The Political Impact of Social Penumbras

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Delivered by Andrew Gelman (Statistics Professor, Columbia University) at the 2016 New York R Conference on April 8th and 9th at Work-Bench.

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The Political Impact of Social Penumbras

  1. 1. q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 0.00.20.40.60.81.0 Data on putts in pro golf Distance from hole (feet) Probabilityofsuccess 1346/1443 577/694 337/455 208/353 149/272 136/256 111/240 69/217 67/200 75/237 52/202 46/192 54/174 28/167 27/201 31/195 33/191 20/147 24/152 1/33
  2. 2. q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 0.00.20.40.60.81.0 What's the probability of making a golf putt? Distance from hole (feet) Probabilityofsuccess Logistic regression, a = 2.2, b = −0.3 2/33
  3. 3. Geometry-based model x R r −2σ 0 2σ 3/33
  4. 4. Stan code data { int J; int n[J]; real x[J]; int y[J]; real r; real R; } parameters { real<lower=0> sigma; } model { real p[J]; for (j in 1:J) p[j] <- 2*Phi(asin((R-r)/x[j]) / sigma) - 1; y ~ binomial(n, p); }
  5. 5. q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 0.00.20.40.60.81.0 What's the probability of making a golf putt? Distance from hole (feet) Probabilityofsuccess Geometry−based model, sigma = 1.5 5/33
  6. 6. q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 0.00.20.40.60.81.0 Two models fit to the golf putting data Distance from hole (feet) Probabilityofsuccess Logistic regression, a = 2.2, b = −0.3 Geometry−based model, sigma = 1.5 6/33
  7. 7. A tougher model 1. Sum of declining exponentials: y = a1e−b1x + a2e−b2x 2. Statistical version: yi = (a1e−b1xi + a2e−b2xi ) · i 7/33
  8. 8. Stan code data { int N; vector[N] x; vector[N] y;} parameters { vector[2] log_a; ordered[2] log_b; real<lower=0> sigma;} transformed parameters { vector<lower=0>[2] a; vector<lower=0>[2] b; a <- exp(log_a); b <- exp(log_b);} model { vector[N] ypred; ypred <- a[1]*exp(-b[1]*x) + a[2]*exp(-b[2]*x); y ~ lognormal(log(ypred), sigma); }
  9. 9. Simulate fake data in R # Set up the true parameter values a <- c(.8, 1) b <- c(2, .1) sigma <- .2 # Simulate data x <- (1:1000)/100 N <- length(x) ypred <- a[1]*exp(-b[1]*x) + a[2]*exp(-b[2]*x) y <- ypred*exp(rnorm(N, 0, sigma)) 9/33
  10. 10. Fit the model in Stan Inference for Stan model: exponentials. 4 chains, each with iter=1000; warmup=500; thin=1; post-warmup draws per chain=500, total post-warmup draws=2000. mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat a[1] 1.00 0.00 0.03 0.95 0.99 1.00 1.02 1.05 494 1 a[2] 0.70 0.00 0.08 0.56 0.65 0.69 0.75 0.87 620 1 b[1] 0.10 0.00 0.00 0.09 0.10 0.10 0.10 0.11 532 1 b[2] 1.71 0.02 0.34 1.15 1.48 1.67 1.90 2.49 498 1 sigma 0.19 0.00 0.00 0.19 0.19 0.19 0.20 0.20 952 1 10/33
  11. 11. Try again with new parameter values mean se_mean sd 2.5% 25% 50% 75% 9 a[1] 1.33e+00 0.54 0.77 0.00 1.28 1.77e+00 1.79e+00 1.82 a[2] 2.46e+294 Inf Inf 0.00 0.00 0.00e+00 1.77e+00 2.66e b[1] 1.00e-01 0.04 0.06 0.00 0.10 1.30e-01 1.30e-01 1.40 b[2] 3.09e+305 Inf Inf 0.13 0.50 1.15e+109 4.77e+212 5.28e sigma 2.00e-01 0.00 0.00 0.19 0.19 2.00e-01 2.00e-01 2.00 11/33
  12. 12. Informative prior distribution log_a ~ normal(0, 1); log_b ~ normal(0, 1); 12/33
  13. 13. Happy ending mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat a[1] 1.56 0.09 0.32 0.65 1.52 1.72 1.75 1.79 13 1.25 a[2] 0.32 0.08 0.28 0.06 0.14 0.22 0.37 1.13 13 1.20 b[1] 0.13 0.00 0.01 0.10 0.12 0.13 0.13 0.14 22 1.14 b[2] 1.94 0.20 2.29 0.14 0.22 1.26 3.00 7.34 127 1.05 sigma 0.20 0.00 0.00 0.19 0.19 0.20 0.20 0.21 656 1.00 13/33
  14. 14. The political impact of social penumbras Andrew Gelman and Yotam Margalit Department of Statistics and Department of Political Science Columbia University, New York 8 Apr 2016 14/33
  15. 15. Sen. Rob Portman (R-Ohio)
  16. 16. 1996: co-sponsored the Defense of Marriage Act, defining marriage as one man and one woman Sen. Rob Portman (R-Ohio)
  17. 17. 1996: co-sponsored the Defense of Marriage Act, defining marriage as one man and one woman 1999: voted for a measure prohibiting same-sex couples from adopting children. Sen. Rob Portman (R-Ohio)
  18. 18. 1996: co-sponsored the Defense of Marriage Act, defining marriage as one man and one woman 1999: voted for a measure prohibiting same-sex couples from adopting children. 2011: “openly hostile” record on gay rights led to a mass protest of students at the University of Michigan against Portman speaking at the graduation ceremony Sen. Rob Portman (R-Ohio)
  19. 19. 1996: co-sponsored the Defense of Marriage Act, defining marriage as one man and one woman 1999: voted for a measure prohibiting same-sex couples from adopting children. 2011: “openly hostile” record on gay rights led to a mass protest of students at the University of Michigan against Portman speaking at the graduation ceremony “Rob believes marriage is a sacred bond between one man and one woman”—Portman spokesman to Cleveland Plain Dealer at the time of the protest Sen. Rob Portman (R-Ohio)
  20. 20. Sen. Rob Portman (R-Ohio) 16/33
  21. 21. 2013: “I’m announcing today a change of heart [for] gay marriage. . . My son came to Jane, my wife, and I, told us that he was gay, and that it was not a choice, and that it’s just part of who he is, and that’s who he’d been that way for as long as he could remember.” Sen. Rob Portman (R-Ohio) 16/33
  22. 22. 2013: “I’m announcing today a change of heart [for] gay marriage. . . My son came to Jane, my wife, and I, told us that he was gay, and that it was not a choice, and that it’s just part of who he is, and that’s who he’d been that way for as long as he could remember.” “I’ve come to the conclusion that . . . [marriage] is something that we should allow people to do . . . and to have the joy and stability of marriage that I’ve had for over 26 years.” Sen. Rob Portman (R-Ohio) 16/33
  23. 23. 2013: “I’m announcing today a change of heart [for] gay marriage. . . My son came to Jane, my wife, and I, told us that he was gay, and that it was not a choice, and that it’s just part of who he is, and that’s who he’d been that way for as long as he could remember.” “I’ve come to the conclusion that . . . [marriage] is something that we should allow people to do . . . and to have the joy and stability of marriage that I’ve had for over 26 years.” Portman also mentioned his consultation with former Vice President Dick Cheney, whose own daughter’s coming out: “forced him to re-think the issue too, and over time, he changed his view on it” Sen. Rob Portman (R-Ohio) 16/33
  24. 24. Research questions 1. To what extent does familiarity with members of a certain social group influence people’s views on public policies related to that group? 17/33
  25. 25. Penumbra 18/33
  26. 26. Social penumbra Size and the shape of the penumbra can relate to the political salience and influence of a social group 19/33
  27. 27. Research questions 1. To what extent does familiarity with members of a certain social group influence people’s views on public policies related to that group? 2. To what extent does the social penumbra of a group—its shape and size—matter for explaining public preferences on key policies? 20/33
  28. 28. Penumbras and change in public opinion? 2004: Karl Rove puts gay marriage on the ballot in key states to help mobilize mass support in favor of Bush 2012: Karl Rove criticizes the Democrats for “using the issue of gay marriage for political gain” 21/33
  29. 29. Our data Panel design Two surveys administered by YouGov 12 months apart 3,000 respondents in wave 1; 2,106 re-interviewed in wave 2 Penumbra membership in 14 social groups and 8 names Attitude questions on 12 related policies Also GSS in 2006 and 2014
  30. 30. Active Military q Immigrant in Past 5 Yrs NRA Member Abortion in Past 5 Yrs Lost Job Last Year Muslim Gay/Lesbian Currently Unemployed Mortgage Underwater No Health Insurance Care for Elder Gun Owner Receive Govt Welfare Serious Health Problem Group size (area of red circle) and penumbras (areas of black circles indicate close family, close family + close friends, and close family + close friends + others known) compared to the population of American adults (light gray circle) 23/33
  31. 31. Walter q Rose q Bruce q Tina q Kyle q Emily q Jose q Maria q Walter+Rose+...+Emily q Jose + Maria q All 8 names Number of people with each name (area of red circle) and penumbra (areas of black circle indicates number of people who know at least one person with this name) compared to the population of American adults (light gray circle) 24/33
  32. 32. Know any Mortgage Underwater? sd 9% Know any Gun Owner? sd 7% Know any Gay/Lesbian? sd 6% Know any Immigrant in Past 5 Yrs? sd 5% Know any NRA Member? sd 5% Know any Active Military? sd 5% Know any Muslim? sd 4% Know any Receive Govt Welfare? sd 4% Know any No Health Insurance? sd 4% Know any Currently Unemployed? sd 3% Know any Lost Job Last Year? sd 3% Know any Care for Elder? sd 2% Know any Serious Health Problem? sd 2% Know any Abortion in Past 5 Yrs? sd 1% 25/33
  33. 33. Are you conservative? sd 5% Do you attend church regularly? sd 8% Know any Rose? sd 2% Know any Emily? sd 2% Know any Walter? sd 3% Know any Bruce? sd 3% Know any Tina? sd 3% Know any Kyle? sd 5% Know any Maria? sd 6% Know any Jose? sd 10% Shades of blue: People in these states are more likely to know someone of that group Shades of tan: Less likely to know someone of that group 26/33
  34. 34. Family OtherFriends 012 q q q q q q q q q Active Military Family OtherFriends 012 q q q q q q q q q Immigrant in Past 5 Yrs Family OtherFriends 012 q q qq q q q q q NRA Member Family OtherFriends 012 q q q q q q q q q Abortion in Past 5 Yrs Family OtherFriends 012 q q q q q q q q q Lost Job Last Year Family OtherFriends 012 q q q q q q q q q Muslim Family OtherFriends 012 q q q q q q q q q Gay/Lesbian Family OtherFriends 012 q q q q q q q q q Currently Unemployed Family OtherFriends 012 q q q q q q q q q Mortgage Underwater Family OtherFriends 012 q q q q q q q q q No Health Insurance Family OtherFriends 012 q q qq q qq q q Care for Elder Family OtherFriends 012345 q q q q q q q q q Gun Owner Family OtherFriends 012 q q q q q q q q q Receive Govt Welfare Family OtherFriends 012 q q q q q q q q q Serious Health Problem Average number of people known in each group, among Democrats (blue), Independents (purple), and Republicans (red) 27/33
  35. 35. Family OtherFriends 012 q q q q q q q q q Active Military Family OtherFriends 012 q q q q q q q q q Immigrant in Past 5 Yrs Family OtherFriends 012 q q q q q q q q q NRA Member Family OtherFriends 012 q q q q q qq q q Abortion in Past 5 Yrs Family OtherFriends 012 q q q q q q q q q Lost Job Last Year Family OtherFriends 012 q q q q q q q q q Muslim Family OtherFriends 0123 q q q q q q q q q Gay/Lesbian Family OtherFriends 012 q q q q q q q q q Currently Unemployed Family OtherFriends 012 q q q q q q q q q Mortgage Underwater Family OtherFriends 012 q q q q q q q q q No Health Insurance Family OtherFriends 012 q q q q q q q q q Care for Elder Family OtherFriends 012345 q q q q q q q q q Gun Owner Family OtherFriends 012 q q q q q q q q q Receive Govt Welfare Family OtherFriends 012 q q q q q q q q q Serious Health Problem Average number of people known in each group, among low, middle, and high−income respondents (indicated by thin, intermediate, and thick lines) 28/33
  36. 36. Is penumbra membership associated with group-relevant attitudes? Do you think the number of immigrants from foreign countries who are permitted to come to the United States to live should be increased, decreased, or left the same as it is now? Do you agree or disagree: Homosexual couples should have the right to marry one another. Some are calling for the government to provide tax breaks for family expenditures on care provision for elderly family members. Others worry that such tax breaks would add to the national debt. Do you support or oppose providing tax breaks for care provision to the elderly?
  37. 37. More policy questions related to core groups Would you support or oppose a law requiring a nationwide ban on the sale of assault weapons? Which comes closest to your point of view: As a general rule, do you think the United States should be willing to use military force around the world, or the United States should be very reluctant to use military force? Do you agree or disagree with the following statement: “It is the responsibility of the federal government to make sure that all Americans have healthcare coverage.” Etc.
  38. 38. 2.03.04.0 Active Military Penumbra score Avgattitudeon MilitaryForce 0 1 2 3 2.03.04.0 Immigrant in Past 5 Yrs Penumbra score Avgattitudeon AllowIllegalImmigrant 0 1 2 3 2.03.04.0 NRA Member Penumbra score Avgattitudeon NOTWeaponBan 0 1 2 3 2.03.04.0 Abortion in Past 5 Yrs Penumbra score Avgattitudeon LegalAbortion 0 1 2 3 2.03.04.0 Lost Job Last Year Penumbra score Avgattitudeon UnemployedBenefits 0 1 2 3 2.03.04.0 Muslim Penumbra score Avgattitudeon NOTMuslimairportscreen 0 1 2 3 2.03.04.0 Gay/Lesbian Penumbra score Avgattitudeon HomesexualMarriage 0 1 2 3 2.03.04.0 Currently Unemployed Penumbra score Avgattitudeon UnemployedBenefits 0 1 2 3 2.03.04.0 Mortgage Underwater Penumbra score Avgattitudeon PreventForceclosure 0 1 2 3 2.03.04.0 No Health Insurance Penumbra score Avgattitudeon GovtHealthcare 0 1 2 3 2.03.04.0 Care for Elder Penumbra score Avgattitudeon Taxbreak 0 1 2 3 2.03.04.0 Gun Owner Penumbra score Avgattitudeon NOTWeaponBan 0 1 2 3 2.03.04.0 Receive Govt Welfare Penumbra score Avgattitudeon PublicAssistance 0 1 2 3 2.03.04.0 Serious Health Problem Penumbra score Avgattitudeon GovtHealthcare 0 1 2 3 31/33
  39. 39. Coefs predicting change in attitude, given entrance into the penumbra −0.2 −0.1 0.0 0.1 0.2 Serious Health Problem Receive Govt Welfare Gun Owner Care for Elder No Health Insurance Mortgage Underwater Currently Unemployed Gay/Lesbian Muslim Muslim Muslim Lost Job Last Year Abortion in Past 5 Yrs NRA Member Immigrant in Past 5 Yrs Immigrant in Past 5 Yrs Immigrant in Past 5 Yrs Active Military q q q q q q q q q q q q q q q q q q Small but nonzero effects No effects with cross-predictions, reverse-time predictions 32/33
  40. 40. Summary Social penumbras are a politically meaningful concept Penumbra membership is associated with group-related policy views. Entering a penumbra can lead to attitude shifts Penumbra’s shape might help explain speed and patterns of change in public opinion

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