The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model of Voting:
Theory and Empirics
Theory
Background
Example: Candidate
Competition
CSLS Empirical Methods Workshop
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
November 16, 2012
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
Kevin M. Quinn
UC Berkeley
.1
Overview
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
• very basic introduction to theoretical ideas behind spatial
models of voting
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.2
Overview
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
• very basic introduction to theoretical ideas behind spatial
models of voting
• very basic introduction to attempts to estimate parameters
of spatial models
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.2
Overview
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
• very basic introduction to theoretical ideas behind spatial
models of voting
• very basic introduction to attempts to estimate parameters
of spatial models
• exposure to some results from some work in this area (no
claim of representativeness)
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.2
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
• actors
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
• actors
• preferences
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
• actors
• preferences
• behavioral assumptions (sincere vs. strategic behavior)
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
• actors
• preferences
• behavioral assumptions (sincere vs. strategic behavior)
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
• institutions (rules of the game)
.3
Background
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The key ingredients:
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
• policy space
• actors
• preferences
• behavioral assumptions (sincere vs. strategic behavior)
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
• institutions (rules of the game)
• information (important but we will ignore this today)
.3
The Spatial Model of
Voting:
Theory and
Empirics
Background
Theory
Background
Utility of Alternative
Utility
Function
Utility
Utility of Status Quo
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Alternative
●
Ideal Point
Status Quo
●
Latent
Dimension
Example: Newspaper
Editorial Boards
Misconceptions
.4
The Spatial Model of
Voting:
Theory and
Empirics
Background
Theory
Background
Utility of Alternative
Utility
Function
Utility
Utility of Status Quo
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Alternative
●
Ideal Point
Status Quo
●
Latent
Dimension
Example: Newspaper
Editorial Boards
Misconceptions
Additional examples on board.
.4
Candidate Competition
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
In class example
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.5
The Median Voter Theorem
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Assume an odd number of voters and a uni-dimensional policy
space.
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.6
The Median Voter Theorem
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Assume an odd number of voters and a uni-dimensional policy
space.
Voters have single-peaked preferences.
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.6
The Median Voter Theorem
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Assume an odd number of voters and a uni-dimensional policy
space.
Voters have single-peaked preferences.
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
The policy position corresponding to the median voter’s ideal
point is a stable outcome in that it defeats all alternatives in a
binary majority rule vote.
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.6
The Median Voter Theorem
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Assume an odd number of voters and a uni-dimensional policy
space.
Voters have single-peaked preferences.
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
The policy position corresponding to the median voter’s ideal
point is a stable outcome in that it defeats all alternatives in a
binary majority rule vote.
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
NB: The uni-dimensional policy space is very important for this
result.
.6
Statutory Interpretation
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
The following is based on Ferejohn and Weingast. 1992. “A
Positive Theory of Statutory Interpretation.” International
Review of Law and Economics.
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.7
Statutory Interpretation
Three interpretative stances a court might take:
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.8
Empirics
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.9
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Theory of Voting
Theory
Background
Example: Candidate
Competition
Utility of Alternative
Utility
Function
Utility of Status Quo
The Median Voter Theorem
Example: Statutory
Interpretation
Utility
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Alternative
●
Ideal Point
Status Quo
●
Latent
Dimension
Example: Newspaper
Editorial Boards
Misconceptions
.10
The Spatial Model as an Empirical Model
Let i index votes and j index voters
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.11
The Spatial Model as an Empirical Model
Let i index votes and j index voters
The Spatial Model of
Voting:
Theory and
Empirics
(o)
xi : status quo point
(a)
xi : alternative point
θj : j’s most preferred policy
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.11
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Let i index votes and j index voters
(o)
xi : status quo point
(a)
xi : alternative point
θj : j’s most preferred policy
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Random utility of
(o)
xi
for j:
(o)
uij
= −|θj −
(o)
xi |2
+
(o)
δij
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.11
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Let i index votes and j index voters
(o)
xi : status quo point
(a)
xi : alternative point
θj : j’s most preferred policy
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Random utility of
(o)
xi
Random utility of
(a)
xi
for j:
(o)
uij
for j:
(a)
uij
= −|θj −
(o)
xi |2
= −|θj −
(a)
xi |2
+
(o)
δij
+
(a)
δij
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.11
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Let i index votes and j index voters
(o)
xi : status quo point
(a)
xi : alternative point
θj : j’s most preferred policy
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Random utility of
(o)
xi
Random utility of
(a)
xi
for j:
(o)
uij
for j:
(a)
uij
= −|θj −
(o)
xi |2
= −|θj −
(a)
xi |2
+
(o)
δij
+
(a)
δij
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Utility difference:
(o)
Example: Newspaper
Editorial Boards
Misconceptions
(a)
yij∗ = uij − uij
(a) (a)
= [xi xi
(o) (o)
(o)
− xi xi ] + 2[xi
(a)
(o)
(a)
− xi ]θj + [δij − δij ]
= αi + βi θj + ij
with ij ∼ N (0, 1)
.11
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Let i index votes and j index voters
(o)
xi : status quo point
(a)
xi : alternative point
θj : j’s most preferred policy
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Random utility of
(o)
xi
Random utility of
(a)
xi
for j:
(o)
uij
for j:
(a)
uij
= −|θj −
(o)
xi |2
= −|θj −
(a)
xi |2
+
(o)
δij
+
(a)
δij
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Utility difference:
(o)
Example: Newspaper
Editorial Boards
Misconceptions
(a)
yij∗ = uij − uij
(a) (a)
= [xi xi
(o) (o)
(o)
− xi xi ] + 2[xi
(a)
(o)
(a)
− xi ]θj + [δij − δij ]
= αi + βi θj + ij
with ij ∼ N (0, 1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(yij∗ > 0|αi , βi , θj ) = Φ(αi + βi θj )
.11
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Theory
Background
Example: Candidate
Competition
The likelihood function is proportional to:
p(y|α, β, θ) =
n Y
m
Y
i=1 j=1
The Median Voter Theorem
Example: Statutory
Interpretation
1−yij
Φ(αi + βi θj )yij [1 − Φ(αi + βi θj )]
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.12
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Theory
Background
Example: Candidate
Competition
The likelihood function is proportional to:
p(y|α, β, θ) =
n Y
m
Y
i=1 j=1
The Median Voter Theorem
Example: Statutory
Interpretation
1−yij
Φ(αi + βi θj )yij [1 − Φ(αi + βi θj )]
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Identification issues
Misconceptions
.12
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Theory
Background
Example: Candidate
Competition
The likelihood function is proportional to:
p(y|α, β, θ) =
n Y
m
Y
i=1 j=1
The Median Voter Theorem
Example: Statutory
Interpretation
1−yij
Φ(αi + βi θj )yij [1 − Φ(αi + βi θj )]
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Identification issues
Misconceptions
Coding of y
.12
The Spatial Model as an Empirical Model
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Cutpoints / Cutlines:
Example: Candidate
Competition
The Median Voter Theorem
The point of indifference between the status quo and
alternative is the point where the probability of choosing either
one is 0.5 or equivalently where αi + βi θ∗ = 0.
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.13
The Spatial Model as an Empirical Model
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Cutpoints / Cutlines:
Example: Candidate
Competition
The Median Voter Theorem
The point of indifference between the status quo and
alternative is the point where the probability of choosing either
one is 0.5 or equivalently where αi + βi θ∗ = 0.
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Elementary algebra reveals that the cutpoint for vote i is
Example: Newspaper
Editorial Boards
Misconceptions
∗
θ = −αi /βi
.13
The Spatial Model as an Empirical Model
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
Interpretation
αi : related to baseline propensity to see a y = 1 on vote i
βi : sign determines whether y = 1 is a “left” or “right” vote,
absolute value related to strength of association between latent
θ and observed votes on i
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
θj : latent ideal point for voter j
.14
The Spatial Model as an Empirical Model
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
Interpretation
αi : related to baseline propensity to see a y = 1 on vote i
βi : sign determines whether y = 1 is a “left” or “right” vote,
absolute value related to strength of association between latent
θ and observed votes on i
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
θj : latent ideal point for voter j
.14
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Theory
Background
Latent Dimension
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Thomas
Slope < 0
Rehnquist
Scalia
Kennedy
Minority (0)
Stevens
Ginsburg
Souter
Latent Dimension
The Median Voter Theorem
O'Connor
Stevens
Ginsburg
Breyer
Souter
Majority (1)
Thomas
Rehnquist
Scalia
Grutter v. Bollinger
Slope > 0
Minority (0)
Rehnquist
O.Connor
Kennedy
Breyer
Minority (0)
Slope ≈ 0
O.Connor
Kennedy
Gratz v. Bollinger
Breyer
Majority (1)
Thomas
Scalia
Stevens
Ginsburg
Souter
Majority (1)
Example: Candidate
Competition
Blakely v. Washington
Example: Newspaper
Editorial Boards
Misconceptions
Latent Dimension
.15
The Spatial Model of
Voting:
Theory and
Empirics
The Spatial Model as an Empirical Model
Theory
Background
Latent Dimension
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Thomas
Slope < 0
Rehnquist
Scalia
Kennedy
Minority (0)
Stevens
Ginsburg
Souter
Latent Dimension
The Median Voter Theorem
O'Connor
Stevens
Ginsburg
Breyer
Souter
Majority (1)
Thomas
Rehnquist
Scalia
Grutter v. Bollinger
Slope > 0
Minority (0)
Rehnquist
O.Connor
Kennedy
Breyer
Minority (0)
Slope ≈ 0
O.Connor
Kennedy
Gratz v. Bollinger
Breyer
Majority (1)
Thomas
Scalia
Stevens
Ginsburg
Souter
Majority (1)
Example: Candidate
Competition
Blakely v. Washington
Example: Newspaper
Editorial Boards
Misconceptions
Latent Dimension
Relationship to IRT models for standardized tests
.15
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
How might this work?
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.16
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.17
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.18
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.19
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Previous figures from Clinton, Jackman, and Rivers. 2004.
“The Most Liberal Senator?”. PS: Political Science and Politics.
805-811.
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.20
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.21
The US Congress
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
Previous figure from Clinton, Jackman, and Rivers. 2004. “The
Statistical Analysis of Roll Call Data”. APSR. 98: 355-370.
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.22
The US Supreme Court
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
How might this work?
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.23
The Spatial Model of
Voting:
Theory and
Empirics
The US Supreme Court
Unidimensional Summary
Theory
Background
Example: Candidate
Competition
Thomas
Scalia
Rehnquist
Kennedy
O'Connor
Breyer
Souter
Ginsburg
Stevens
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
Single Dimension
Cutlines
n=495
5−4 split
.24
The Spatial Model of
Voting:
Theory and
Empirics
The US Supreme Court
Theory
Supreme Court Voting Over Time
Background
Example: Candidate
Competition
McReynolds
New Deal Court
Butler
Sutherland
Van Devanter
Sanford
Rehnquist
Roberts
Alito
Jackson
Burton
Frankfurter
Minton
Vinson
Reed
Clark
Byrnes
O'Connor
The Spatial Model as an
Empirical Model
Stone
Powell
Example: The US Congress
White
Stewart
Example: The US Supreme
Court
Souter
Breyer
Ginsburg
Blackmun
Holmes
Brandeis
Example: Newspaper
Editorial Boards
Stevens
Pre−New Deal
Lochner Court
Cardozo
Example: Statutory
Interpretation
Empirics
Kennedy
Burger
Harlan
Hughes
Whittaker
Misconceptions
Goldberg
Rutledge
Murphy
Brennan
Warren
Fortas
Marshall
Black
Douglas
1920
The Median Voter Theorem
Scalia
Roberts
Taft
McKenna
Latent Dimension
Thomas
1940
Voting
splits
1960
1980
2000
Term
.25
The US Supreme Court
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.26
The US Supreme Court
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
This figure and previous from: Pritchett. 1941. “Divisions of
Opinion Among Justices of the U.S. Supreme Court,
1939-1941.” APSR. 35: 890-898.
.27
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
How might we measure the political positions of newspaper
editorial boards?
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.28
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Political Positions of Newspapers
• 495 Supreme Court cases from 1994-2004 terms
• 25 major newspapers
• 1500 editorial-case positions
• We personally read and checked the coding for each of
the 1500 editorial positions
1: clearly in favor of majority position
0: clearly against majority position
?: unclear but covered
• This simple coding allows a simple item response theory
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
model to be used to compare the newspapers and justices
to each other.
More detail in:
Ho and Quinn. 2008. “Measuring Explicit Political Positions of
Media.” Quarterly Journal of Political Science. 3: 353-377.
.29
The Spatial Model of
Voting:
Theory and
Empirics
Newspaper Editorial Boards
Theory
Background
Newspaper
Code
Washington Times
Atlanta Journal
Investor's Business Daily
Atlanta Constitution
Rocky Mountain News
Miami Herald
San Diego Union Tribune
Minneapolis Star Tribune
Cleveland Plain Dealer
Detroit Free Press
Atlanta Journal Constitution
Philidelphia Inquirer
Arizona Republic
Boston Globe
Chicago Sun−Times
Dallas Morning News
San Francisco Chronicle
Houston Chronicle
New York Post
Chicago Tribune
Washington Post
Los Angeles Times
New York Times
Wall Street Journal
USA Today
WT
AJ
INV
AC
RMN
MH
SDUT
MST
CPD
DFP
AJC
PI
AR
BG
CST
DMN
SFC
HC
NYP
CT
WP
LAT
NYT
WSJ
USA
Circulation (1000s)
Observation Period
Example: Candidate
Competition
Editorials
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
500
1000
1500
2000
1994
1996
1998
2000
2002
2004
20
40
60
80
100
120
.30
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
The court reached one of its lowest moments of the term when
it ruled in favor of the Boy Scouts’ right to exclude gay members.
The four dissenters – Justices Stevens, Ginsburg, Breyer and
Souter – did not challenge the principle that an organization cannot
be forced to adopt an unwanted message. But the dissenters
correctly noted that the Boy Scouts had failed to show that
admitting gays was fundamentally incompatible with the
organization’s core mission, the test the court has traditionally
applied to groups trying to escape an anti-discrimination law.
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
James Dale, the excluded Eagle Scout, deserved better. So did
the rest of the nation.
.31
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
THE QUESTION of whether the Boy Scouts can discriminate
against gays pits core values of free association against important
anti-discrimination principles: legally, a tough call. We thought that
the scouts, especially given their unusual quasi-public status, could
lawfully be stopped from excluding gays. A sharply divided
Supreme Court yesterday disagreed, holding that the scouts’ First
Amendment rights trump a New Jersey anti-discrimination law that
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
forbids discrimination on the basis of sexual orientation. The
opinion is more a comment on the First Amendment’s broad scope
than a validation of prejudice. The Boy Scouts’ discrimination
against gays remains as offensive and wrong a position following
the court’s decision as it was before.
.32
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
In another important case in which the justices arrived at the
proper decision, the court declared that the Boy Scouts of America
have a right to exclude homosexuals as leaders. By a narrow 5-4
margin, the court ruled that private, nonprofit organizations, like the
scouts, have a First Amendment right to "free association." As
such, they may not be forced to accept members or leaders whose
views or comportment are contrary to that for which the private
organization stands.
Critics of the court’s decision argue that the justices have given
groups, like the scouts, a license to discriminate. But had the court
come down the other way, then a group like the NAACP could be
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
forced to accept, say, a Ku Klux Klan member; and the B’nai B’rith
could be forced to accept a neo-Nazi in its midst.
.33
Newspaper Editorial Boards
The Spatial Model of
Voting:
Theory and
Empirics
Today, lawyers have become the pre-eminent befuddlers of
common sense. Among the dangerous nonsense purveyed by
these folks is the recent attempt to compel the Boy Scouts of
America - a traditionalist youth group whose mission is to help
make young men "morally straight" -to accept a homosexual
scoutmaster and avowed gay rights activist. All this, on
"anti-discrimination" grounds.
Wednesday, the Supreme Court rejected the idea, which had
been upheld by the New Jersey Supreme Court, that the Boy
Scouts had no fundamental right to exclude would-be members
who do not subscribe to or conform with the organization’s most
basic tenets. In this particular instance, the Boy Scouts withdrew
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
the membership of former Assistant Scoutmaster James Dale, an
adult volunteer, after learning of his homosexual lifestyle. This, of
course, put the Boy Scouts in the gunsights as one of the last
remaining bastions of American culture that has not bowed to the
gay agenda - which demands not merely live-and-let live tolerance,
but total acceptance - indeed, emphatic endorsement.
.34
The Spatial Model of
Voting:
Theory and
Empirics
Newspaper Editorial Boards
Theory
Background
Ideal Point Estimates
Example: Candidate
Competition
Newspaper Ranks
The Median Voter Theorem
Thomas
Scalia
INV
NYP
WT
WSJ
Rehnquist
RMN
Kennedy
AJ
CST
O'Connor
CPD
CT
SDUT
AR
HC
AC
AJC
PI
DMN
BG
Breyer
USA
Souter
MH
WP
LAT
Ginsburg
SFC
MST
DFP
Stevens
NYT
INV
NYP
WT
WSJ
RMN
AJ
CST
CPD
CT
SDUT
AR
HC
AC
AJC
PI
DMN
BG
USA
MH
WP
LAT
SFC
MST
DFP
NYT
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
●
●
●
●
●
Posterior Rank
●
Prior
●
−3
−2
−1
0
Legend
1
2
3
0
0.1
0.2
0.3
0.4
0.5+
Probability
Ideology
.35
The Spatial Model of
Voting:
Theory and
Empirics
Newspaper Editorial Boards
Theory
Background
Example: Candidate
Competition
All Top Newspapers
1.0
The Median Voter Theorem
Empirics
The Spatial Model as an
Empirical Model
0.6
Unweighted
Example: The US Congress
Example: The US Supreme
Court
0.4
Density
0.8
Example: Statutory
Interpretation
Weighted by Circulation
0.2
Example: Newspaper
Editorial Boards
−3
−2
−1
0
Scalia
Thomas
Rehnquist
Justices
O'Connor
Kennedy
Breyer
Souter
Ginsburg
Stevens
4
2
0
Density
0.0
Misconceptions
1
2
3
Political Position
.36
Misconceptions
Some scholars have expressed concern about the use of ideal
point models to study judicial behavior.
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
In some cases, this seems to be a knee jerk reaction against
quantification of judicial behavior.
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
In other cases, more sophisticated concerns are raised about
the data coding, modeling assumptions, and properties of the
estimates.
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
Most of the following examples are from Ho and Quinn. 2010.
“How Not to Lie with Judicial Votes: Misconceptions,
Measurement, and Models.” California Law Review.
.37
The Spatial Model of
Voting:
Theory and
Empirics
Every Case Is Counted Equally
Theory
Background
Example: Candidate
Competition
Example: Statutory
Interpretation
Grutter v. Bollinger
Empirics
O'Connor
Stevens
Ginsburg
Breyer
Souter
Majority (1)
Thomas
Rehnquist
Scalia
O.Connor
Kennedy
Gratz v. Bollinger
Breyer
Majority (1)
Thomas
Scalia
Stevens
Ginsburg
Souter
Majority (1)
The Median Voter Theorem
Blakely v. Washington
The Spatial Model as an
Empirical Model
Example: The US Congress
Latent Dimension
Latent Dimension
Example: The US Supreme
Court
Thomas
Rehnquist
Scalia
Kennedy
Slope < 0
Minority (0)
Stevens
Ginsburg
Souter
Slope > 0
Minority (0)
Rehnquist
O.Connor
Kennedy
Breyer
Minority (0)
Slope ≈ 0
Example: Newspaper
Editorial Boards
Misconceptions
Latent Dimension
.38
Directional Prior
Weight
Prior
Contested
Cases
Tex v. Cobb
Thomas
Scalia
Rehnquist
Kennedy
O'Connor
Souter
Breyer
Ginsburg
Stevens
Predicted Rank in Latent Dimension After Observing Each Case
Zadvydas v. Davis
Tyler v. Cain
Lorillard Tob v. Reilly
Palazzolo v. R.I.
FEC v. Co Rep Comm
US v. United Foods
Calcano−Martinez v. INS
INS v. St Cyr
NYT v. Tasini
Idaho v. US
US v. Mead Corp.
Duncan v. Walker
Good News Club v. Milford
Kyllo v. US
Kan v. Colo
Nguyen v. INS
United Dominion v. US
Penry v. Johnson
NLRB v. Ky River Care
PGA Tour v. Martin
Buckhannon v. WV HHS
US v. Hatter
Bartnicki v. Vopper
Rogers v. Tenn
Cooper v. Leatherman
Lackawanna DA v. Coss
Daniels v. US
Atwater v. Lago Vista
Alexander v. Sandoval
Easley v. Cromartie
Time
Egelhoff v. Egelhoff
Circuit City v. Adams
Ferguson v. Charleston
Shafer v. SC
Legal Serv v. Velazquez
U Ala v. Garrett
Ill v. McArthur
Brentwood Academy
Seling v. Young
Lopez v. Davis
Gitlitz v. Comm'r IRS
SWANCC v. Corps
Bush v. Gore
Indianapolis v. Edmond
Every Case Is Counted Equally
The Spatial Model of
Voting:
Theory and
Empirics
Theory
2000 Term Votes (chronological)
Background
Thomas
Scalia
Rehnquist
Kennedy
O'Connor
Souter
Breyer
Ginsburg
Stevens
Example: Candidate
Competition
Minority
The Median Voter Theorem
Majority
Final
rank
Ideal
point
evolution
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Misconceptions
Example: Newspaper
Editorial Boards
8−9
7−8
5−6
3−4
2−3
1−2
Time
.39
Unidimensional Models are Useless in a Multidimensional
World
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The idea that something as complicated as Supreme Court
decisionmaking can be captured with a uni-dimensional spatial
model is very counterintuitive (outrageous???) to many
scholars of the court.
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
.40
The Spatial Model of
Voting:
Theory and
Empirics
Unidimensional Models are Useless in a Multidimensional
World
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Ideal Point Estimates
Cases Consistent with Unidimensionality
Cases Inconsistent with Unidimensionality
Empirics
Breyer
●
●
Thomas
●
Scalia
●
●
●
●
●
●
●
Stevens
Dimension 1
●
●
●
Dimension 2
Kennedy
Souter
Example: The US Congress
●
Dimension 2
Dimension 2
●
●
Rehnquist
●
●
●
●
●
Ginsburg
The Spatial Model as an
Empirical Model
O'Connor
●
●
Example: The US Supreme
Court
●
●
●
Example: Newspaper
Editorial Boards
Misconceptions
●
Dimension 1
Dimension 1
.41
The Spatial Model of
Voting:
Theory and
Empirics
How Statutory Cases Differ
Theory
Background
0.1
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
Not Significantly Less Than Null Value
Empirics
0.0
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
●
●●
●
−0.1
Fraction Statutory Votes Correctly Classified (Actual − Null)
Unidimensional Models are Useless in a Multidimensional
World
●
●
●
●
●
1940
1950
●
1960
●
●
●
Example: Newspaper
Editorial Boards
Misconceptions
●
●
●
●
●
●
●
Significantly Less Than Null Value
1970
1980
1990
2000
Term
Comparison of ability to classify votes on cases with Westlaw
Key Number Statutory Construction and Operation (361VI)
relative to null distribution formed from all nonunanimous cases
in term.
.42
The Spatial Model of
Voting:
Theory and
Empirics
Selection Bias Creates Serious Problems
50
50
40
Biased Case Selection
40
Simple Random Sampling
Theory
Frequency
20
30
Example: Candidate
Competition
The Median Voter Theorem
Example: Statutory
Interpretation
10
●
●
−2
●
●
●
●
●
−1
0
Cutpoints
1
●
●
0
0
10
Frequency
20
30
Background
2
Empirics
●
●
−2
Cardinal Ideal Points
●
●
●
●
●
−1
0
Cutpoints
1
●
●
2
Expected Ranks of Ideal Points
●
●
●
●
●
●
●
−2 −1 0
1
2
3
Simple Random Sampling
Example: Newspaper
Editorial Boards
Misconceptions
●
●
●
●
●
−3
Example: The US Supreme
Court
●
2
●
Example: The US Congress
●
Biased Case Selection
4
6
8
Biased Case Selection
−4
−2
0
2
●
●
The Spatial Model as an
Empirical Model
●
2
4
6
8
Simple Random Sampling
.43
The Spatial Model of
Voting:
Theory and
Empirics
All Estimates from Latent Variable Models Are Sensitive to
Arbitrary Modeling Assumptions
Theory
Background
Example: Candidate
Competition
The Median Voter Theorem
Cardinal Comparisons
Example: Statutory
Interpretation
Ordinal Comparisons
−4
−2
0
Cutpoints
2
4
−4
−2
0
2
4
Ideal Point (Model 1)
6
8
7
6
Example: The US Supreme
Court
5
●
Example: Newspaper
Editorial Boards
●
●
Misconceptions
●
1
−6
Example: The US Congress
4
●● ●
−4
−2
●
●●
Empirics
The Spatial Model as an
Empirical Model
●
●
3
0
●
●
●
●
2
Expected Rank (Model 2)
4
2
●
−6
0.10
0.20
Model 2
Ideal Point (Model 2)
Model 1
0.00
Prior Density
0.30
6
9
Prior Density of Cutpoints
●
1
2
3
4
5
6
7
8
9
Expected Rank (Model 1)
.44
All Estimates from Latent Variable Models Are Sensitive to
Arbitrary Modeling Assumptions
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
Evolution of Justice Blackmun
Natural Court
The Median Voter Theorem
Rehnquist
Example: Statutory
Interpretation
Latent Dimension
Latent Dimension
Empirics
Burger
Powell
Stewart
White
Blackmun
Stevens
Natural
court
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
Brennan
Marshall
1970
1975
1980 1985
Term
1990
1975
1977
1979
Term
.45
All Estimates from Latent Variable Models Are Sensitive to
Arbitrary Modeling Assumptions
The Spatial Model of
Voting:
Theory and
Empirics
Theory
Background
Example: Candidate
Competition
Term
1998
1999
2000
2001
2002
Justice
Kennedy
O’Connor
O’Connor
O’Connor
O’Connor
Prob. Median
0.574
0.901
0.992
> 0.999
0.998
The Median Voter Theorem
Example: Statutory
Interpretation
Empirics
The Spatial Model as an
Empirical Model
Example: The US Congress
Example: The US Supreme
Court
Example: Newspaper
Editorial Boards
Misconceptions
(from Martin, Quinn, & Epstein, 2005)
These are useful summaries under a very wide range of
assumptions.
.46