The Spatial Model of Voting: Theory and Empirics · The Spatial Model of Voting: Theory and ... The...
68
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 .1 The Spatial Model of Voting: Theory and Empirics CSLS Empirical Methods Workshop November 16, 2012 Kevin M. Quinn UC Berkeley
Transcript of The Spatial Model of Voting: Theory and Empirics · The Spatial Model of Voting: Theory and ... The...
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.1
The Spatial Model of Voting:Theory and EmpiricsCSLS Empirical Methods Workshop
November 16, 2012
Kevin M. QuinnUC Berkeley
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.2
Overview
• very basic introduction to theoretical ideas behind spatialmodels of voting
• very basic introduction to attempts to estimate parametersof spatial models
• exposure to some results from some work in this area (noclaim of representativeness)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.2
Overview
• very basic introduction to theoretical ideas behind spatialmodels of voting
• very basic introduction to attempts to estimate parametersof spatial models
• exposure to some results from some work in this area (noclaim of representativeness)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.2
Overview
• very basic introduction to theoretical ideas behind spatialmodels of voting
• very basic introduction to attempts to estimate parametersof spatial models
• exposure to some results from some work in this area (noclaim of representativeness)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors• preferences• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space
• actors• preferences• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors
• preferences• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors• preferences
• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors• preferences• behavioral assumptions (sincere vs. strategic behavior)
• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors• preferences• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)
• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.3
Background
The key ingredients:
• policy space• actors• preferences• behavioral assumptions (sincere vs. strategic behavior)• institutions (rules of the game)• information (important but we will ignore this today)
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.4
Background
LatentDimension
Util
ity
●● ●
UtilityFunction
Idea
l Poi
nt
Alte
rnat
ive
Sta
tus
Quo
Utility of Status Quo
Utility of Alternative
Additional examples on board.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.4
Background
LatentDimension
Util
ity
●● ●
UtilityFunction
Idea
l Poi
nt
Alte
rnat
ive
Sta
tus
Quo
Utility of Status Quo
Utility of Alternative
Additional examples on board.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.5
Candidate Competition
In class example
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.6
The Median Voter Theorem
Assume an odd number of voters and a uni-dimensional policyspace.
Voters have single-peaked preferences.
The policy position corresponding to the median voter’s idealpoint is a stable outcome in that it defeats all alternatives in abinary majority rule vote.
NB: The uni-dimensional policy space is very important for thisresult.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.6
The Median Voter Theorem
Assume an odd number of voters and a uni-dimensional policyspace.
Voters have single-peaked preferences.
The policy position corresponding to the median voter’s idealpoint is a stable outcome in that it defeats all alternatives in abinary majority rule vote.
NB: The uni-dimensional policy space is very important for thisresult.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.6
The Median Voter Theorem
Assume an odd number of voters and a uni-dimensional policyspace.
Voters have single-peaked preferences.
The policy position corresponding to the median voter’s idealpoint is a stable outcome in that it defeats all alternatives in abinary majority rule vote.
NB: The uni-dimensional policy space is very important for thisresult.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.6
The Median Voter Theorem
Assume an odd number of voters and a uni-dimensional policyspace.
Voters have single-peaked preferences.
The policy position corresponding to the median voter’s idealpoint is a stable outcome in that it defeats all alternatives in abinary majority rule vote.
NB: The uni-dimensional policy space is very important for thisresult.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.7
Statutory Interpretation
The following is based on Ferejohn and Weingast. 1992. “APositive Theory of Statutory Interpretation.” InternationalReview of Law and Economics.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.8
Statutory Interpretation
Three interpretative stances a court might take:
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.9
Empirics
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.10
The Spatial Theory of Voting
LatentDimension
Util
ity
●● ●
UtilityFunction
Idea
l Poi
nt
Alte
rnat
ive
Sta
tus
Quo
Utility of Status Quo
Utility of Alternative
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.11
The Spatial Model as an Empirical ModelLet i index votes and j index voters
x (o)i : status quo point
x (a)i : alternative pointθj : j ’s most preferred policy
Random utility of x (o)i for j : u(o)
ij = −|θj − x (o)i |2 + δ
(o)ij
Random utility of x (a)i for j : u(a)
ij = −|θj − x (a)i |2 + δ
(a)ij
Utility difference:
y∗ij = u(o)
ij − u(a)ij
= [x (a)i x (a)
i − x (o)i x (o)
i ] + 2[x (o)i − x (a)
i ]θj + [δ(o)ij − δ
(a)ij ]
= αi + βiθj + εij
with εij ∼ N (0,1)
If yij = 1 is a vote for the status quo:
Pr(yij = 1|αi , βi , θj ) = Pr(y∗ij > 0|αi , βi , θj ) = Φ(αi + βiθj )
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.12
The Spatial Model as an Empirical Model
The likelihood function is proportional to:
p(y|α,β,θ) =n∏
i=1
m∏j=1
Φ(αi + βiθj )yij [1− Φ(αi + βiθj )]1−yij
Identification issues
Coding of y
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.12
The Spatial Model as an Empirical Model
The likelihood function is proportional to:
p(y|α,β,θ) =n∏
i=1
m∏j=1
Φ(αi + βiθj )yij [1− Φ(αi + βiθj )]1−yij
Identification issues
Coding of y
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.12
The Spatial Model as an Empirical Model
The likelihood function is proportional to:
p(y|α,β,θ) =n∏
i=1
m∏j=1
Φ(αi + βiθj )yij [1− Φ(αi + βiθj )]1−yij
Identification issues
Coding of y
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.13
The Spatial Model as an Empirical Model
Cutpoints / Cutlines:
The point of indifference between the status quo andalternative is the point where the probability of choosing eitherone is 0.5 or equivalently where αi + βiθ
∗ = 0.
Elementary algebra reveals that the cutpoint for vote i is
θ∗ = −αi/βi
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.13
The Spatial Model as an Empirical Model
Cutpoints / Cutlines:
The point of indifference between the status quo andalternative is the point where the probability of choosing eitherone is 0.5 or equivalently where αi + βiθ
∗ = 0.
Elementary algebra reveals that the cutpoint for vote i is
θ∗ = −αi/βi
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.14
The Spatial Model as an Empirical Model
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 latentθ and observed votes on i
θj : latent ideal point for voter j
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.14
The Spatial Model as an Empirical Model
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 latentθ and observed votes on i
θj : latent ideal point for voter j
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.15
The Spatial Model as an Empirical Model
Blakely v. Washington
Latent Dimension
Slope ≈ 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Gratz v. Bollinger
Latent Dimension
Slope > 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Grutter v. Bollinger
Latent Dimension
Slope < 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O'C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Relationship to IRT models for standardized tests
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.15
The Spatial Model as an Empirical Model
Blakely v. Washington
Latent Dimension
Slope ≈ 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Gratz v. Bollinger
Latent Dimension
Slope > 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Grutter v. Bollinger
Latent Dimension
Slope < 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O'C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Relationship to IRT models for standardized tests
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.16
The US Congress
How might this work?
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.17
The US Congress
From Clinton, Jackman, and Rivers. 2004. “The Most LiberalSenator?”. PS: Political Science and Politics. 805-811.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.18
The US Congress
From Clinton, Jackman, and Rivers. 2004. “The Most LiberalSenator?”. PS: Political Science and Politics. 805-811.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.19
The US Congress
From Clinton, Jackman, and Rivers. 2004. “The Most LiberalSenator?”. PS: Political Science and Politics. 805-811.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.20
The US Congress
Previous figures from Clinton, Jackman, and Rivers. 2004.“The Most Liberal Senator?”. PS: Political Science and Politics.805-811.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.21
The US Congress
From Clinton, Jackman, and Rivers. 2004. “The StatisticalAnalysis of Roll Call Data”. APSR. 98: 355-370.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.22
The US Congress
Previous figure from Clinton, Jackman, and Rivers. 2004. “TheStatistical Analysis of Roll Call Data”. APSR. 98: 355-370.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.23
The US Supreme Court
How might this work?
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.24
The US Supreme Court
Unidimensional Summary
Single Dimension
StevensGinsburg
SouterBreyer
O'ConnorKennedy
RehnquistScalia
Thomas
Cutlinesn=495
5−4 split
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.25
The US Supreme Court
Supreme Court Voting Over Time
Term
Pre
−N
ew D
eal
Loch
ner
Cou
rt
New
Dea
l Cou
rt
Votingsplits
1920 1940 1960 1980 2000
Late
nt D
imen
sion
McKenna
Taft
Sanford
Holmes
Van Devanter
Sutherland
Cardozo
Brandeis
Butler
McReynolds
Hughes
Roberts
StoneReed
Black
Frankfurter
Douglas
Murphy
Byrnes
Jackson
Rutledge
BurtonVinsonMinton
Clark
Warren
Harlan
Whittaker
Brennan
StewartWhite
Goldberg
FortasMarshall
Burger
Blackmun
Powell
Rehnquist
Stevens
O'Connor
Scalia
Kennedy
Souter
Thomas
GinsburgBreyer
RobertsAlito
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.26
The US Supreme Court
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.27
The US Supreme Court
This figure and previous from: Pritchett. 1941. “Divisions ofOpinion Among Justices of the U.S. Supreme Court,1939-1941.” APSR. 35: 890-898.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.28
Newspaper Editorial Boards
How might we measure the political positions of newspapereditorial boards?
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.29
Newspaper Editorial Boards
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 positions1: clearly in favor of majority position0: clearly against majority position?: unclear but covered
• This simple coding allows a simple item response theorymodel to be used to compare the newspapers and justicesto each other.
More detail in:
Ho and Quinn. 2008. “Measuring Explicit Political Positions ofMedia.” Quarterly Journal of Political Science. 3: 353-377.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.30
Newspaper Editorial Boards
Newspaper
USA TodayWall Street Journal
New York TimesLos Angeles Times
Washington PostChicago Tribune
New York PostHouston Chronicle
San Francisco ChronicleDallas Morning NewsChicago Sun−Times
Boston GlobeArizona Republic
Philidelphia InquirerAtlanta Journal Constitution
Detroit Free PressCleveland Plain Dealer
Minneapolis Star TribuneSan Diego Union Tribune
Miami HeraldRocky Mountain News
Atlanta ConstitutionInvestor's Business Daily
Atlanta JournalWashington Times
Code
USAWSJNYTLATWPCTNYPHCSFCDMNCSTBGARPIAJCDFPCPDMSTSDUTMHRMNACINVAJWT
Circulation (1000s)
500 1000 1500 2000
Observation Period
1994 1996 1998 2000 2002 2004
Editorials
20 40 60 80 100 120
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.31
Newspaper Editorial Boards
The court reached one of its lowest moments of the term whenit ruled in favor of the Boy Scouts’ right to exclude gay members.The four dissenters – Justices Stevens, Ginsburg, Breyer andSouter – did not challenge the principle that an organization cannotbe forced to adopt an unwanted message. But the dissenterscorrectly noted that the Boy Scouts had failed to show thatadmitting gays was fundamentally incompatible with theorganization’s core mission, the test the court has traditionallyapplied to groups trying to escape an anti-discrimination law.
James Dale, the excluded Eagle Scout, deserved better. So didthe rest of the nation.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.32
Newspaper Editorial Boards
THE QUESTION of whether the Boy Scouts can discriminateagainst gays pits core values of free association against importantanti-discrimination principles: legally, a tough call. We thought thatthe scouts, especially given their unusual quasi-public status, couldlawfully be stopped from excluding gays. A sharply dividedSupreme Court yesterday disagreed, holding that the scouts’ FirstAmendment rights trump a New Jersey anti-discrimination law thatforbids discrimination on the basis of sexual orientation. Theopinion is more a comment on the First Amendment’s broad scopethan a validation of prejudice. The Boy Scouts’ discriminationagainst gays remains as offensive and wrong a position followingthe court’s decision as it was before.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.33
Newspaper Editorial Boards
In another important case in which the justices arrived at theproper decision, the court declared that the Boy Scouts of Americahave a right to exclude homosexuals as leaders. By a narrow 5-4margin, the court ruled that private, nonprofit organizations, like thescouts, have a First Amendment right to "free association." Assuch, they may not be forced to accept members or leaders whoseviews or comportment are contrary to that for which the privateorganization stands.
Critics of the court’s decision argue that the justices have givengroups, like the scouts, a license to discriminate. But had the courtcome down the other way, then a group like the NAACP could beforced to accept, say, a Ku Klux Klan member; and the B’nai B’rithcould be forced to accept a neo-Nazi in its midst.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.34
Newspaper Editorial Boards
Today, lawyers have become the pre-eminent befuddlers ofcommon sense. Among the dangerous nonsense purveyed bythese folks is the recent attempt to compel the Boy Scouts ofAmerica - a traditionalist youth group whose mission is to helpmake young men "morally straight" -to accept a homosexualscoutmaster and avowed gay rights activist. All this, on"anti-discrimination" grounds.
Wednesday, the Supreme Court rejected the idea, which hadbeen upheld by the New Jersey Supreme Court, that the BoyScouts had no fundamental right to exclude would-be memberswho do not subscribe to or conform with the organization’s mostbasic tenets. In this particular instance, the Boy Scouts withdrewthe membership of former Assistant Scoutmaster James Dale, anadult volunteer, after learning of his homosexual lifestyle. This, ofcourse, put the Boy Scouts in the gunsights as one of the lastremaining bastions of American culture that has not bowed to thegay agenda - which demands not merely live-and-let live tolerance,but total acceptance - indeed, emphatic endorsement.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.35
Newspaper Editorial Boards
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Ideal Point Estimates
Ideology
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
NYTStevens
DFPMSTSFC
GinsburgLATWPMH
SouterUSA
BreyerBG
DMNPI
AJCACHCAR
SDUTCT
CPDO'Connor
CSTAJ
KennedyRMN
RehnquistWSJ
WTNYPINV
ScaliaThomas
Prior ●
−3 −2 −1 0 1 2 3
Newspaper Ranks
Posterior Rank
NYTDFPMSTSFCLATWPMH
USABG
DMNPI
AJCACHCAR
SDUTCT
CPDCST
AJRMNWSJ
WTNYPINV
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
Probability0 0.1 0.2 0.3 0.4 0.5+
Legend
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.36
Newspaper Editorial Boards
All Top Newspapers
Den
sity
0.0
0.2
0.4
0.6
0.8
1.0
Weighted by Circulation
Unweighted
−3 −2 −1 0 1 2 3
02
4
Political Position
Den
sity
Reh
nqui
st
Ste
vens
O'C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
g
Bre
yer Justices
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.37
Misconceptions
Some scholars have expressed concern about the use of idealpoint models to study judicial behavior.
In some cases, this seems to be a knee jerk reaction againstquantification of judicial behavior.
In other cases, more sophisticated concerns are raised aboutthe data coding, modeling assumptions, and properties of theestimates.
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.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.38
Every Case Is Counted Equally
Blakely v. Washington
Latent Dimension
Slope ≈ 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Gratz v. Bollinger
Latent Dimension
Slope > 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O.C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
Grutter v. Bollinger
Latent Dimension
Slope < 0
Min
ority
(0)
Maj
ority
(1)
Reh
nqui
st
Ste
vens
O'C
onno
r
Sca
lia
Ken
nedy
Sou
ter
Tho
mas
Gin
sbur
gB
reye
r
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.39
Every Case Is Counted Equally
Time 2000 Term Votes (chronological)
StevensGinsburg
BreyerSouter
O'ConnorKennedy
RehnquistScalia
Thomas
ContestedCases
Weight
Prio
r
Dire
ctio
nal P
rior
Indi
anap
olis
v. E
dmon
d
Bus
h v.
Gor
e
SW
AN
CC
v. C
orps
Gitl
itz v
. Com
m'r
IRS
Lope
z v.
Dav
is
Sel
ing
v. Y
oung
Bre
ntw
ood
Aca
dem
y
Ill v
. McA
rthu
r
U A
la v
. Gar
rett
Lega
l Ser
v v.
Vel
azqu
ez
Sha
fer
v. S
C
Fer
guso
n v.
Cha
rlest
on
Circ
uit C
ity v
. Ada
ms
Ege
lhof
f v. E
gelh
off
Tex
v. C
obb
Eas
ley
v. C
rom
artie
Ale
xand
er v
. San
dova
l
Atw
ater
v. L
ago
Vis
ta
Dan
iels
v. U
S
Lack
awan
na D
A v
. Cos
s
Coo
per
v. L
eath
erm
an
Rog
ers
v. T
enn
Bar
tnic
ki v
. Vop
per
US
v. H
atte
r
Buc
khan
non
v. W
V H
HS
PG
A T
our
v. M
artin
NLR
B v
. Ky
Riv
er C
are
Pen
ry v
. Joh
nson
Uni
ted
Dom
inio
n v.
US
Ngu
yen
v. IN
S
Kan
v. C
olo
Kyl
lo v
. US
Goo
d N
ews
Clu
b v.
Milf
ord
Dun
can
v. W
alke
r
US
v. M
ead
Cor
p.
Idah
o v.
US
NY
T v
. Tas
ini
INS
v. S
t Cyr
Cal
cano
−M
artin
ez v
. IN
S
US
v. U
nite
d F
oods
FE
C v
. Co
Rep
Com
m
Pal
azzo
lo v
. R.I.
Loril
lard
Tob
v. R
eilly
Tyle
r v.
Cai
n
Zad
vyda
s v.
Dav
is
Predicted Rank in Latent Dimension After Observing Each CaseStevens
GinsburgBreyerSouter
O'ConnorKennedy
RehnquistScalia
Thomas
Minority
Majority
1−2
2−33−4
5−67−88−9
Finalrank
Time
Idealpoint
evolution
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.40
Unidimensional Models are Useless in a MultidimensionalWorld
The idea that something as complicated as Supreme Courtdecisionmaking can be captured with a uni-dimensional spatialmodel is very counterintuitive (outrageous???) to manyscholars of the court.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.41
Unidimensional Models are Useless in a MultidimensionalWorld
Ideal Point Estimates
Dimension 1
Dim
ensi
on 2
●
●
●
●
●
●
●
●
●
Stevens
Scalia
Thomas
Rehnquist
Kennedy
O'ConnorBreyer
SouterGinsburg
Cases Consistent with Unidimensionality
Dimension 1
Dim
ensi
on 2
●
●
●
●
●
●
●
●
●
Cases Inconsistent with Unidimensionality
Dimension 1
Dim
ensi
on 2
●
●
●
●
●
●
●
●
●
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.42
Unidimensional Models are Useless in a MultidimensionalWorld
1940 1950 1960 1970 1980 1990 2000
How Statutory Cases Differ
Term
Fra
ctio
n S
tatu
tory
Vot
es C
orre
ctly
Cla
ssifi
ed (
Act
ual −
Nul
l)
−0.
10.
00.
1
●●
●
●●
●
●
●
●
●
●●●
●●
●
● ●● ●
Significantly Less Than Null Value
Not Significantly Less Than Null Value
Comparison of ability to classify votes on cases with WestlawKey Number Statutory Construction and Operation (361VI)relative to null distribution formed from all nonunanimous casesin term.
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.43
Selection Bias Creates Serious Problems
Simple Random Sampling
Cutpoints
Fre
quen
cy
−2 −1 0 1 2
010
2030
4050
● ● ● ● ● ● ● ● ●
Biased Case Selection
Cutpoints
Fre
quen
cy
−2 −1 0 1 2
010
2030
4050
● ● ● ● ● ● ● ● ●
−3 −2 −1 0 1 2 3
−4
−2
02
Cardinal Ideal Points
Simple Random Sampling
Bia
sed
Cas
e S
elec
tion
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
2 4 6 8
24
68
Expected Ranks of Ideal Points
Simple Random Sampling
Bia
sed
Cas
e S
elec
tion
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.44
All Estimates from Latent Variable Models Are Sensitive toArbitrary Modeling Assumptions
−4 −2 0 2 4
0.00
0.10
0.20
0.30
Prior Density of Cutpoints
Model 1
Model 2
Cutpoints
Prio
r D
ensi
ty
−6 −4 −2 0 2 4 6
−6
−4
−2
02
46
Cardinal Comparisons
●
●
●
●
●
●
●
● ●
Ideal Point (Model 1)
Idea
l Poi
nt (
Mod
el 2
)
Ordinal Comparisons
●
●
●
●
●
●
●
●
●
Expected Rank (Model 1)
Exp
ecte
d R
ank
(Mod
el 2
)
1 2 3 4 5 6 7 8 9
12
34
56
78
9
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.45
All Estimates from Latent Variable Models Are Sensitive toArbitrary Modeling Assumptions
1970 1975 1980 1985 1990
Evolution of Justice Blackmun
Term
Late
nt D
imen
sion
Naturalcourt
Natural Court
Term1975 1977 1979
Late
nt D
imen
sion
Stewart
MarshallBrennan
White
Burger
Blackmun
Powell
Rehnquist
Stevens
The Spatial Model ofVoting:
Theory andEmpirics
TheoryBackground
Example: CandidateCompetition
The Median Voter Theorem
Example: StatutoryInterpretation
EmpiricsThe Spatial Model as anEmpirical Model
Example: The US Congress
Example: The US SupremeCourt
Example: NewspaperEditorial Boards
Misconceptions
.46
All Estimates from Latent Variable Models Are Sensitive toArbitrary Modeling Assumptions
Term Justice Prob. Median1998 Kennedy 0.5741999 O’Connor 0.9012000 O’Connor 0.9922001 O’Connor > 0.9992002 O’Connor 0.998
(from Martin, Quinn, & Epstein, 2005)
These are useful summaries under a very wide range ofassumptions.
