SUPPLEMENTARY INFORMATION Letters https://doi.org/10.1038/s41562-018-0302-y In the format provided by the authors and unedited. Asking about social circles improves election predictions M. Galesic 1,2 *, W. Bruine de Bruin 3,4,5, M. Dumas 1,6, A. Kapteyn 5, J. E. Darling 5,7 and E. Meijer 5 1 Santa Fe Institute, Santa Fe, NM, USA. 2 Max Planck Institute for Human Development, Berlin, Germany. 3 Centre for Decision Research, Leeds University Business School, University of Leeds, Leeds, UK. 4 Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA. 5 Center for Economic and Social Research, University of Southern California, Los Angeles, CA, USA. 6 London School of Economics, London, UK. 7 VHA Health Services Research and Development Center for the Study of Healthcare Innovation, Implementation, and Policy, VHA Greater Los Angeles Health Care System, Los Angeles, CA, USA. *e-mail: galesic@santafe.edu Nature Human Behaviour www.nature.com/nathumbehav 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
Supplementary Information Asking about social circles improves election predictions M. Galesic 1,2,*, W. Bruine de Bruin 3-5, M. Dumas 1,6, A. Kapteyn 5, J.E. Darling 5,7, E. Meijer 5 1 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501. 2 Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany. 3 Centre for Decision Research, Leeds University Business School, University of Leeds, Maurice Keyworth Building, Leeds LS2 9JT, UK. 4 Department of Engineering and Public Policy, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh PA 15213. 5 Center for Economic and Social Research, University of Southern California, 635 Downey Way, Los Angeles, CA 90089-3332. 6 London School of Economics, Houghton St, London WC2A 2AE, UK. 7 VHA Health Services Research and Development Center for the Study of Healthcare Innovation, Implementation, and Policy, VHA Greater Los Angeles Health Care System, Los Angeles, CA, USA *galesic@santafe.edu, Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 1
Difference in support Clinton - Trump Supplementary Figure 1. Own and social-circle reports for nine different groups of participants, defined by the correspondence of their voting a week before the election and their actual voting behaviour. Participants whose actual voting behaviour was in line with their stated had social circles with higher percentage of individuals intending to vote for the same candidate (panels on the diagonal, A, E, and I). In contrast, participants who switched from their intended candidate to another candidate (panels B and D) had more heterogeneous social circles, equally likely to support both main candidates. Also interesting are participants who said they would not vote but who did vote (panels G and H). Both they and their social circles showed much stronger preference for a particular candidate over time than the participants who said they would not vote and indeed did not (panel I). Finally, participants who said they would vote but did not had similar profiles as those who said they would vote for a particular candidate and did so (panels C vs. A, and F vs. E), suggesting that most non-voters ended up not voting for reasons unrelated to their voting preferences. Data are for N=1,263 individuals who participated in USC s survey waves in August, September, early November, and immediately after the election. Shown are unweighted probabilities of voting for Trump and Clinton that participants provided for themselves and their social circles. Participants were classified as being likely to vote for a particular candidate only if they reported more than 50% chance that they would vote in the election; otherwise they were classified as will not vote. Error bars show ±1 standard error. 2
Voted for:trump, State:RR Voted for:clinton, State:RR Percentage of social circle supporting Trump Voted for:trump, State:DR Voted for:trump, State:DD Percentage of social circle supporting Clinton Voted for:clinton, State:DR Voted for:clinton, State:DD Age:18-34 Age:35-64 Age:65+ Supplementary Figure 2. Changes in percentage of like-minded members of their social circle, for participants who voted for different candidates, belonged to different age groups, and were from different states (RR: predicted Republican voted Republican; DR: predicted Democrat voted Republican; DD: predicted Democrat voted Democrat). Error bars are ±1 standard error. Data are for N=1,263 individuals who participated in all four study waves. Shown are unweighted proportions of participants social circles that they reported would vote (or had voted) for their preferred candidate. 3
Voted for:trump, State:RR Voted for:clinton, State:RR Percentage of social circle supporting Trump Voted for:trump, State:DR Voted for:trump, State:DD Percentage of social circle supporting Clinton Voted for:clinton, State:DR Voted for:clinton, State:DD Edu:Up to high school Edu:Some college Edu:BA or higher Supplementary Figure 3. Changes in percentage of like-minded members of their social circle, for participants who voted for different candidates, belonged to different education (Edu) groups, and were from different states (RR: predicted Republican voted Republican; DR: predicted Democrat voted Republican; DD: predicted Democrat voted Democrat). Error bars are ±1 standard error. Data are for N=1,263 individuals who participated in all four study waves. Shown are unweighted proportions of participants social circles that they reported would vote (or had voted) for their preferred candidate. 4
Supplementary Table 1. Social-circle reports provided a week before the election contribute to the explanation of post-election reports of voting behaviour, over and above own voting and election-winner expectations. Results of linear regressions for voting in the election (vs. not) and voting for different candidates. Voting behaviour reported post-election (November 9-21) Voted at all Voted for Trump Voted for Clinton Voted for other candidate Model with only own voting (October 31-November 7).94**.97**.96**.82** Constant 2.46 (1.97) 3.11** (.).53 (.86) -.16 (.53) AIC 11,351 9,501 9,636 9,165 Model with own voting + social-circle reports (October 31-November 7).91**.** Social-circle reports.10**.15**.14**.09 (.06) Constant -3.20 (2.62) -.74 (1.06) -2.48* (1.08) -.49 (.57) AIC 11,342 9,473 9,618 9,165 Model with own voting + social-circle reports + election-winner expectations (October 31-November 7).** Social-circle reports.15**.14**.09 (.06) Election-winner expectations.01 -.03 -.07 (.08) Constant -.92 (1.24) -1.58 (1.51) -.48 (.57) AIC 9,475 9,620 9,166 Note: Analysis of voting vs. not voting is based on N=1,263 individuals who participated in the USC election poll in August, September, late October/early November, and immediately after the election. Analyses of voting for Trump, Clinton, and other candidates are based on those participants who voted in the election (N=1,086). Regression coefficients for own voting, social-circle reports and election-winner expectations refer to the behaviour mentioned in the associated column header. All estimates are unweighted. *p<.05, **p<=.01. Binary correlations (Pearson r) between own and social circles are for voting.41, for Trump.75, for Clinton.74, for other.43. Variance inflation factors for models with social-circle reports are nevertheless low: for voting 1.2, for Trump 2.5, for Clinton 2.5, for Other 1.2. Even though the criteria analysed here are all binary variables, we present linear rather than logit regressions for several reasons 17 : (a) our starting hypothesis was that participants correctly report their actual voting probabilities P i, rather than overestimating small values and underestimating large ones, which would be implied by a logit model with P i as an explanatory variable; (b) implementing this hypothesis into a logit model with ln(p i/(1-p i)) as an explanatory variable would leave many cases undefined as many respondents gave either a 0% or a % answer; (c) our explanatory variables are probabilities that bound most of the predictions to a range of approximately 0% to %; (d) linear regression provides a convenient way of assessing our predictors (own and social-circle reports). If they are perfect, their linear coefficients should sum to 1, and the intercept should be indistinguishable from 0. The fact that we observe roughly such a pattern in all linear regressions except the one for other candidates suggests that own and social-circle reports are good predictors of own voting. These conclusions were completely supported by additional logit regression analyses. AIC=Akaike Information Criterion. 5
Supplementary Table 2a. Social-circle reports provided in August contribute to the explanation of voting in September, over and above own voting provided in August. Results of linear regressions for to vote in the election and to vote for different candidates. Intention to vote Intentions reported September 12-24 Intention to vote Intention to vote for Trump vs. for Clinton vs. another candidate another candidate Intention to vote for other candidate vs. Trump or Clinton Model with only own voting (August 8-20).86**.94**.94**.84** Constant 13.5** (1.18) 3.46** (.56) 2.32** (.) 1.78** (.48) AIC 10,130 10,368 10,416 10,422 Model with own voting + social-circle reports (August 8-20).83**.** Social-circle reports.07** (0.02).10**.09**.12** Constant 9.76** (1.48) 1.23 (.71).01 (.76) 1.4 (.49) AIC 10,115 10,344 10,396 10,9 Note: Analysis of voting vs. not voting is based on N=1,263 individuals who participated in the USC election poll in August, September, late October/early November, and immediately after the election. Regression coefficients for own voting and social-circle reports refer to the behaviour mentioned in the associated column header. All estimates are unweighted. *p<.05, **p<=.01. Election-winner expectations do not contribute to explanation of own, except for Clinton (b =.05, SE =.02, p =.04, AIC = 10,393). 6
Supplementary Table 2b. Social-circle reports provided in September contribute to the explanation of voting in late October and November, over and above own voting provided in September. Results of linear regressions for to vote in the election and to vote for different candidates. Intention to vote Intentions reported from October 31 to November 7 Intention to vote Intention to vote Intention to vote for for Trump vs. for Clinton vs. other candidate vs. another candidate another candidate Trump or Clinton Model with only own voting (September 12-24).84**.97**.95**.78** Constant 15.2** (1.52) 3.53** (.77) 2.92** (.83).44 (.61) AIC 10,673 11,135 11,279 11,018 Model with own voting + social-circle reports (September 12-24).81**.91**.74** Social-circle reports.09**.10**.13**.11** (.04) Constant 10.94** (1.84).95 (1.03) -.37 (1.08).10 (.62) AIC 10,659 11,123 11,259 11,013 Note: Analysis of voting vs. not voting is based on N=1,263 individuals who participated in the USC election poll in August, September, late October/early November, and immediately after the election. Regression coefficients for own voting and social-circle reports refer to the behaviour mentioned in the associated column header. All estimates are unweighted. *p<.05, **p<=.01. Election-winner expectations do not contribute to explanation of own, except for Clinton (b =.08, SE =.03, p =.02, AIC = 11,256). 7
Supplementary Table 3. Relation between reported voting and actual voting behaviour: Percentage (N) of participants for each combination of and behavior. Did not vote Total voting behaviour 14% (177) Voting behaviour reported post-election (November 9-21) Voted for Trump % (502) Voted for Clinton 38% (484) Voted for other 7% (87) Voted unknown a 1% (13) Total voting % (1,263) (October 31 November 7) Will not vote b 87% (125) 5% (7) 6% (8) 1% (2) 1% (2) 11% (144) Will vote for Trump 3% (17) 94% (458) 1% (7) 0% (1) 1% (3) 38% (486) Will vote for Clinton 4% (22) 3% (13) 91% (454) 2% (8) 1% (3) % (500) Will vote for Other 11% (10) 9% (9) 5% (5) 72% (68) 3% (3) 8% (95) Undecided 8% (3) 39% (15) 26% (10) 21% (8) 5% (2) 3% (38) Note: Columns 2 6 sum to %. The intended candidate is defined as the one to whom the participant assigned the highest probability of voting for (if several candidates are given the same probability, the participant is coded as undecided). a Participants who reported they had voted but not for whom. Results are for N=1,263 individuals who participated in survey waves in August, September, late October/early November, and immediately after the election. b Participants who said there was a less than 50% chance they would vote in the election. 8
Supplementary Table 4. Dynamic interplay between own and social circles over time: results of vector autoregression modeling 23,24 Trump voters Clinton voters Other voters coef. (SE) coef. (SE) coef. (SE) Voting in the election Own Lag 1 own 0.96** (0.20) 1.18** (0.28) 0.86** (0.27) Lag 1 social circle 0.20** (0.08) 0.17* (0.08) 0.33 (0.20) Social circle Lag 1 own 1.05** (0.35) -0.25 (0.35) 0.19 (0.17) Lag 1 social circle 0.38** (0.15) -0.09 (0.11) 0.27 (0.29) Voting for a particular candidate Own Lag 1 own 1.46** (0.23) 2.16** (0.52) 4.70 (3.65) Lag 1 social circle 0.65** (0.18) 1.24* (0.51) 0.31 (0.79) Social circle Lag 1 own 0.69** (0.15) -0.35 (0.22) -2.49 (1.97) Lag 1 social circle 0.64** (0.13) -0.35 (0.23) -0.09 (0.44) Note: Analyses are based on unweighted probabilities to vote for Trump and Clinton, which participants provided for themselves and their social circles. See main text for additional details. Results are for N=1,263 individuals who participated in survey waves in August, September, late October/early November, and immediately after the election. *p<.05. **p.01. 9
Supplementary Table 5. Social circles influence voting behaviour of Trump and Clinton voters: Granger causality tests 23,24 for the influence of social circles as reported in the current wave on own to vote in the next wave, and vice versa, for the influence of own to vote in the current wave on social circle reports in the next wave Trump voters Clinton voters Other voters χ 2 p χ 2 p χ 2 p Voting in the election Social circles cause own 6.24.012 4.87.027 2.70. Own cause social circles 9.12.003 0.50.481 1.20.273 Voting for a particular candidate Social circles cause own 13.15.000 5.87.015 0.16.693 Own cause social circles 21.93.000 0.12.116 1..206 Note: Analyses are based on unweighted probabilities of voting for Trump and Clinton, which participants provided for themselves and their social circles. Results are for N=1,263 individuals who participated in survey waves in August, September, late October/early November, and immediately after the election. 10
Supplementary Table 6. Repeated-measures analysis of variance to test the extent and moderators of average levels ( between individuals ) and changes over time ( within individuals ) in percentage of like-minded voters Trump voters Clinton voters F p F p Between individuals Age 5.76.003 1.20.302 Education 0.37.693 0.32.723 State category 0.58.558 4.41.013 Age Education 1.10.356 1.49.205 Age State category 0..525 1.07.369 Education State category 1.97.098 1.62.168 Within individuals Wave 9.82.000 4..010 Wave Age 2.89.021 0.17.954 Wave Education 0.85.494 0.68.4 Wave State category 3.72.005 0.11.979 Wave Age Education 0.92.497 0.42.908 Wave Age State category 2.01.043 0.58.792 Wave Education State category 1.91.055 2.25.022 Adjusted R 2.64.65 Note: Age is coded as up to 34, 35 64, and 65+ years. Education is coded as high school or less, some college, college or more. States are coded as predicted Republican voted Republican, predicted Democrat voted Republican, and predicted Democrat voted Democrat. Supplementary Figs. 2 and 3 illustrate statistically reliable interactions, noted here in bold. Higher order interactions are not statistically reliable. Greenhouse Geisser epsilon is.99 for Trump voters and.98 for Clinton voters; Huynh Feldt correction for sphericity is used for withinindividual estimates. Results are for N=1,263 individuals who participated in survey waves in August, September, late October/early November, and immediately after the election. The results can be interpreted as follows (see also Supplementary Figs. 2 and 3): For Trump voters, homogenization of social circles was particularly pronounced among older voters, aged 65 or older, in particular in states that voted Republican (including those critical states that were predicted to vote Democrat). In states that voted Democrat, Trump voters in this age group started to homogenize a bit later than in states voting Republican (from September rather than from August 2016). Trump voters in other age groups showed a bit less homogenization, although there was a positive trend among younger groups in strongly Republican states. Education played an additional role, with less educated Trump voters homogenizing more and faster than more educated ones across states. For Clinton voters, age did not predict homogenization, but education and state did. In strongly Republican states, Clinton voters with higher education had the least homogeneous social circles. However, in strongly Democrat states, more educated Clinton voters had somewhat more homogeneous circles than less educated ones, in particular earlier in the election period (in August 2016). 11