5cm probabilistic models in political...
TRANSCRIPT
Probabilistic Models in Political Science
Pablo Barber
´
a
Center for Data ScienceNew York University
www.pablobarbera.com
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Two approaches to the study of social media and politics:
1. How social media platforms transform politicalcommunication
. Are social media creating ideological “echo
chambers”?
2. Social media as digital traces of political behavior. Can we infer latent individual traits (e.g. political
ideology) from online ties (follows, likes...)?
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Inferring political ideology using Twitter data
I Two common patterns about social behavior:1. Homophily: clustering in social networks along common
traits (“birds of a feather tweet together”)2. Selective exposure: preference for information that
reinforces current views and for avoiding opinionchallenges.
I Social media networks replicate offline networks.I
Key assumption: individuals prefer to follow politicalaccounts they perceive to be ideologically close.
I These decisions contain information about allocation ofscarce resource (attention).
I Use this information to estimate ideological locations ofpoliticians and individuals on the latent same scale.
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Political Accounts
NYTimeskrugman
senrobportman
maddow
FiveThirtyEight
HRC
WhiteHouseBarackObama
Bar
ackO
bam
a
Whi
teH
ouse
GO
P
mad
dow
FoxN
ews
HR
C
...
pol.
acco
unt
m
ryanpetrik 1 1 0 1 0 1 . . .user 2 0 0 1 0 1 0 . . .user 3 0 0 1 0 1 0 . . .user 4 1 1 0 0 0 1 . . .user 5 0 1 0 0 0 1 . . .
. . .user n 0 1 1 0 0 0 . . .
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Spatial following model
I Users’ and politicians’ ideology (✓i
and �j
) are defined aslatent variables to be estimated.
I Data: “following” decisions, a matrix of binary choices (Yij
).I Spatial following model: for n users, indexed by i , and m
political accounts, indexed by j :
P(yij
= 1|↵j
, �i
, �, ✓i
, �j
) = logit�1⇣↵
j
+ �i
� �(✓i
� �j
)2⌘
where:↵
j
measures popularity of politician j
�i
measures political interest of user i
� is a normalizing constant
More
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Intuition of the model
Probability that Twitter user i follows politician j , as a function ofthe user’s ideology:
φj1 = −1.51 αj1 = 3.51φj2 = 1.09 αj2 = 2.59
−2 0 2θi, Ideology of Twitter user i
Pr(y
ij=
1)
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Estimation
I Goal of learning:I ✓
i
: ideological positions of users i = 1, . . . , n
I �j
: ideological positions of political accounts j = 1, . . . , m
I Likelihood function:
p(y|✓,�, ↵,�, �) =nY
i=1
mY
j=1
logit�1(⇡ij
)y
ij (1 � logit�1(⇡ij
))1�y
ij
where ⇡ij
= ↵j
+ �i
� �(✓i
� �j
)2
I Exact inference is intractable ! MCMC (approx. inference)I Estimation:
I First stage: HMC in Stan with random sample of Y to computeposterior distribution of j-indexed parameters.
I Second stage: parallelized MH in R for rest of i-indexedparameters (assuming independence), on NYU’s HPC.
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Data
Im = list of 620 popular political accounts in the U.S.! Legislators, president, candidates, other political figures,
media outlets, journalists, interest groups. . .
In = followers of at least one of these accounts! 30.8M users (⇠75% of U.S. users)! 100K of these were matched with voter files
I States: AK, CA, FL, OH, PA.I Unique, perfect matches on first and last name, and county.
I Code:I Method: github.com/pablobarbera/twitter ideologyI Applications: github.com/SMAPPNYU/echo chambersI Data collection: streamR, Rfacebook packages for R
(available on CRAN)I Data analysis: github.com/pablobarbera/pytwools (python)
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Results
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@sensanders@HillaryClinton
@nancypelosi@VP
@BarackObamaMedian House DMedian Senate D
@senjohnmccainMedian Senate R
Median House R@sentedcruz
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@motherjones@maddow
@NPR@msnbc
@nytimes@cnnbrk
@washingtonpost@FoxNews
@DRUDGE_REPORT@glennbeck
@limbaugh
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@HRC@glaad
@OccupyWallSt@dailykos
@aclu@hrw
@BrookingsInst@RANDCorporation
@CatoInstitute@AEI
@Heritage@nra
@redstatePolitical Actors Media Interest Groups
−1.5 0.0 1.5 −1.5 0.0 1.5 −1.5 0.0 1.5Position on latent ideological scale
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Validation
This method is able to correctly classify and scale Twitter userson the left-right dimension:
1. Political accountsI Correlation with measures based on roll-call votes.
2. Ordinary citizensI Individual and aggregate-level survey responsesI Voting registration files
It is also able to predict change over time.
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Political elites
Ideal Points of Members of the 113th U.S. Congress
House Senate
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ρD = 0.63
ρR = 0.46
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ρD = 0.66
ρR = 0.63
−2
−1
0
1
2
−2 −1 0 1 2 −2 −1 0 1 2Estimated Twitter Ideal Points
Ideo
logy
Est
imat
es B
ased
on
Roll−
Cal
l Vot
es(S
imon
Jack
man
's id
eal p
oint
est
imat
es)
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Ordinary Users
Comparison with ideology estimates from aggregated surveys(Lax and Phillips, 2012; Tausanovitch and Warshaw, 2013)
AL
AZ
AR
CA
CO
CTDE
FL
GA
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
NH
NJNM
NY
NC
ND
OH
OK
OR
PA
RI
SCSD
TN
TX
UT
VT
VA
WA
WV
WI
WY
ρ = −0.916
40%
45%
50%
55%
−0.4 −0.2 0.0 0.2 0.4 0.6Ideology of Median Twitter User in Each State
Mea
n Li
bera
l Opi
nion
(Lax
and
Phi
llips
, 201
2) ρ = 0.791
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−1.0
−0.5
0.0
0.5
−0.6 −0.4 −0.2 0.0 0.2 0.4Ideology of Median Twitter User in Each City
Publ
ic P
refe
renc
e Es
timat
e(T
ausa
novi
tch
and
War
shaw
, 201
3)
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Ordinary Users
Republicans are more conservative than Democrats
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Arkansas California Florida Ohio Pennsylvania
−2
−1
0
1
2
Dem Rep Dem Rep Dem Rep Dem Rep Dem RepParty Registration
θ i, T
witt
er−B
ased
Ideo
logy
Est
imat
es
Predictive accuracy for party affiliation is 83%
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Application: Ideology of Presidential Candidates
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@washingtonpost@nytimes
@msnbc@JimWebbUSA
@HillaryClinton@POTUS
@LincolnChafee@MotherJones
@GovernorOMalley@SenSanders
@SenWarren
@tedcruz@RealBenCarson
@ScottWalker@RandPaul@rushlimbaugh
@BobbyJindal@GovernorPerry
@GovernorPataki@JohnKasich@marcorubio@DRUDGE_REPORT@RepPaulRyan
@GrahamBlog@GovMikeHuckabee
@JebBush@RickSantorum
@FoxNews@GovChristie@CarlyFiorina
@realDonaldTrump@WSJ
Aver
age
Rep
ublic
anin
114
th C
ongr
ess
Aver
age
Twitt
er U
ser
Aver
age
Dem
ocra
tin
114
th C
ongr
ess
−2 −1 0 1 2Position on latent ideological scale
Twitter ideology scores of potential Democratic and Republican presidential primary candidates
Barbera “Who is the most conservative Republican candidate forpresident?” The Washington Post, June 16 2015
19 / 54
Application: Twitter as an Ideological Echo Chamber?Tweets mentioning Obama Tweets mentioning Romney
0
50K
100K
−2 0 2 −2 0 2Estimated Ideology
Co
un
t o
f S
en
t Tw
ee
ts
Obama Romney
−2
−1
0
1
2
−2 −1 0 1 2 −2 −1 0 1 2Estimated Ideology of Author
Est
ima
ted
Id
eo
log
y o
f R
etw
ee
ter
0.00%
0.25%
0.50%
0.75%
1.00%
1.25%
% of Tweets
Barbera (2015) “Birds of the Same Feather Tweet Together: BayesianIdeal Point Estimation Using Twitter Data.” Political Analysis
20 / 54
Application: Twitter as an Ideological Echo Chamber?
Barbera, Jost, Nagler, Tucker, & Bonneau (2015) “Tweeting From Leftto Right: Is Online Political Communication More Than an EchoChamber?” Psychological Science
21 / 54
Other applications
Ideology of media outletsIdeological AsymmetriesMultidimensional Policy Spaces
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Two approaches to the study of social media and politics:
1. How social media platforms transform politicalcommunication
. As voters are able to directly interact with politicians,
does the quality of political representation improve?
Social media as digital traces of political behavior. Are legislators’ and citizens’ social media messages a
valid proxy for the attention they give to different political
issues?
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Political Representation
Public Opinion Policy
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Political Representation
Issues Voters Discuss Issues Legislators Discuss
Do Legislators Accurately Represent Voters’ Interests?Who Leads? Who Follows?
Barbera, Nagler, Egan, Bonneau, Jost, & Tucker (2014) “Leaders orFollowers? Measuring Political Responsiveness in the U.S. CongressUsing Social Media Data.” APSA Conference Paper.
25 / 54
Outline
1. Analyze tweets sent by Members of U.S. Congress and theirfollowers using topic modeling techniques.
2. Estimate the importance (frequency of discussion) of 100different issues in the revealed expressed political agenda forlegislators and constituents
3. Political Congruence: are Members of Congressdiscussing the same set of issues as their constituents?
4. Political Responsiveness: do topics discussed byMembers of Congress temporally precede or follow topicsdiscussed by the voters?
26 / 54
Data
651,116 tweets by Members of U.S. Congress, from Jan. 1, 2013 toDec. 31, 2014 (113th Congress), collected by the Social Media andPolitical Participation Lab (SMaPP) using Twitter’s Streaming API.
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0
10
20
Feb−13 May−13 Aug−13 Nov−13 Feb−14 May−14 Aug−14 Nov−14 Feb−15
Twee
ts p
er W
eek
Membersof Congress
●
●
●
●
House DemocratsHouse Republicans
Senate DemocratsSenate Republicans
27 / 54
Citizens’ Tweets
Collected all tweets for 3 samples of citizens:1. Informed public:
I Followers of 5 major media outlets (CNN, FoxNews, MSNBC,NYT, WSJ) located in U.S. (filtered by time zone)
I Random sample of 10,000 (out of ⇠30M)2. Republican Party Supporters:
I Follow 3+ Rep MCs and no Dem MCsI Random sample of 10,000 (out of 203,140)
3. Democratic Party Supporters:I Follow 3+ Dem MCs and no Rep MCsI Random sample of 10,000 (out of 67,843)
28 / 54
Table : Number of tweets in dataset
Group N Avg. Min Max TweetsHouse Republicans 238 1,215 70 8,857 267,311House Democrats 207 1,177 113 5,993 222,491Senate Republicans 46 1,532 73 6,627 67,412Senate Democrats 56 1,616 150 10,736 87,307Informed Public 10K 948 2 5,861 9,487,382Rep. Supporters 10K 1,091 2 8,804 10,911,813Dem. Supporters 10K 1,306 2 5,122 13,058,947Period of analysis: January 1, 2013 to December 31, 2014.
29 / 54
Political Representation
Public Opinion Policy
Media
Media data:I 273,007 tweets from 36 largest media outlets in U.S. (print,
broadcast, online) over same period.
30 / 54
From Tweets to Topics
4 steps in our analysis1. Tweets from Members of Congress are preprocessed and
split by day, party and chamber (N=2,920 documents)2. Latent Dirichlet Allocation (Blei, 2003):
I Each document is a mixture over K = 100 latent topics.I Topics are distributions over V = 75, 000 n-grams (up to
trigrams, selected by frequency; keeping hashtags)I Estimated parameters:
� Distribution of n-grams over topics (K ⇥ V )✓ Distribution of topics over documents (K ⇥ N)
3. Similar text processing for tweets from citizens and NYTtweets (split by day and group)
4. Using simulation, compute posterior distribution of ✓F
forobserved n-grams for citizens and media
31 / 54
Latent Dirichlet allocation (LDA)I
Topic models are powerful tools for exploring large data setsand for making inferences about the content of documents
!"#$%&'() *"+,#)
+"/,9#)1+.&),3&'(1"65%51
:5)2,'0("'1.&/,0,"'1-
.&/,0,"'12,'3$14$3,5)%1&(2,#)1
6$332,)%1
)+".()165)&65//1)"##&.1
65)7&(65//18""(65//1
- -
I Many applications in information retrieval, documentsummarization, and classification
Complexity+of+Inference+in+Latent+Dirichlet+Alloca6on+David+Sontag,+Daniel+Roy+(NYU,+Cambridge)+
W66+Topic+models+are+powerful+tools+for+exploring+large+data+sets+and+for+making+inferences+about+the+content+of+documents+
Documents+ Topics+poli6cs+.0100+
president+.0095+obama+.0090+
washington+.0085+religion+.0060+
Almost+all+uses+of+topic+models+(e.g.,+for+unsupervised+learning,+informa6on+retrieval,+classifica6on)+require+probabilis)c+inference:+
New+document+ What+is+this+document+about?+
Words+w1,+…,+wN+ ✓Distribu6on+of+topics+
�t =�
p(w | z = t)�
…+
religion+.0500+hindu+.0092+
judiasm+.0080+ethics+.0075+
buddhism+.0016+
sports+.0105+baseball+.0100+soccer+.0055+
basketball+.0050+football+.0045+
…+ …+
weather+ .50+finance+ .49+sports+ .01+
I LDA is one of the simplest and most widely used topicmodels
32 / 54
Latent Dirichlet Allocation
I Document = random mixture over latent topicsI Topic = distribution over n-grams
Probabilistic model with 3 steps:1. Choose ✓
i
⇠ Dirichlet(↵)
2. Choose �k
⇠ Dirichlet(�)
3. For each word in document i :I Choose a topic z
m
⇠ Multinomial(✓i
)I Choose a word w
im
⇠ Multinomial(�i,k=z
m
)
where:↵=parameter of Dirichlet prior on distribution of topics over docs.✓
i
=topic distribution for document i
�=parameter of Dirichlet prior on distribution of words over topics�
k
=word distribution for topic k
33 / 54
EstimationI Applications that aggregate by author or day outperform
tweet-level analyses (Hong and Davidson, 2010)I K is fixed at 100 based on cross-validated model fit.
●
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● ●● ● ● ● ●
Perplexity
logLikelihood
0.80
0.85
0.90
0.95
1.00
10 20 30 40 50 60 70 80 90 100 110 120Number of topics
Rat
io w
rt wo
rst v
alue
I Text is parsed with scikit-learn in pythonI Estimation: Collapsed Gibbs Sampler in C++ (Griffits and
Steyvers, 2004), ported to R by Grun and Hornik (2011)34 / 54
Validation
j.mp/lda-congress-demo
35 / 54
Congruence
Are Members of Congress discussing the same set of issues astheir constituents?
Table : Contemporaneous Pearson Correlations in Topic Distribution
Dem RepGroup Mcs MCsDemocratic Members of Congress 1.00 0.22Republican Members of Congress 0.22 1.00Informed Public 0.33 0.39Republican Party Supporters 0.17 0.62Democratic Party Supporters 0.58 0.33Media 0.39 0.61
36 / 54
Responsiveness
Do legislators influence the public? Does the public influencelegislators?
To explore causal relationships between topic distributions, weuse a Granger-causality framework (Granger, 1969):I Regress proportion of tweets on topic k at time t by each
group on lagged proportions for all groups, using five lags.I Do legislators’ tweets predict tweets by the public, controlling
for the media, and vice versa?! Changes in tweets as proxies for changes in salience of
issues
37 / 54
Results: Democratic legislators
Public Legislators0.09
<0.00
Media
0.01
0.25
0.09
0.04
38 / 54
Results: Republican legislators
Public Legislators0.03
<0.00
Media
0.01
0.25
0.11
0.07
39 / 54
Conclusions
1. Social media as variable2. Social media as data
Future work / open questions:I More complex generative models for tweets that exploit
platform features (Author-Topic; Dynamic; Hierarchical)I Text- vs network-based estimates of political ideologyI Predicting latent probability to turn out to vote based on
tweet text, using voting registration recordsI Multilingual topic modelingI Detecting irony and sarcasm (Trump!)I Identifying bots and spam with user and text features only
40 / 54
Thanks!
website: pablobarbera.com
twitter: @p barbera
github: pablobarbera
41 / 54
Backup slides (index)
Model with covariatesModel identificationUnequal representationComparative responsiveness
42 / 54
Model with Covariates
Baseline model:
P(yij
= 1) = logit�1⇣↵
j
+ �i
� �(✓i
� �j
)2⌘
Model with geographic covariate:
P(yij
= 1) = logit�1⇣↵
j
+ �i
� �(✓i
� �j
)2 + �s
ij
⌘
where s
ij
= 1 if user i and political actor j are located in thesame state, and s
ij
= 0 otherwise.
� ⇡ 1.20 and � ⇡ 0.90
43 / 54
Model with CovariatesComparing Parameter Estimates Across Different Model
Specifications
φj, Elites' Ideology Estimates θi, Users' Ideology Estimates
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−2
−1
0
1
2
−2 −1 0 1 2 −2 −1 0 1 2Parameter Estimates (Model with Geographic Covariate)
Para
mete
r E
stim
ate
s (B
ase
line M
odel)
Index
44 / 54
Identification
P(yijt
= 1) = logit�1⇣↵
j
+ �i
� �(✓it
� �j
)2⌘
Additive aliasing:
= logit�1⇣(↵
j
+ k) + (�i
� k) � �(✓it
� �j
)2⌘
= logit�1⇣↵
j
+ �i
� �((✓it
+ k) � (�j
� k))2⌘
Multiplicative aliasing:
= logit�1⇣↵
j
+ �i
� �
k
2 ((✓it
� �j
) ⇥ k)2⌘
Index
45 / 54
Identifying restrictions
Indeterminacy Approach 1 Approach 2Additive aliasing (1) Fix ↵0
j
= 0 or �0i
= 0 Fix µ↵ = 0 or µ� = 0Additive aliasing (2) Fix �0
j
= +1 or ✓0i
= +1 Fix µ� = 0 or µ✓ = 0Multiplicative aliasing Fix �00
j
= �1 or ✓00i
= �1 Fix �� = 1 or �✓ = 1
phi theta
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−2.5
0.0
2.5
−2.5
0.0
2.5
Ap
pro
ach
1A
pp
roa
ch 2
−2.5 0.0 2.5 −2.5 0.0 2.5Estimated value of parameter
True v
alu
e o
f para
mete
r
Index46 / 54
Application: Ideology of Media Outlets and Journalists●
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Mother JonesNew YorkerMSNBCThink ProgressDaily Kos
SlateAl JazeeraNPR NewsThe AtlanticTIME
New York TimesFiveThirtyEightLos Angeles TimesSalon
Huffington PostNewsweek
ABC NewsCBS News
U.S. NewsCNNChristian Science MonitorCNBCWashington PostUSA TodayFinancial Times
The EconomistReuters
Wall Street JournalForbesPolitico
The HillWashington Times
Fox NewsDrudge ReportReal Clear Politics
Red State
−2 −1 0 1Estimated Ideological Ideal Point
(Accounts Weighted by Number of Followers)
Barbera & Sood (2014) “Follow Your Ideology: A Measure ofIdeological Location of Media Sources”, MPSA Conference
Index
47 / 54
Application: Ideology of Media Outlets and Journalists
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Fox NewsUSA Today
Wall Street JournalCBS NewsU.S. NewsABC News
CNNABC
Washington PostNBC News
Los Angeles TimesTIME
Time MagazineNew York Times
NPR NewsMSNBC
−1 0 1 2φj, Estimated Ideological Ideal Points
Barbera & Sood (2014) “Follow Your Ideology: A Measure ofIdeological Location of Media Sources”, MPSA Conference
Index
47 / 54
Application: Ideological Asymmetries in Pol. Comm.
●
●
●
●
●
●
●
●
●
●
●
●
Super Bowl
Newtown Shooting
Oscars 2014
Syria
Winter Olympics
Boston Marathon
Minimum Wage
Marriage Equality
Budget
Gov. Shutdown
State of the Union
2012 Election
0.00 0.25 0.50 0.75 1.00Estimated Rate of Cross−Ideological Retweeting
(Exponentiated Coefficient from Poisson Regression)
● LiberalsConservatives
Barbera, Jost, Nagler, Tucker, & Bonneau (2015) “Tweeting From Leftto Right: Is Online Political Communication More Than an EchoChamber?” Psychological Science
Index
48 / 54
Application: Multidimensional Policy Spaces in Europe
P(yij
= 1) = logit
�1
↵
i
+ �j
�dX
k=1
�d
(✓ik
� �jk
)2
!
Estimated ideological positions for 120 parties in 28 European countriesLeft-Right Dimension Pro/Anti-European Union Dimension
Grunen
AN0 2011
FPO
OVPSPO
FDL
ERC
C
CD&V
CDA
CDU−CSU
KD
CU
Cs
ODS
DL
PO
CpE
Syriza
Cons
DPP
DIMAR
SLD PD
D66Ecol.
Reform
Verts
Fine Gael
Centre
M5SLNNK
FDP
FI
GD
ZZA
GL
Green
Green U
ANEL
Labour
PL
PvdALab
PiS
SEL
FG
V
Left
Lib
LibDem
FPVenstre
Mod.Coalition
FN
PN
NEOS
ND
N−VANSiLN
VLD
Sinn Fein
PASOK
PVV
PC
VVD
Piraten
Podemos PSL
PP
IRL
MR
Reform
SNP
SDS
CDS
SAPSocDem
SPD
SD
PS
SP
PS
sp.a
SF
Fianna Fail
PSOE
SD
Linke
Finns
UPM
UCD
UDIUPyD
UKIP
IU
SP
Unity
r=0.81
0.0
2.5
5.0
7.5
10.0
0.0 2.5 5.0 7.5 10.0Ideology estimates (Surveys)
Ideo
logy
esti
mat
es (T
witt
er)
Grunen
AN0 2011
FPO
OVP
SPO
FDL
ERC
C
CD&VCDA
KDCU
Cs
ODS
DL
POSyriza
Cons
DPP
DIMAR
SLD
PD D66
Ecol.
Reform
VertsFine Gael
Centre
M5S
LNNK
FDP
FI
GD
ZZAGLGreen
Green UANEL
Labour
PL PvdA
Lab
PiSSEL
FGV Left
LibLibDem
FP
Venstre
Mod.
Coalition
FN
PNNEOSND
N−VA
LN
VLD
Sinn Fein
PASOK
PVV
PC
VVD
Piraten
PodemosPSL
PPIRL
MRReformSNP
SDS CDS
SAPSocDem
SPD
SDSPPS
sp.a
SFFianna Fail
PSOE
SD
Linke
Finns
UPMUCDUPyD
UKIP
IU
SP
Unity
r=0.77
0.0
2.5
5.0
7.5
10.0
0.0 2.5 5.0 7.5 10.0Ideology estimates (Surveys)
Ideo
logy
esti
mat
es (T
witt
er)
Barbera, Popa, & Schmitt (2015) “Analyzing the CommonMultidimensional Political Space for Voters, Parties, and Legislators inEurope”, MPSA Conference
Index
49 / 54
Unequal representation
We also analyze whether correspondence between citizensand legislators is higher for:I Co-partisans (party supporters)I Issues owned by each party (e.g. economy for Republicans;
social issues for Democrats)I Constituents (vs general public)I Informed public vs random sample of U.S. Twitter usersI Individuals with income above median
50 / 54
Electoral Institutions and Political Representation
What institutional configurations foster better representation?
Theoretical expectationsCountry Government Instit. Congr. Responsiv.Germany Coalition Prop. High LowSpain Single-party Prop. Medium MediumUK Coalition Maj. Medium MediumFrance Single-party Maj. Low High
Barbera & Bølstad (2015) “A Comparative Study of the Qualityof Political Representation Using Social Media Data”, EPSAConference Paper. Index
51 / 54
Electoral Institutions and Political Representation
j.mp/EPSA-lda-demoIndex
52 / 54