Supporting information for: Affective polarization and the salience of elections Electoral Studies Enrique Hernández, Eva Anduiza and Guillem Rico Universitat Autònoma de Barcelona APPENDIX A: Operationalization and descriptive data Figure A1: Countries and elections included in the analyses 2 Figure A2: Google searches for main parties and candidates one month before/after election day in 4 countries. 3 Figure A3: Average timing of interviews in each election study. 4 Table A1: Correlation between main variables Affective Time since Ideological Positive party Age Income Gender Education Labor market polarization election day polarization attachment status Time since election day -0.0233 Ideological polarization 0.476 -0.0219 Positive party attachment 0.353 -0.0373 0.164 Age 0.0950 -0.0117 0.0330 0.103 Income -0.0139 -0.0104 0.00128 0.0447 -0.176 Gender 0.0301 -0.000928 0.0354 -0.0325 -0.00975 -0.0867 Education -0.0406 -0.0298 -0.0407 0.0731 -0.125 0.315 -0.0339 Labor market status 0.0711 -0.0269 0.0349 0.0259 0.370 -0.286 0.183 -0.233 Rural/Urban -0.0130 -0.0629 -0.0128 0.0414 -0.0513 0.131 0.0160 0.182 -0.0585 Table A2: Operationalization and descriptive statistics of main variables Wording / Coding Mean SD Min Max Affective polarization Affective polarization (spread) measure coded following equations 1 and 2 (based on Wagner (2019) 2.37 1.11 0 7.65 Time since election day Number of days that passed between the election day and the day when each respondent was interviewed. 41.57 62.63 0 362 Time since election day (log) Natural log transformation of the variable measuring the number of days that passed between election day 3.1 1.08 0 5.89 and the day when each respondent was interviewed Time since election day (rescaled) Number of days that passed between the election day and the day when each respondent was interviewed -0.05 0.46 -0.35 2.29 rescaled following Gelman (2008). The variable is transformed by subtracting its mean and dividing it by two times its standard deviation. Time since election day (log rescaled) Natural log transformation of the variable measuring the number of days that passed between election day 0 0.5 -1.43 1.29 and the day when each respondent was interviewed rescaled following Gelman (2008). The variable was first log transformed and then rescaled following Gelman (2008) Ideological polarization Ideological polarization measure coded following equations 1 and 2 but based on each respondent placement 2.46 1.02 0 7.68 of each of the parties included in the CSES on the 0-10 left-right scale instead of the extent to which they like or dislike these parties (based on Wagner 2019) Positive party attachment Variable measuring how close citizens feel to the party they identify with. The variable measuring the 1.26 1.09 0 3 strength of party identification is based on the 3 categories item IMD3005_4 from the IMD CSES dataset, which we reverse code so that higher values imply greater closeness to a party. This survey item directly captures how close citizens feel to the party they identify with. We add an additional residual category (=0) to this variable based on the responses to IMD3005_1, IMD3005_2, and IMD3005_3. This residual category represents respondents who do not feel close to any party. Respondents are assigned the value 0 in this variable if they fulfill two conditions. First, these respondents declared that they did not feel close (code 5 in IMD3005_1) or closer (code 5 in IMD3005_2) to any party. Second, these respondents were, at the same time, coded either as missing (code 9999999), or were not capable (don’t know answer) or refused naming the party they feel close to (codes 9999998 and 9999997) in question IMD3005_3. Note that in some 5 countries the question on leaners (IMD3005_2) was not asked and this is likely to reduce the share of respondents who are presented with item IMD3005_4. These country-elections are: Australia (2004, 2013), Canada (1997), Switzerland (2007), Latvia (2011, 2014), Norway (2005, 2009, 2013), New Zealand (1996), Slovenia (1996, 2008, 2011). Age Age of respondents 47 16.83 16 102 Age (rescaled) Age of respondent rescaled following Gelman (2008). 0 0.49 -0.9 1.61 Income Categorical variable measuring the household income of respondents in 5 categories (from lowest income 3 1.39 1 5 group = 1 to highest income group = 5) Gender Catgorical variable measuring the gender of respondents in 2 categories (1= Male 2= Female) 1.52 0.5 1 2 Education Categorical variable measuring the level of education of respondents in 5 categories, ranging from no 2.1 1.2 0 4 education = 0 to university education = 4 Labor market status Categorical variable measuring the labor market status of individuals in 6 categories 2.32 1.68 1 7 Rural/Urban Categorical variable mesuaring whether the respondent lives in a village = 1, a small town = 2, the suburbs 2.57 1.21 1 4 of a large city = 3, or a large city = 4. Maximum affect Maximum level of affect for the party(ies) respondents like the most. That is, the variable captures the 7.87 1.99 0 10 highest score assigned in like-dislike scale to any party by each respondent. Minimum affect Minimum level of affect for the party(ies) respondents like the laest. That is, the variable captures the lowest 1.46 1.82 0 10 score assigned in like-dislike scale to any party by each respondent. 6 Figure A4: Distribution of main variables Note: Y-axis with different scales 7 APPENDIX B: Additional results (affective polarization spread measure) Table B1: Impact of time since election day on affective polarization (numeric covariates rescaled).1 (1) (2) (3) (4) (5) Time since election day -0.38*** -0.33*** -0.36*** -0.62*** (0.03) (0.03) (0.03) (0.07) Time since election day (squared) 0.11** (0.04) Time since election day (log) -0.15*** (0.01) Constant 2.39*** 2.39*** 2.36*** 2.39*** (0.05) (0.05) (0.05) (0.04) Observations 116027 116027 116027 116027 116027 Elections 99 99 99 99 99 Country-election random-intercepts Yes Yes Yes Yes No Individual-level covariates No Yes Yes Yes Yes Country-election fixed-effects No No No No Yes Note: Models 1-4 are mixed effects linear models. Model 5 is a non-parametric series regression with a cross- validation criterion used to select the optimal number of terms in a third-order B-spline basis function. In model 5, coefficients report average marginal effects estimates based on the average of derivatives. Standard errors in parentheses (in Model 5 robust standard errors are reported). *p < 0.05, ** p < 0.01, *** p < 0.001 Table B2: Impact of time since election day on affective polarization (numeric covariates not rescaled). (1) (2) (3) (4) (5) Time since election day -0.003*** -0.002*** -0.003*** -0.004*** (0.000) (0.000) (0.000) (0.000) Time since election day (squared) 0.000** (0.000) Time since election day (log) -0.070*** (0.006) Constant 2.524*** 2.503*** 2.498*** 2.606*** (0.047) (0.049) (0.047) (0.049) Observations 116027 116027 116027 116027 116027 Elections 99 99 99 99 99 Country-election random-intercepts Yes Yes Yes Yes No Individual-level covariates No Yes Yes Yes Yes Country-election fixed-effects No No No No Yes Note: Models 1-4 are mixed effects linear models. Model 5 is a non-parametric series regression with a cross- validation criterion used to select the optimal number of terms in a third-order B-spline basis function. In model 5, coefficients report average marginal effects estimates based on the average of derivatives. Standard errors in parentheses (in Model 5 robust standard errors are reported). *p < 0.05, ** p < 0.01, *** p < 0.001 1 To facilitate the interpretation of the results we rescale numeric covariates (time since election day and age) by subtracting their mean and dividing them by two times their standard deviation (see data and methods section). 8 Table B3: Impact of time since election day on the evaluation of the most- and least-liked parties: mixed-effects linear models (numeric covariates rescaled). (1. Most (2. Least (3. Most (4. Least (5. Most (6. Least liked party) liked party) liked party) liked party) liked party) liked party) Time since election day -0.45*** 0.38*** -0.48*** 0.46*** (0.05) (0.05) (0.06) (0.05) Time since election day (squared) 0.08 -0.29*** (0.06) (0.06) Time since election day (log) -0.20*** 0.20*** (0.02) (0.02) Constant 7.92*** 1.73*** 7.89*** 1.81*** 7.92*** 1.72*** (0.06) (0.08) (0.06) (0.08) (0.06) (0.07) Observations 116027 116027 116027 116027 116027 116027 Elections 99 99 99 99 99 99 Country-election random-intercepts Yes Yes Yes Yes Yes Yes Individual-level covariates Yes Yes Yes Yes Yes Yes Note: Standard errors in parentheses. *p < 0.05, ** p < 0.01, *** p < 0.001 Figure B1: Time since election day (log transformed) and affective polarization Note: Based on Model 4 of Table B2 in the Appendix. The histogram in the background summarizes the distribution of the log transformed variable measuring the number of days that passed between the election day and the day when each respondent was interviewed. 9 Figure B2: Estimates of the effects of “time since election day” on affective polarization excluding one country at a time. Note: All estimates are based on a mixed-effects linear model with country-election random intercepts and individual level-covariates. The variable time since-election day is rescaled, so that a one-unit increase represents the effect of a change in two standard deviations. That is, the estimates replicate the results of Model 2 of Table B1, excluding one country a time. 10 Figure B3: Estimates of the effects of “time since election day” on affective polarization excluding one election at a time. Note: All estimates are based on a mixed-effects linear model with country-election random intercepts and individual level-covariates. The variable time since-election day is rescaled, so that a one-unit increase represents the effect of a change in two standard deviations. That is, the estimates replicate the results of Model 2 of Table B1, excluding one election a time. 11 Figure B4: Estimates of the effects of “time since election day” (not rescaled) on affective polarization using different windows of days after election day. Note: All estimates are based on mixed-effects linear models with country-election random intercepts and individual level-covariates. The plot is based on 356 different models that include a limited number of days after the election (x-axis). Like in Table B2, the variable measuring the time since election day is not rescaled. Therefore, the point estimates represent the effect of an increase in one day after the election on affective polarization. That is, the estimates replicate the results of Model 2 of Table B2, varying the number of days included in the estimation sample. Dashed lines represent 95 percent confidence intervals around point estimates. 12 Figure B5: Quantile regression model of affective polarization and the time since election day Note: The solid black line reports the estimates of the effect of the time since election day on affective polarization at different points of the distribution of affective polarization (obtained through a quantile regression). The shaded area summarizes a 95 percent confidence interval around those estimates. The estimation is based on a quantile regression model that includes the same individual-level covariates as those models summarized in Table B1 as well as country-election fixed-effects. The dotted red line represents the effects of the time since election day on affective polarization estimated through an OLS regression model and its corresponding 95 confidence intervals. The overlap between the confidence intervals of the quantile regression and the OLS regression indicates that there is no significant variation in the estimated effects of time since election day depending on the level of affective polarization of individuals. 13 Table B4: Summary of results of generalized random-intercepts linear structural equation model (1) Equation 1: Affective polarization Ideological polarization 0.388*** (0.00) Positive party attachment 0.295*** (0.00) Time since election day -0.128*** (0.03) Individual-level covariates Yes M2[country-election] 1 (Constrained) (.) Constant 1.153*** Equation 2: Ideological polarization (0.03) Time since election day -0.297*** (0.03) Individual-level covariates Yes M1[country-election] 1 (Constrained) (.) Constant 2.445*** Equation 3: Positive party attachment (0.05) Time since election day -0.272*** (0.03) Individual-level covariates Yes M3[country-election] 1 (Constrained) (.) Constant 1.054*** Random-intercepts variances: (0.05) M1[country-election] 0.251*** M2[country-election] 0.070*** M3[country-election] 0.169*** Error variances: Affective polarization 0.742*** Ideological polarization 0.837*** Positive party attachment 1.005*** Observations 113943 Elections 99 * p < 0.05, ** p < 0.01, *** p < 0.001 14 Table B5: Summary of results of generalized random-intercepts linear structural equation model (time since election day variable log transformed) (1) Equation 1: Affective polarization Ideological polarization 0.389*** Positive party attachment 0.295*** Time since election day (log) -0.064*** Individual-level covariates Yes M2[country-election] 1 (Constrained) (.) Constant 1.151*** Equation 2: Ideological polarization (0.03) Time since election day (log) -0.143*** Individual-level covariates Yes M1[country-election] 1 (Constrained) (.) Constant 2.448*** Equation 3: Positive party attachment (0.05) Time since election day (log) -0.119*** (0.03) Individual-level covariates Yes M3[country-election] 1 (Constrained) (.) Constant 1.069*** Random-intercepts variances: (0.05) M1[country-election] 0.223*** M2[country-election] 0.068*** M3[country-election] 0.164*** Error variances: Affective polarization 0.742*** Ideological polarization 0.837*** Positive party attachment 1.005*** Observations 113943 Elections 99 * p < 0.05, ** p < 0.01, *** p < 0.001 15 Figure B6: Main paths from generalized structural equation model). Table B6: Mediation analysis: Total, direct and indirect effects of time since election day on affective polarization (time since election day variable log transformed) Effect p-value Proportion of total effect Total effect -0.15 -11.03 1.00 Direct effect -0.06 -5.11 0.41 Mediated by ideological polarization -0.05 -11.27 0.36 Mediated by positive party attachment -0.03 -8.62 0.23 Note: Based on the model summarized in Table B5 16 APPENDIX C: Alternative operationalization of affective polarization (distance measure) The distance measure of affective polarization is also based on the 0-10 like-dislike score respondents attribute to each of parties included in the CSES. This operationalization measures the weighted average affective distance from one’s most liked party to all other parties (Wagner, 2019). To operationalize the distance measure, we follow again the notation proposed by Wagner (2019). Therefore, affective polarization is measured as: 𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸𝑖 𝑃 2 = √∑ 𝑣𝑝 (𝑙𝑖𝑘𝑒𝑖𝑝 − 𝑙𝑖𝑘𝑒𝑚𝑎𝑥,𝑖 ) (3) 𝑝=1 where 𝑙𝑖𝑘𝑒𝑚𝑎𝑥 is the 0-10 score assigned to the most liked party by individual 𝑖 , and 𝑝 is the number of parties without the most liked party (see Wagner (2019) for further details about the operationalization of this measure). This measure, therefore, excludes those who assign the same like-dislike score to all parties in each CSES post-electoral study. Table D1: Impact of time since election day on affective polarization (distance measure): Mixed-effects linear regressions (numeric covariates rescaled) (1) (2) (3) (4) Time since election day -0.45*** -0.38*** -0.47*** (0.05) (0.05) (0.05) Time since election day (squared) 0.25*** (0.06) Time since election day (log) -0.20*** (0.02) Constant 3.86*** 3.82*** (0.07) (0.07) Observations 111242 111242 111242 111242 Elections 99 99 99 99 Country-election random-intercepts Yes Yes Yes Yes Individual-level covariates No Yes Yes Yes Note: Standard errors in parentheses. *p < 0.05, ** p < 0.01, *** p < 0.001 17 Figure D1: Main paths from generalized structural equation model (distance measure) Table D2: Mediation analysis: Total, direct and indirect effects of time since election day on affective polarization (distance measure) Effect p-value Proportion of total effect Total effect -0.40 -7.50 Direct effect -0.10 -1.99 0.24 Mediated by ideological polarization -0.17 -9.81 0.43 Mediated by positive party attachment -0.13 -8.50 0.33 18