the political impact of social penumbras

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Data on putts in pro golf

Distance from hole (feet)

Pro

babi

lity

of s

ucce

ss

1346/1443

577/694

337/455

208/353

149/272136/256

111/240

69/21767/200

75/237

52/20246/192

54/174

28/167

27/20131/195

33/19120/147

24/152

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What's the probability of making a golf putt?


Pro

babi

lity

of s

ucce

ss

Logistic regression, a = 2.2, b = −0.3

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Geometry-based model

x

Rr

−2σ 0 2σ3/33

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);

}

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What's the probability of making a golf putt?


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lity

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ucce

ss

Geometry−based model, sigma = 1.5

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Two models fit to the golf putting data


Pro

babi

lity

of s

ucce

ss

Logistic regression, a = 2.2, b = −0.3

Geometry−based model, sigma = 1.5

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A tougher model

1. Sum of declining exponentials:

y = a1e−b1x + a2e

−b2x

2. Statistical version:

yi = (a1e−b1xi + a2e

−b2xi ) · εi

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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);

}

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Simulate fake data in R

# Set up the true parameter valuesa <- c(.8, 1)b <- c(2, .1)sigma <- .2

# Simulate datax <- (1:1000)/100N <- length(x)ypred <- a[1]*exp(-b[1]*x) + a[2]*exp(-b[2]*x)y <- ypred*exp(rnorm(N, 0, sigma))

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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 Rhata[1] 1.00 0.00 0.03 0.95 0.99 1.00 1.02 1.05 494 1a[2] 0.70 0.00 0.08 0.56 0.65 0.69 0.75 0.87 620 1b[1] 0.10 0.00 0.00 0.09 0.10 0.10 0.10 0.11 532 1b[2] 1.71 0.02 0.34 1.15 1.48 1.67 1.90 2.49 498 1sigma 0.19 0.00 0.00 0.19 0.19 0.19 0.20 0.20 952 1

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Try again with new parameter values

mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhata[1] 1.33e+00 0.54 0.77 0.00 1.28 1.77e+00 1.79e+00 1.82e+00 2 44.23a[2] 2.46e+294 Inf Inf 0.00 0.00 0.00e+00 1.77e+00 2.66e+188 2000 NaNb[1] 1.00e-01 0.04 0.06 0.00 0.10 1.30e-01 1.30e-01 1.40e-01 2 33.64b[2] 3.09e+305 Inf Inf 0.13 0.50 1.15e+109 4.77e+212 5.28e+298 2000 NaNsigma 2.00e-01 0.00 0.00 0.19 0.19 2.00e-01 2.00e-01 2.00e-01 65 1.06

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Informative prior distribution

log_a ~ normal(0, 1);log_b ~ normal(0, 1);

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Happy ending

mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhata[1] 1.56 0.09 0.32 0.65 1.52 1.72 1.75 1.79 13 1.25a[2] 0.32 0.08 0.28 0.06 0.14 0.22 0.37 1.13 13 1.20b[1] 0.13 0.00 0.01 0.10 0.12 0.13 0.13 0.14 22 1.14b[2] 1.94 0.20 2.29 0.14 0.22 1.26 3.00 7.34 127 1.05sigma 0.20 0.00 0.00 0.19 0.19 0.20 0.20 0.21 656 1.00

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The political impact of social penumbras

Andrew Gelman and Yotam Margalit

Department of Statistics and Department of Political ScienceColumbia University, New York

8 Apr 2016

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I 1996: co-sponsored the Defense of Marriage Act,defining marriage as one man and one woman

I 1999: voted for a measure prohibiting same-sexcouples from adopting children.

I 2011: “openly hostile” record on gay rights led toa mass protest of students at the University ofMichigan against Portman speaking at thegraduation ceremony

I “Rob believes marriage is a sacred bond betweenone man and one woman”—Portman spokesmanto Cleveland Plain Dealer at the time of theprotest

I Sen. RobPortman(R-Ohio)

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I 2013: “I’m announcing today a change of heart[for] gay marriage. . .My son came to Jane, mywife, and I, told us that he was gay, and that itwas not a choice, and that it’s just part of whohe is, and that’s who he’d been that way for aslong as he could remember.”

I “I’ve come to the conclusion that . . . [marriage] issomething that we should allow people to do. . . and to have the joy and stability of marriagethat I’ve had for over 26 years.”

I Portman also mentioned his consultation withformer Vice President Dick Cheney, whose owndaughter’s coming out: “forced him to re-thinkthe issue too, and over time, he changed his viewon it”

I Sen. RobPortman(R-Ohio)

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Research questions

1. To what extent does familiarity with members of a certainsocial group influence people’s views on public policies relatedto that group?

17/33

Penumbra

18/33

Social penumbra

I Size and the shape of the penumbra can relate to the politicalsalience and influence of a social group

19/33

Research questions

1. To what extent does familiarity with members of a certainsocial group influence people’s views on public policies relatedto that group?

2. To what extent does the social penumbra of a group—itsshape and size—matter for explaining public preferences onkey policies?

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Penumbras and change in public opinion?

I 2004: Karl Rove puts gay marriage on the ballot in key statesto help mobilize mass support in favor of Bush

I 2012: Karl Rove criticizes the Democrats for “using the issueof gay marriage for political gain”

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Our data

I Panel designI Two surveys administered by YouGov 12 months apartI 3,000 respondents in wave 1; 2,106 re-interviewed in wave 2I Penumbra membership in 14 social groups and 8 namesI Attitude questions on 12 related policiesI Also GSS in 2006 and 2014

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Active Military

●

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)

Notes: Group sizes given from various internet sources. Penumbras estimated from our 2013 survey. Proportions are indicated by areas, with the gray circle in each caserepresenting the entire U.S. adult population. The data show oddities arising from ambiguity in survey responses (what counts as "a serious health problem," "governmentwelfare," etc.), confusions about definitions (for example, of active military service), and secret−keeping (for example, not everyone learns that you have had an abortion).

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Walter

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Rose

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Bruce

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Tina

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Kyle

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Emily

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Jose

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Maria

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Walter+Rose+...+Emily

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Jose + Maria

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All 8 names

Number of people with each name (area of red circle) and penumbra (areas of black circle indicates number of peoplewho know at least one person with this name) compared to the population of American adults (light gray circle)

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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%

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

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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

Family OtherFriends

01

2

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Active Military

Family OtherFriends

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2

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Immigrant in Past 5 Yrs

Family OtherFriends

01

2

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NRA Member

Family OtherFriends

01

2

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Abortion in Past 5 Yrs

Family OtherFriends

01

2

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Lost Job Last Year

Family OtherFriends

01

2●

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Muslim

Family OtherFriends

01

2

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Gay/Lesbian

Family OtherFriends

01

2

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Currently Unemployed

Family OtherFriends

01

2

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Mortgage Underwater

Family OtherFriends

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2

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No Health Insurance

Family OtherFriends

01

2●

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Care for Elder

Family OtherFriends

01

23

45

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Gun Owner

Family OtherFriends

01

2

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Receive Govt Welfare

Family OtherFriends

01

2

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Serious Health Problem

Average number of people known in each group, among Democrats (blue), Independents (purple), and Republicans (red)

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Family OtherFriends

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Active Military

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Family OtherFriends

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NRA Member

Family OtherFriends

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2

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Family OtherFriends

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2

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Lost Job Last Year

Family OtherFriends

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2

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Muslim

Family OtherFriends

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23

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Gay/Lesbian

Family OtherFriends

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2

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Family OtherFriends

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Mortgage Underwater

Family OtherFriends

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2

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No Health Insurance

Family OtherFriends

01

2●

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Care for Elder

Family OtherFriends

01

23

45

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Gun Owner

Family OtherFriends

01

2

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Average number of people known in each group, among low, middle, and high−income respondents(indicated by thin, intermediate, and thick lines)

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Is penumbra membership associated with group-relevantattitudes?

I Do you think the number of immigrants from foreign countrieswho are permitted to come to the United States to live shouldbe increased, decreased, or left the same as it is now?

I Do you agree or disagree: Homosexual couples should have theright to marry one another.

I Some are calling for the government to provide tax breaks forfamily expenditures on care provision for elderly familymembers. Others worry that such tax breaks would add to thenational debt. Do you support or oppose providing tax breaksfor care provision to the elderly?

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More policy questions related to core groups

I Would you support or oppose a law requiring a nationwide banon the sale of assault weapons?

I Which comes closest to your point of view: As a general rule,do you think the United States should be willing to usemilitary force around the world, or the United States should bevery reluctant to use military force?

I Do you agree or disagree with the following statement: “It isthe responsibility of the federal government to make sure thatall Americans have healthcare coverage.”

I Etc.

30/33

2.0

3.0

4.0

Active Military

Penumbra score

Avg

atti

tude

on

Mili

tary

For

ce

0 1 2 3

2.0

3.0

4.0


Penumbra score

Avg

atti

tude

on

Allo

w Il

lega

l Im

mig

rant

0 1 2 3

2.0

3.0

4.0

NRA Member

Penumbra score

Avg

atti

tude

on

NO

T W

eapo

n B

an

0 1 2 3

2.0

3.0

4.0


Penumbra score

Avg

atti

tude

on

Leg

al A

bort

ion

0 1 2 3

2.0

3.0

4.0

Lost Job Last Year

Penumbra score

Avg

atti

tude

on

Une

mpl

oyed

Ben

efits

0 1 2 32.

03.

04.

0

Muslim

Penumbra score

Avg

atti

tude

on

NO

T M

uslim

air

port

scr

een

0 1 2 3

2.0

3.0

4.0

Gay/Lesbian

Penumbra score

Avg

atti

tude

on

Hom

esex

ual M

arria

ge

0 1 2 3

2.0

3.0

4.0


Penumbra score

Avg

atti

tude

on

Une

mpl

oyed

Ben

efits

0 1 2 3

2.0

3.0

4.0

Mortgage Underwater

Penumbra score

Avg

atti

tude

on

Pre

vent

For

cecl

osur

e

0 1 2 3

2.0

3.0

4.0

No Health Insurance

Penumbra score

Avg

atti

tude

on

Gov

t Hea

lthca

re

0 1 2 3

2.0

3.0

4.0

Care for Elder

Penumbra score

Avg

atti

tude

on

Tax

bre

ak

0 1 2 3

2.0

3.0

4.0

Gun Owner

Penumbra score

Avg

atti

tude

on

NO

T W

eapo

n B

an

0 1 2 3

2.0

3.0

4.0


Penumbra score

Avg

atti

tude

on

Pub

lic A

ssis

tanc

e

0 1 2 3

2.0

3.0

4.0


Penumbra score

Avg

atti

tude

on

Gov

t Hea

lthca

re

0 1 2 3

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Coefs predicting change in attitude,given entrance into the penumbra

−0.2 −0.1 0.0 0.1 0.2

Serious Health ProblemReceive Govt Welfare

Gun OwnerCare for Elder

No Health InsuranceMortgage UnderwaterCurrently Unemployed

Gay/LesbianMuslimMuslimMuslim

Lost Job Last YearAbortion in Past 5 Yrs

NRA MemberImmigrant in Past 5 YrsImmigrant in Past 5 YrsImmigrant in Past 5 Yrs

Active Military

●

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I Small but nonzero effectsI No effects with cross-predictions, reverse-time predictions

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Summary

I Social penumbras are a politically meaningful conceptI Penumbra membership is associated with group-related policy

views.I Entering a penumbra can lead to attitude shiftsI Penumbra’s shape might help explain speed and patterns of

change in public opinion

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the political impact of social penumbras

Data & Analytics