranked First Share of List Vote × Ranked Second 1.023 (.024) 1.141 (.019) 1.004 (.019) 1.062 (.012) .983 (.008) 1.011 (.017) .998 (.011) 1.037 (.015) Share of List Vote × Ranked Third Share of List Vote × Ranked Fourth Share of List Vote × Ranked Fifth Share of List Vote × Ranked Sixth 1.066 (.075) .707 (.025) .809 (.018) .817 (.044) .852 (.053) .711 (.026) .846 (.014) .823 (.042) .780 (.045) .691 (.030) .795 (.014) .787 (.045) .730 (.052) .653 (.031) .782 (.014) .765 (.047) 4.999 (1.238) -.494 (.857) -4.331 (.718) .259 (.241) .078 (.093) .200 (.078) 6.174 (.944) 3.093 (.482) 5.053 (1.054) 6.944 (.676) 5.507 (.574) 5.900 (.686) 1.197 (.304) .926 (.286) 5.107 (.786) 6.147 (.815) 5.123 (.536) 5.400 (.695) Preference Based Rank: First Second Third Fourth Fifth Sixth 44.518 (1.949) 29.490 (1.840) 11.205 (1.385) 7.002 (.423) 5.502 (.117) 3.885 (.239) Party Fixed Effects No No Yes No No Candidate Fixed Effects No No No Yes No Candidate × Year Fixed Effects No No No No Yes R-Squared .777 .953 .965 .980 .982 Number of Observations 882,061 882,061 882,061 882,061 882,061 Notes: Entries are coefficients and standard errors from regressing the variables shown on the left on a candidate's vote share. Heteroskedasticity robust standard errors are clustered by state and reported in parentheses. See the Data Appendix for the precise definition and source of each variable. Independent Variable Table 5: Estimating the Extent of Strategic Voting Share of Candidate Vote (1) (2) (3) (4) Share of List Vote × Non-Contender Share of List Vote × Contender Non-Contender .688 (.050) 1.165 (.018) .724 (.016) 1.063 (.014) .698 (.020) .982 (.010) (5) .657 (.019) 1.004 (.012) 6.366 .303 6.673 .698 (.221) (.328) (.731) (.020) Contender 33.678 -1.353 3.402 .982 (1.275) (.553) (.595) (.010) Party Fixed Effects No No Yes No No Candidate Fixed Effects No No No Yes No Candidate × Year Fixed Effects No No No No Yes R-Squared .620 .950 .965 .980 .982 Number of Observations 882,061 882,061 882,061 882,061 882,061 Notes: Entries are coefficients and standard errors from estimating equation (4) by ordinary least squares. The structural break is estimated to occur at κ=.064. Heteroskedasticity robust standard errors are clustered by state and reported in parentheses. See the Data Appendix for the precise definition and source of each variable. Table 6: Comparative Statics Share of Strategic Voters Candidate Candidate × Year Fixed Effects Fixed Effects Restriction Baseline By Availability of Close Substitute: Allied Party's Candidate in the Race Only Rival Parties' Candidates in the Race By Closeness of Race Based on Preferences: less than 5% between First and Second more than 5% between First and Second By Ex Post Closeness of Race: less than 5% between First and Second more than 5% between First and Second By Year: 2005 2009 .302 (.020) .343 (.019) .328 (.015) .093 (.019) .362 (.015) .093 (.019) .351 (.027) .317 (.021) .350 (.026) .339 (.022) .350 (.026) .307 (.021) .360 (.026) .336 (.022) .452 (.027) .251 (.020) --- Notes: Entries are coefficients and standard errors on 1-λ using different subsamples of the data. The respective restriction is indicated on the left of each row. See the Data Appendix for the precise definition and source of each variable. Table 7: Candidate-List-Vote Gradient among Second Ranked Candidates Distance to First Ranked Candidate Based on Preferences: < 2% behind First Ranked Candidate 2% to 5% behind First Ranked Candidate 5% to 10% behind First Ranked Candidate 10% to 15% behind First Ranked Candidate > 15% behind First Ranked Candidate Based on Ex Post Outcome of Races: < 2% behind First Ranked Candidate 2% to 5% behind First Ranked Candidate 5% to 10% behind First Ranked Candidate 10% to 15% behind First Ranked Candidate > 15% behind First Ranked Candidate Candidate Fixed Effects Slope Candidate × Year Fixed Effects 1.026 (.013) 1.019 (.012) 1.057 (.015) 1.041 (.021) 1.018 (.025) 1.025 (.013) 1.019 (.012) 1.058 (.015) 1.044 (.021) 1.033 (.023) 1.022 (.020) 1.043 (.014) 1.047 (.014) 1.058 (.022) 1.007 (.018) 1.025 (.020) 1.042 (.014) 1.049 (.014) 1.061 (.024) 1.022 (.016) Notes: Entries denote the candidate-list-vote gradient for second ranked candidates, by distance to the first ranked one. The respective cutoffs are shown in the column on the left. Heteroskedasticity robust standard errors are clustered by state and reported in parentheses. Table 8: Sensitivity Analysis Using Alternative Classifications of Contenders Classification of Contenders Share of Strategic Voters Candidate Candidate × Year Fixed Effects Fixed Effects Baseline (Preference Based, Original Cutoff) .302 (.020) .343 (.019) Ex Post Outcome of Races (Original Cutoff) .299 (.016) .345 (.018) .255 (.026) .268 (.024) .293 (.021) .306 (.019) .238 (.026) .295 (.029) .307 (.027) .331 (.021) .352 (.017) .282 (.030) .269 (.023) .274 (.022) .290 (.018) .308 (.015) .277 (.021) .310 (.027) .317 (.026) .337 (.020) .350 (.018) .350 (.018) Ranked First or Second Based on Preferences .243 (.027) .284 (.030) Ranked First, Second, or Third Based on Preferences .269 (.023) .299 (.023) Ranked First or Second Based on Ex Post Outcome .264 (.024) .305 (.029) Ranked First, Second, or Third Based on Ex Post Outcome .334 (.013) .371 (.013) Finished First or Second in Last Federal Election .250 (.027) .287 (.032) Finished First, Second, or Third in Last Federal Election .289 (.014) .319 (.015) Finish in Last Federal Election (Original Cutoff) .274 (.022) .316 (.026) .252 (.026) .256 (.026) .271 (.023) .279 (.021) .252 (.023) .291 (.031) .296 (.030) .313 (.027) .322 (.024) .293 (.026) Preference Based Using Different Cutoffs: < 1% behind Second Ranked Candidate < 2% behind Second Ranked Candidate < 5% behind Second Ranked Candidate < 8% behind Second Ranked Candidate Electoral District × Year Specific Cutoffs Ex Post Outcome of Races Using Different Cutoffs: < 1% behind Second Ranked Candidate < 2% behind Second Ranked Candidate < 5% behind Second Ranked Candidate < 8% behind Second Ranked Candidate Electoral District × Year Specific Cutoffs Finish in Last Federal Election Using Different Cutoffs: < 1% behind Second Ranked Candidate < 2% behind Second Ranked Candidate < 5% behind Second Ranked Candidate < 8% behind Second Ranked Candidate Estimated Electoral District × Year Specific Cutoffs Notes: Entries are coefficients and standard errors on 1-λ using alternative classifications of "contender." The respective definition is shown in the column on the left. Heteroskedasticity robust standard errors are clustered by state and reported in parentheses. Table 9: Additional Sensitivity and Robustness Checks Restriction Share of Strategic Voters Candidate Candidate × Year Fixed Effects Fixed Effects Baseline .302 (.020) .343 (.019) Weighted by Number of Party Supporters .295 (.032) .334 (.028) Including "Other" Party Candidates .319 (.021) .351 (.019) In States without Overhang Mandates .346 (.014) .378 (.013) Difference Estimator .285 (.025) .347 (.027) Notes: Entries are coefficients and standard errors on the share of strategic voters, i.e. 1-λ, using different subsamples of the data and weighting schemes. The respective restriction is indicated on the left of each row. See the Data Appendix for the precise definition and source of each variable. Independent Variable Share of List Vote × Contender Share of List Vote × Non-Contender Table 10: Correlates of Strategic Voting Share of Candidate Vote (1) (2) (3) (4) 1.008 1.008 1.008 1.008 (.009) (.009) (.009) (.009) .666 .644 .664 .605 (.031) (.029) (.030) (.033) Share of List Vote × Non-Contender × Population Density Share of List Vote × Non-Contender × Fraction of Voters Female Share of List Vote × Non-Contender × Income Tax Revenue per Capita (5) 1.008 (.009) .679 (.022) -.005 (.007) .019 (.023) -.271 (.078) Share of List Vote .244 × Non-Contender × Fraction of Voters under Age 30 (.074) Candidate × Year Fixed Effects Yes Yes Yes Yes Yes R-Squared .984 .984 .984 .984 .984 Number of Observations 120,700 120,700 120,700 120,700 120,700 Notes: Entries are coefficients and standard errors from estimating specifications analogous to equation (4) by ordinary least squares, with a structural break at κ=.064. Heteroskedasticity robust standard errors are clustered by state and reported in parentheses. For ease of interpretation, covariates interacted with Share of List Vote × Non-Contender have been demeaned. In addition to the variables shown in the table, indicator variables for missing values on each covariate are also included in the regressions. See the Data Appendix for the precise definition and source of each variable. Table 11: Actual vs Predicted Ranking of Candidates, 2009 Federal Elections Predicted Rank (as Fraction of Actual Rank) 2 3 4 Actual Rank 1 5 1 94.6% 5.1% 0.3% 0.0% 0.0% 2 5.1% 91.8% 3.1% 0.0% 0.0% 3 0.3% 3.1% 88.1% 7.5% 1.0% 4 0.0% 0.0% 8.2% 86.1% 5.8% 5 0.0% 0.0% 0.3% 6.5% 93.2% Notes: Entries denote the frequency with which the predictions of the structural model in Section 7 coincide with observed outcomes, considering only candidates of the 5 major parties. Table 12: Voters' Partial Preference Orderings First Choice Candidate CDU/CSU Second Choice Candidate (as Fraction of First Choice) CDU/CSU SPD FDP The Left Green Party -- 26.8% 50.0% 8.1% 15.1% SPD 16.1% -- 0.3% 15.5% 68.0% FDP 98.9% 0.6% -- 0.1% 0.4% The Left 18.0% 60.4% 0.1% -- 21.5% Green Party 14.5% 77.1% 0.4% 8.1% -- Notes: Entries denote the simulated relative frequency of voters' second choice candidate, conditional on their first choice. See Appendix D for details on the simulation. Table 13: Joint Distribution of District Winners under Sincere and Strategic Voting District Winner with Sincere Voters CDU/CSU District Winner with Sincere and Strategic Voters CDU/CSU SPD FDP The Left Green Party 70.8% 1.7% 0.0% 1.0% 0.3% SPD 6.5% 16.7% 0.0% 0.3% 0.0% FDP 0.0% 0.0% 0.0% 0.0% 0.0% The Left 0.0% 0.3% 0.0% 1.7% 0.0% Green Party 0.3% 0.0% 0.0% 0.0% 0.3% Notes: Entries compare the simulated distribution of district winners in a first-past-the-post system with only sincere voters (left column) to the one that would obtain with a mixture of types (top row). Summing across columns gives the percentage of districts that would acrue to a particular party if all voters behaved sincerely, whereas summing across rows gives a party's share of districts if 26.3% of voters behaved strategically. Consequently, adding the entries on the diagonal shows that about 90% of districts would accrue to the same party. See Appendix D for details on the simulation.