test

PROBLEMS AND EXERCISES

Problems and exercises 1. Visualization and basic exploration of data

For the problems in this chapter, we will use the United States Supreme Court decisions in the Rehnquist court (1986–2005) for the year 1997 (Rehnquist_SupremeCourt). The data consist of the nine justices’ decisions on m cases (for the sake of simplicity, a 1 reflects agreement with the majority decision, while a 0 reflects agreement with the minority decision). First we will focus on visualizing both networks.

a First, visualize the two-mode network. Do there appear to be any patterns with respect to the clustering of the justices?

RSV<-Rehnquist_SupremeCourt$Votes[78:111,]

DIM1<-dim(RSV)

#To be able to use different colors and shapes, for the one mode and the second mode, we create a vector with 0 for actors and 1 for events.

RC1<-c(rep(0, DIM1[1]),rep(1, DIM1[1]))

RC1

## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

## [39] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

#We also create our own labeling:

LABELS1<-c(substr(rownames(RSV),1,3),substr(colnames(RSV),1,3))

LABELS1

## [1] "E07" "E07" "E08" "E08" "E08" "E08" "E08" "E08" "E08" "E08" "E08" "E08"

## [13] "E09" "E09" "E09" "E09" "E09" "E09" "E09" "E09" "E09" "E09" "E10" "E10"

## [25] "E10" "E10" "E10" "E10" "E10" "E10" "E10" "E10" "E11" "E11" "Reh" "Ste"

## [37] "O_C" "Sca" "Ken" "Sou" "Tho" "Gin" "Bre"

#Now let's draw the network:

par(mar = c(0, 0, 0, 0))

sna::gplot(RSV,

mode = "fruchtermanreingold",

gmode="twomode",

#Labels

displaylabels=TRUE,

label = LABELS1,

label.cex=.7,

label.pos=5,

#Edges

usearrows=FALSE,

#Vertices

vertex.cex=RC1*.5+1.7,

vertex.rot=45,

vertex.col=RC1*7)

b Next, we focus on visualizing the relationship among justices vis-à-vis court decisions on cases. Create a projected network of relations among justices. How would you interpret the values in each of the off-diagonal cells of the resulting one-mode affiliation network? What about the values in the diagonal cells of the matrix?

xTwoModeToOneMode(t(Rehnquist_SupremeCourt$Votes[78:111,]))

## Rehnquist Stevens O_Connor Scalia Kennedy Souter Thomas Ginsberg

## Rehnquist 27 7 21 21 25 17 22 13

## Stevens 7 14 7 3 11 12 4 11

## O_Connor 21 7 26 20 23 16 21 13

## Scalia 21 3 20 23 22 13 23 9

## Kennedy 25 11 23 22 30 19 23 14

## Souter 17 12 16 13 19 23 14 16

## Thomas 22 4 21 23 23 14 24 10

## Ginsberg 13 11 13 9 14 16 10 18

## Breyer 12 11 13 8 14 16 8 14

## Breyer

## Rehnquist 12

## Stevens 11

## O_Connor 13

## Scalia 8

## Kennedy 14

## Souter 16

## Thomas 8

## Ginsberg 14

## Breyer 18

c Finally, we focus on the relationship between court cases vis-à-vis the justices. For this, we project the two-mode matrix into a one-mode matrix of relationships among cases. How would you interpret the values in each of the off-diagonal cells of the resulting onemode projection network? What about the values in the diagonal cells of the matrix?

xTwoModeToOneMode(Rehnquist_SupremeCourt$Votes[78:111,])

## E078_Abr97 E079_Ago97 E080_Ass97 E081_Bab97 E082_Bog97 E083_Boa97

## E078_Abr97 5 5 5 5 3 5

## E079_Ago97 5 5 5 5 3 5

## E080_Ass97 5 5 8 8 4 5

## E081_Bab97 5 5 8 8 4 5

## E082_Bog97 3 3 4 4 5 3

## E083_Boa97 5 5 5 5 3 5

## E084_Cam97 2 2 4 4 3 2

## E085_Cha97 4 4 7 7 5 4

## E086_Cit97 4 4 5 5 4 4

## E087_Cit97 5 5 7 7 4 5

## E088_Com97 4 4 6 6 4 4

## E089_De_97 3 3 6 6 3 3

## E090_Gen97 5 5 8 8 4 5

## E091_Gli97 2 2 4 4 2 2

## E092_Har97 5 5 6 6 4 5

## E093_Ida97 5 5 5 5 3 5

## E094_Jef97 5 5 8 8 4 5

## E095_Kan97 5 5 5 5 3 5

## E096_Lam97 4 4 5 5 4 4

## E097_Law97 1 1 4 4 2 1

## E098_Lin97 1 1 4 4 2 1

## E099_Mar97 4 4 7 7 3 4

## E100_Met97 2 2 5 5 3 2

## E101_McM97 5 5 5 5 3 5

## E102_O__97 5 5 5 5 3 5

## E103_Old97 1 1 4 4 3 1

## E104_Pri97 5 5 5 5 3 5

## E105_Rai97 5 5 7 7 4 5

## E106_Ric97 1 1 4 4 2 1

## E107_Sar97 2 2 5 5 3 2

## E108_Tim97 5 5 6 6 3 5

## E109_Tur97 2 2 4 4 3 2

## E110_U_S97 5 5 7 7 4 5

## E111_U_S97 5 5 6 6 4 5

## E084_Cam97 E085_Cha97 E086_Cit97 E087_Cit97 E088_Com97 E089_De_97

## E078_Abr97 2 4 4 5 4 3

## E079_Ago97 2 4 4 5 4 3

## E080_Ass97 4 7 5 7 6 6

## E081_Bab97 4 7 5 7 6 6

## E082_Bog97 3 5 4 4 4 3

## E083_Boa97 2 4 4 5 4 3

## E084_Cam97 5 5 2 4 4 5

## E085_Cha97 5 8 5 6 6 6

## E086_Cit97 2 5 6 4 5 4

## E087_Cit97 4 6 4 7 5 5

## E088_Com97 4 6 5 5 7 6

## E089_De_97 5 6 4 5 6 7

## E090_Gen97 4 7 5 7 6 6

## E091_Gli97 4 5 3 3 4 5

## E092_Har97 3 5 4 6 5 4

## E093_Ida97 2 4 4 5 4 3

## E094_Jef97 4 7 5 7 6 6

## E095_Kan97 2 4 4 5 4 3

## E096_Lam97 2 4 4 5 4 3

## E097_Law97 3 4 3 3 4 5

## E098_Lin97 4 5 2 3 4 5

## E099_Mar97 3 6 4 6 5 5

## E100_Met97 4 5 4 4 5 6

## E101_McM97 2 4 4 5 4 3

## E102_O__97 2 4 4 5 4 3

## E103_Old97 4 5 3 3 4 5

## E104_Pri97 2 4 4 5 4 3

## E105_Rai97 3 6 5 6 6 5

## E106_Ric97 4 5 2 3 4 5

## E107_Sar97 4 5 4 4 5 6

## E108_Tim97 3 5 4 6 4 4

## E109_Tur97 4 4 3 4 4 5

## E110_U_S97 3 6 5 6 6 5

## E111_U_S97 3 5 4 6 5 4

## E090_Gen97 E091_Gli97 E092_Har97 E093_Ida97 E094_Jef97 E095_Kan97

## E078_Abr97 5 2 5 5 5 5

## E079_Ago97 5 2 5 5 5 5

## E080_Ass97 8 4 6 5 8 5

## E081_Bab97 8 4 6 5 8 5

## E082_Bog97 4 2 4 3 4 3

## E083_Boa97 5 2 5 5 5 5

## E084_Cam97 4 4 3 2 4 2

## E085_Cha97 7 5 5 4 7 4

## E086_Cit97 5 3 4 4 5 4

## E087_Cit97 7 3 6 5 7 5

## E088_Com97 6 4 5 4 6 4

## E089_De_97 6 5 4 3 6 3

## E090_Gen97 8 4 6 5 8 5

## E091_Gli97 4 5 2 2 4 2

## E092_Har97 6 2 6 5 6 5

## E093_Ida97 5 2 5 5 5 5

## E094_Jef97 8 4 6 5 8 5

## E095_Kan97 5 2 5 5 5 5

## E096_Lam97 5 1 5 4 5 4

## E097_Law97 4 3 2 1 4 1

## E098_Lin97 4 4 2 1 4 1

## E099_Mar97 7 3 5 4 7 4

## E100_Met97 5 4 3 2 5 2

## E101_McM97 5 2 5 5 5 5

## E102_O__97 5 2 5 5 5 5

## E103_Old97 4 4 2 1 4 1

## E104_Pri97 5 2 5 5 5 5

## E105_Rai97 7 3 6 5 7 5

## E106_Ric97 4 4 2 1 4 1

## E107_Sar97 5 4 3 2 5 2

## E108_Tim97 6 3 5 5 6 5

## E109_Tur97 4 3 3 2 4 2

## E110_U_S97 7 3 6 5 7 5

## E111_U_S97 6 2 6 5 6 5

## E096_Lam97 E097_Law97 E098_Lin97 E099_Mar97 E100_Met97 E101_McM97

## E078_Abr97 4 1 1 4 2 5

## E079_Ago97 4 1 1 4 2 5

## E080_Ass97 5 4 4 7 5 5

## E081_Bab97 5 4 4 7 5 5

## E082_Bog97 4 2 2 3 3 3

## E083_Boa97 4 1 1 4 2 5

## E084_Cam97 2 3 4 3 4 2

## E085_Cha97 4 4 5 6 5 4

## E086_Cit97 4 3 2 4 4 4

## E087_Cit97 5 3 3 6 4 5

## E088_Com97 4 4 4 5 5 4

## E089_De_97 3 5 5 5 6 3

## E090_Gen97 5 4 4 7 5 5

## E091_Gli97 1 3 4 3 4 2

## E092_Har97 5 2 2 5 3 5

## E093_Ida97 4 1 1 4 2 5

## E094_Jef97 5 4 4 7 5 5

## E095_Kan97 4 1 1 4 2 5

## E096_Lam97 5 2 1 4 3 4

## E097_Law97 2 5 4 4 5 1

## E098_Lin97 1 4 5 4 4 1

## E099_Mar97 4 4 4 7 4 4

## E100_Met97 3 5 4 4 6 2

## E101_McM97 4 1 1 4 2 5

## E102_O__97 4 1 1 4 2 5

## E103_Old97 2 4 4 3 5 1

## E104_Pri97 4 1 1 4 2 5

## E105_Rai97 5 3 3 6 4 5

## E106_Ric97 1 4 5 4 4 1

## E107_Sar97 3 5 4 4 6 2

## E108_Tim97 4 2 2 5 3 5

## E109_Tur97 3 4 3 3 5 2

## E110_U_S97 5 3 3 6 4 5

## E111_U_S97 5 2 2 5 3 5

## E102_O__97 E103_Old97 E104_Pri97 E105_Rai97 E106_Ric97 E107_Sar97

## E078_Abr97 5 1 5 5 1 2

## E079_Ago97 5 1 5 5 1 2

## E080_Ass97 5 4 5 7 4 5

## E081_Bab97 5 4 5 7 4 5

## E082_Bog97 3 3 3 4 2 3

## E083_Boa97 5 1 5 5 1 2

## E084_Cam97 2 4 2 3 4 4

## E085_Cha97 4 5 4 6 5 5

## E086_Cit97 4 3 4 5 2 4

## E087_Cit97 5 3 5 6 3 4

## E088_Com97 4 4 4 6 4 5

## E089_De_97 3 5 3 5 5 6

## E090_Gen97 5 4 5 7 4 5

## E091_Gli97 2 4 2 3 4 4

## E092_Har97 5 2 5 6 2 3

## E093_Ida97 5 1 5 5 1 2

## E094_Jef97 5 4 5 7 4 5

## E095_Kan97 5 1 5 5 1 2

## E096_Lam97 4 2 4 5 1 3

## E097_Law97 1 4 1 3 4 5

## E098_Lin97 1 4 1 3 5 4

## E099_Mar97 4 3 4 6 4 4

## E100_Met97 2 5 2 4 4 6

## E101_McM97 5 1 5 5 1 2

## E102_O__97 5 1 5 5 1 2

## E103_Old97 1 5 1 3 4 5

## E104_Pri97 5 1 5 5 1 2

## E105_Rai97 5 3 5 7 3 4

## E106_Ric97 1 4 1 3 5 4

## E107_Sar97 2 5 2 4 4 6

## E108_Tim97 5 2 5 5 2 3

## E109_Tur97 2 4 2 3 3 5

## E110_U_S97 5 3 5 7 3 4

## E111_U_S97 5 2 5 6 2 3

## E108_Tim97 E109_Tur97 E110_U_S97 E111_U_S97

## E078_Abr97 5 2 5 5

## E079_Ago97 5 2 5 5

## E080_Ass97 6 4 7 6

## E081_Bab97 6 4 7 6

## E082_Bog97 3 3 4 4

## E083_Boa97 5 2 5 5

## E084_Cam97 3 4 3 3

## E085_Cha97 5 4 6 5

## E086_Cit97 4 3 5 4

## E087_Cit97 6 4 6 6

## E088_Com97 4 4 6 5

## E089_De_97 4 5 5 4

## E090_Gen97 6 4 7 6

## E091_Gli97 3 3 3 2

## E092_Har97 5 3 6 6

## E093_Ida97 5 2 5 5

## E094_Jef97 6 4 7 6

## E095_Kan97 5 2 5 5

## E096_Lam97 4 3 5 5

## E097_Law97 2 4 3 2

## E098_Lin97 2 3 3 2

## E099_Mar97 5 3 6 5

## E100_Met97 3 5 4 3

## E101_McM97 5 2 5 5

## E102_O__97 5 2 5 5

## E103_Old97 2 4 3 2

## E104_Pri97 5 2 5 5

## E105_Rai97 5 3 7 6

## E106_Ric97 2 3 3 2

## E107_Sar97 3 5 4 3

## E108_Tim97 6 3 5 5

## E109_Tur97 3 5 3 3

## E110_U_S97 5 3 7 6

## E111_U_S97 5 3 6 6

Problems and exercises 2. Centrality measures

2 Consider the centrality for the supreme court network. a Using the original two-mode network, which judge is the most and least degree central, and which of the cases is the most and least degree central? What do these values indicate.

xDegreeCentrality(t(Rehnquist_SupremeCourt$Votes[78:111,]))

## TwoMode network

## Degree nDegree

## Rehnquist 27 0.7941176

## Stevens 14 0.4117647

## O_Connor 26 0.7647059

## Scalia 23 0.6764706

## Kennedy 30 0.8823529

## Souter 23 0.6764706

## Thomas 24 0.7058824

## Ginsberg 18 0.5294118

## Breyer 18 0.5294118

xDegreeCentrality(Rehnquist_SupremeCourt$Votes[78:111,])

## TwoMode network

## Degree nDegree

## E078_Abr97 5 0.5555556

## E079_Ago97 5 0.5555556

## E080_Ass97 8 0.8888889

## E081_Bab97 8 0.8888889

## E082_Bog97 5 0.5555556

## E083_Boa97 5 0.5555556

## E084_Cam97 5 0.5555556

## E085_Cha97 8 0.8888889

## E086_Cit97 6 0.6666667

## E087_Cit97 7 0.7777778

## E088_Com97 7 0.7777778

## E089_De_97 7 0.7777778

## E090_Gen97 8 0.8888889

## E091_Gli97 5 0.5555556

## E092_Har97 6 0.6666667

## E093_Ida97 5 0.5555556

## E094_Jef97 8 0.8888889

## E095_Kan97 5 0.5555556

## E096_Lam97 5 0.5555556

## E097_Law97 5 0.5555556

## E098_Lin97 5 0.5555556

## E099_Mar97 7 0.7777778

## E100_Met97 6 0.6666667

## E101_McM97 5 0.5555556

## E102_O__97 5 0.5555556

## E103_Old97 5 0.5555556

## E104_Pri97 5 0.5555556

## E105_Rai97 7 0.7777778

## E106_Ric97 5 0.5555556

## E107_Sar97 6 0.6666667

## E108_Tim97 6 0.6666667

## E109_Tur97 5 0.5555556

## E110_U_S97 7 0.7777778

## E111_U_S97 6 0.6666667

b Considering the projection of the two-mode matrix into a one-mode matrix of relationships among judges. Dichotomize the network using a cutoff of 14 and calculate the degree, closeness and betweenness centrality for this one-mode matrix. What do the different measures mean?

JBJ<-xTwoModeToOneMode(t(Rehnquist_SupremeCourt$Votes[78:111,]))>13

xDegreeCentrality(JBJ)

## Degree nDegree

## Rehnquist 5 0.625

## Stevens 0 0.000

## O_Connor 5 0.625

## Scalia 4 0.500

## Kennedy 7 0.875

## Souter 6 0.750

## Thomas 5 0.625

## Ginsberg 3 0.375

## Breyer 3 0.375

xClosenessCentrality(JBJ)

## FreemanCloseness nFreemanCloseness ReciprocalCloseness

## Rehnquist 12 0.6666667 6.0

## Stevens 24 0.3333333 0.0

## O_Connor 12 0.6666667 6.0

## Scalia 13 0.6153846 5.5

## Kennedy 10 0.8000000 7.0

## Souter 11 0.7272727 6.5

## Thomas 12 0.6666667 6.0

## Ginsberg 14 0.5714286 5.0

## Breyer 14 0.5714286 5.0

## nReciprocalCloseness ValenteForemanCloseness nValenteForemanCloseness

## Rehnquist 0.7500 12 0.7500

## Stevens 0.0000 0 0.0000

## O_Connor 0.7500 12 0.7500

## Scalia 0.6875 11 0.6875

## Kennedy 0.8750 14 0.8750

## Souter 0.8125 13 0.8125

## Thomas 0.7500 12 0.7500

## Ginsberg 0.6250 10 0.6250

## Breyer 0.6250 10 0.6250

xBetweennessCentrality(JBJ)

## Betweenness nBetweenness

## Rehnquist 0.5 0.008928571

## Stevens 0.0 0.000000000

## O_Connor 0.5 0.008928571

## Scalia 0.0 0.000000000

## Kennedy 10.5 0.187500000

## Souter 6.0 0.107142857

## Thomas 0.5 0.008928571

## Ginsberg 0.0 0.000000000

## Breyer 0.0 0.000000000

Problems and exercises 3. Clustering and dual projections

3 The Rehnquist Court was known for its the division between liberal and conservative justices. There are a number of ways of looking for cohesive subgroups in the Supreme Court data. We will explore three of them.

a The first is to use modularity optimization via the dual projection method. Apply the Louvain method to both of your projections and combine them into a blocked incidence matrix. How might you interpret the resulting blocked matrix in terms of a possible division in the court between liberal and conservative justices?

CL2<-xDualLouvainMethod(Rehnquist_SupremeCourt$Votes[78:111,])

CL2

## [[1]]

## CL_4

## E078_Abr97 1

## E079_Ago97 1

## E080_Ass97 2

## E081_Bab97 2

## E082_Bog97 3

## E083_Boa97 1

## E084_Cam97 4

## E085_Cha97 4

## E086_Cit97 3

## E087_Cit97 1

## E088_Com97 4

## E089_De_97 4

## E090_Gen97 2

## E091_Gli97 4

## E092_Har97 1

## E093_Ida97 1

## E094_Jef97 2

## E095_Kan97 1

## E096_Lam97 1

## E097_Law97 4

## E098_Lin97 4

## E099_Mar97 2

## E100_Met97 4

## E101_McM97 1

## E102_O__97 1

## E103_Old97 4

## E104_Pri97 1

## E105_Rai97 1

## E106_Ric97 4

## E107_Sar97 4

## E108_Tim97 1

## E109_Tur97 4

## E110_U_S97 1

## E111_U_S97 1

##

## [[2]]

## CL_5

## Rehnquist 1

## Stevens 2

## O_Connor 3

## Scalia 4

## Kennedy 5

## Souter 2

## Thomas 4

## Ginsberg 2

## Breyer 2

blockmodeling::plot.mat(Rehnquist_SupremeCourt$Votes[78:111,], clu=CL2)

b As with one-mode networks, we can also look for structural equivalence by calculating profile similarities for the rows and columns of the matrix. Since we are mostly interested in the justices, we will only examine row profile similarity. Calculate the profile similarity matrix using Euclidean distance on the rows of the matrix.

SEM2A<-xStructuralEquivalence(t(Rehnquist_SupremeCourt$Votes[78:111,]))

## Note that "Euclidean" and "AbsDiff" result in a matrix where high values represent differences. "MatchesN", "PosMatchesN", "Product", "Pearson", "Kendall" and "Spearman" result in a matrix where high values represent similarities./n

SEM2A

## Rehnquist Stevens O_Connor Scalia Kennedy Souter Thomas Ginsberg

## Rehnquist 0.00000 5.19615 3.31662 2.82843 2.64575 4.00000 2.64575 4.35890

## Stevens 5.19615 0.00000 5.09902 5.56776 4.69042 3.60555 5.47723 3.16228

## O_Connor 3.31662 5.09902 0.00000 3.00000 3.16228 4.12311 2.82843 4.24264

## Scalia 2.82843 5.56776 3.00000 0.00000 3.00000 4.47214 1.00000 4.79583

## Kennedy 2.64575 4.69042 3.16228 3.00000 0.00000 3.87298 2.82843 4.47214

## Souter 4.00000 3.60555 4.12311 4.47214 3.87298 0.00000 4.35890 3.00000

## Thomas 2.64575 5.47723 2.82843 1.00000 2.82843 4.35890 0.00000 4.69042

## Ginsberg 4.35890 3.16228 4.24264 4.79583 4.47214 3.00000 4.69042 0.00000

## Breyer 4.58258 3.16228 4.24264 5.00000 4.47214 3.00000 5.09902 2.82843

## Breyer

## Rehnquist 4.58258

## Stevens 3.16228

## O_Connor 4.24264

## Scalia 5.00000

## Kennedy 4.47214

## Souter 3.00000

## Thomas 5.09902

## Ginsberg 2.82843

## Breyer 0.00000

c The similarity matrix of matches on court decisions among the justices lends itself to hierarchical cluster analysis to better understand the presence of subgroupings among the justices. Submit your similarity matrix to average-linkage hierarchical clustering. What does the cluster diagram tell you about the divisions among the justices?

CL1<-xHierarchicalClustering(SEM2A, Input="Differences", Method="average", NOC=3)

CL1

## CL_3

## Rehnquist 1

## Stevens 2

## O_Connor 1

## Scalia 1

## Kennedy 1

## Souter 3

## Thomas 1

## Ginsberg 3

## Breyer 3

blockmodeling::plot.mat(JBJ, clu=CL1)

d Finally, perform a bi-clique analysis on your data and perform a hierarchical cluster analysis on the bi-clique co-membership of both cases and judges.

BC<-xBiCliques(Rehnquist_SupremeCourt$Votes[78:111,])

BC%*%t(BC)

## E078_Abr97 E079_Ago97 E080_Ass97 E081_Bab97 E082_Bog97 E083_Boa97

## E078_Abr97 12 12 12 12 1 12

## E079_Ago97 12 12 12 12 1 12

## E080_Ass97 12 12 89 89 4 12

## E081_Bab97 12 12 89 89 4 12

## E082_Bog97 1 1 4 4 8 1

## E083_Boa97 12 12 12 12 1 12

## E084_Cam97 0 0 5 5 1 0

## E085_Cha97 4 4 40 40 8 4

## E086_Cit97 4 4 12 12 3 4

## E087_Cit97 12 12 50 50 4 12

## E088_Com97 5 5 32 32 4 5

## E089_De_97 1 1 36 36 1 1

## E090_Gen97 12 12 89 89 4 12

## E091_Gli97 0 0 5 5 0 0

## E092_Har97 12 12 31 31 4 12

## E093_Ida97 12 12 12 12 1 12

## E094_Jef97 12 12 89 89 4 12

## E095_Kan97 12 12 12 12 1 12

## E096_Lam97 4 4 12 12 4 4

## E097_Law97 0 0 4 4 0 0

## E098_Lin97 0 0 5 5 0 0

## E099_Mar97 4 4 37 37 1 4

## E100_Met97 0 0 14 14 1 0

## E101_McM97 12 12 12 12 1 12

## E102_O__97 12 12 12 12 1 12

## E103_Old97 0 0 5 5 1 0

## E104_Pri97 12 12 12 12 1 12

## E105_Rai97 12 12 55 55 4 12

## E106_Ric97 0 0 5 5 0 0

## E107_Sar97 0 0 14 14 1 0

## E108_Tim97 12 12 20 20 1 12

## E109_Tur97 0 0 5 5 1 0

## E110_U_S97 12 12 55 55 4 12

## E111_U_S97 12 12 31 31 4 12

## Rehnquist 8 8 49 49 0 8

## Stevens 0 0 0 0 4 0

## O_Connor 8 8 57 57 0 8

## Scalia 7 7 35 35 4 7

## Kennedy 8 8 52 52 7 8

## Souter 0 0 57 57 5 0

## Thomas 11 11 53 53 7 11

## Ginsberg 0 0 39 39 0 0

## Breyer 0 0 34 34 0 0

## E084_Cam97 E085_Cha97 E086_Cit97 E087_Cit97 E088_Com97 E089_De_97

## E078_Abr97 0 4 4 12 5 1

## E079_Ago97 0 4 4 12 5 1

## E080_Ass97 5 40 12 50 32 36

## E081_Bab97 5 40 12 50 32 36

## E082_Bog97 1 8 3 4 4 1

## E083_Boa97 0 4 4 12 5 1

## E084_Cam97 16 16 0 5 5 16

## E085_Cha97 16 69 8 20 26 41

## E086_Cit97 0 8 19 4 11 5

## E087_Cit97 5 20 4 50 16 16

## E088_Com97 5 26 11 16 53 32

## E089_De_97 16 41 5 16 32 72

## E090_Gen97 5 40 12 50 32 36

## E091_Gli97 5 16 1 1 5 16

## E092_Har97 1 12 4 31 16 5

## E093_Ida97 0 4 4 12 5 1

## E094_Jef97 5 40 12 50 32 36

## E095_Kan97 0 4 4 12 5 1

## E096_Lam97 0 4 4 12 5 1

## E097_Law97 1 5 1 1 5 13

## E098_Lin97 5 16 0 1 5 16

## E099_Mar97 1 15 4 20 11 13

## E100_Met97 5 16 5 5 16 36

## E101_McM97 0 4 4 12 5 1

## E102_O__97 0 4 4 12 5 1

## E103_Old97 5 16 1 1 5 16

## E104_Pri97 0 4 4 12 5 1

## E105_Rai97 1 23 12 31 32 14

## E106_Ric97 5 16 0 1 5 16

## E107_Sar97 5 16 5 5 16 36

## E108_Tim97 1 7 4 20 5 5

## E109_Tur97 5 5 1 5 5 14

## E110_U_S97 1 23 12 31 32 14

## E111_U_S97 1 12 4 31 16 5

## Rehnquist 0 0 11 30 27 31

## Stevens 11 29 7 0 21 36

## O_Connor 11 42 0 34 27 36

## Scalia 0 18 8 23 0 0

## Kennedy 11 43 14 30 35 43

## Souter 11 41 0 30 34 48

## Thomas 0 28 14 34 21 0

## Ginsberg 0 35 12 0 28 40

## Breyer 11 31 0 19 0 40

## E090_Gen97 E091_Gli97 E092_Har97 E093_Ida97 E094_Jef97 E095_Kan97

## E078_Abr97 12 0 12 12 12 12

## E079_Ago97 12 0 12 12 12 12

## E080_Ass97 89 5 31 12 89 12

## E081_Bab97 89 5 31 12 89 12

## E082_Bog97 4 0 4 1 4 1

## E083_Boa97 12 0 12 12 12 12

## E084_Cam97 5 5 1 0 5 0

## E085_Cha97 40 16 12 4 40 4

## E086_Cit97 12 1 4 4 12 4

## E087_Cit97 50 1 31 12 50 12

## E088_Com97 32 5 16 5 32 5

## E089_De_97 36 16 5 1 36 1

## E090_Gen97 89 5 31 12 89 12

## E091_Gli97 5 16 0 0 5 0

## E092_Har97 31 0 31 12 31 12

## E093_Ida97 12 0 12 12 12 12

## E094_Jef97 89 5 31 12 89 12

## E095_Kan97 12 0 12 12 12 12

## E096_Lam97 12 0 12 4 12 4

## E097_Law97 4 1 0 0 4 0

## E098_Lin97 5 5 0 0 5 0

## E099_Mar97 37 1 12 4 37 4

## E100_Met97 14 5 1 0 14 0

## E101_McM97 12 0 12 12 12 12

## E102_O__97 12 0 12 12 12 12

## E103_Old97 5 5 0 0 5 0

## E104_Pri97 12 0 12 12 12 12

## E105_Rai97 55 1 31 12 55 12

## E106_Ric97 5 5 0 0 5 0

## E107_Sar97 14 5 1 0 14 0

## E108_Tim97 20 1 12 12 20 12

## E109_Tur97 5 1 1 0 5 0

## E110_U_S97 55 1 31 12 55 12

## E111_U_S97 31 0 31 12 31 12

## Rehnquist 49 0 19 8 49 8

## Stevens 0 11 0 0 0 0

## O_Connor 57 11 19 8 57 8

## Scalia 35 0 15 7 35 7

## Kennedy 52 11 19 8 52 8

## Souter 57 0 19 0 57 0

## Thomas 53 0 26 11 53 11

## Ginsberg 39 11 0 0 39 0

## Breyer 34 11 0 0 34 0

## E096_Lam97 E097_Law97 E098_Lin97 E099_Mar97 E100_Met97 E101_McM97

## E078_Abr97 4 0 0 4 0 12

## E079_Ago97 4 0 0 4 0 12

## E080_Ass97 12 4 5 37 14 12

## E081_Bab97 12 4 5 37 14 12

## E082_Bog97 4 0 0 1 1 1

## E083_Boa97 4 0 0 4 0 12

## E084_Cam97 0 1 5 1 5 0

## E085_Cha97 4 5 16 15 16 4

## E086_Cit97 4 1 0 4 5 4

## E087_Cit97 12 1 1 20 5 12

## E088_Com97 5 5 5 11 16 5

## E089_De_97 1 13 16 13 36 1

## E090_Gen97 12 4 5 37 14 12

## E091_Gli97 0 1 5 1 5 0

## E092_Har97 12 0 0 12 1 12

## E093_Ida97 4 0 0 4 0 12

## E094_Jef97 12 4 5 37 14 12

## E095_Kan97 4 0 0 4 0 12

## E096_Lam97 12 0 0 4 1 4

## E097_Law97 0 13 5 4 13 0

## E098_Lin97 0 5 16 5 5 0

## E099_Mar97 4 4 5 37 4 4

## E100_Met97 1 13 5 4 36 0

## E101_McM97 4 0 0 4 0 12

## E102_O__97 4 0 0 4 0 12

## E103_Old97 0 5 5 1 16 0

## E104_Pri97 4 0 0 4 0 12

## E105_Rai97 12 1 1 22 5 12

## E106_Ric97 0 5 16 5 5 0

## E107_Sar97 1 13 5 4 36 0

## E108_Tim97 4 0 0 7 1 12

## E109_Tur97 1 4 1 1 14 0

## E110_U_S97 12 1 1 22 5 12

## E111_U_S97 12 0 0 12 1 12

## Rehnquist 8 8 0 22 20 8

## Stevens 0 9 11 0 22 0

## O_Connor 0 0 11 26 0 8

## Scalia 7 0 0 17 0 7

## Kennedy 8 0 0 0 23 8

## Souter 8 11 11 26 26 0

## Thomas 11 0 0 24 0 11

## Ginsberg 0 9 11 17 22 0

## Breyer 0 8 11 15 20 0

## E102_O__97 E103_Old97 E104_Pri97 E105_Rai97 E106_Ric97 E107_Sar97

## E078_Abr97 12 0 12 12 0 0

## E079_Ago97 12 0 12 12 0 0

## E080_Ass97 12 5 12 55 5 14

## E081_Bab97 12 5 12 55 5 14

## E082_Bog97 1 1 1 4 0 1

## E083_Boa97 12 0 12 12 0 0

## E084_Cam97 0 5 0 1 5 5

## E085_Cha97 4 16 4 23 16 16

## E086_Cit97 4 1 4 12 0 5

## E087_Cit97 12 1 12 31 1 5

## E088_Com97 5 5 5 32 5 16

## E089_De_97 1 16 1 14 16 36

## E090_Gen97 12 5 12 55 5 14

## E091_Gli97 0 5 0 1 5 5

## E092_Har97 12 0 12 31 0 1

## E093_Ida97 12 0 12 12 0 0

## E094_Jef97 12 5 12 55 5 14

## E095_Kan97 12 0 12 12 0 0

## E096_Lam97 4 0 4 12 0 1

## E097_Law97 0 5 0 1 5 13

## E098_Lin97 0 5 0 1 16 5

## E099_Mar97 4 1 4 22 5 4

## E100_Met97 0 16 0 5 5 36

## E101_McM97 12 0 12 12 0 0

## E102_O__97 12 0 12 12 0 0

## E103_Old97 0 16 0 1 5 16

## E104_Pri97 12 0 12 12 0 0

## E105_Rai97 12 1 12 55 1 5

## E106_Ric97 0 5 0 1 16 5

## E107_Sar97 0 16 0 5 5 36

## E108_Tim97 12 0 12 12 0 1

## E109_Tur97 0 5 0 1 1 14

## E110_U_S97 12 1 12 55 1 5

## E111_U_S97 12 0 12 31 0 1

## Rehnquist 8 0 8 32 0 20

## Stevens 0 11 0 0 11 22

## O_Connor 8 0 8 32 11 0

## Scalia 7 0 7 23 0 0

## Kennedy 8 11 8 33 0 23

## Souter 0 11 0 34 11 26

## Thomas 11 0 11 41 0 0

## Ginsberg 0 11 0 24 11 22

## Breyer 0 11 0 0 11 20

## E108_Tim97 E109_Tur97 E110_U_S97 E111_U_S97 Rehnquist Stevens

## E078_Abr97 12 0 12 12 8 0

## E079_Ago97 12 0 12 12 8 0

## E080_Ass97 20 5 55 31 49 0

## E081_Bab97 20 5 55 31 49 0

## E082_Bog97 1 1 4 4 0 4

## E083_Boa97 12 0 12 12 8 0

## E084_Cam97 1 5 1 1 0 11

## E085_Cha97 7 5 23 12 0 29

## E086_Cit97 4 1 12 4 11 7

## E087_Cit97 20 5 31 31 30 0

## E088_Com97 5 5 32 16 27 21

## E089_De_97 5 14 14 5 31 36

## E090_Gen97 20 5 55 31 49 0

## E091_Gli97 1 1 1 0 0 11

## E092_Har97 12 1 31 31 19 0

## E093_Ida97 12 0 12 12 8 0

## E094_Jef97 20 5 55 31 49 0

## E095_Kan97 12 0 12 12 8 0

## E096_Lam97 4 1 12 12 8 0

## E097_Law97 0 4 1 0 8 9

## E098_Lin97 0 1 1 0 0 11

## E099_Mar97 7 1 22 12 22 0

## E100_Met97 1 14 5 1 20 22

## E101_McM97 12 0 12 12 8 0

## E102_O__97 12 0 12 12 8 0

## E103_Old97 0 5 1 0 0 11

## E104_Pri97 12 0 12 12 8 0

## E105_Rai97 12 1 55 31 32 0

## E106_Ric97 0 1 1 0 0 11

## E107_Sar97 1 14 5 1 20 22

## E108_Tim97 20 1 12 12 13 0

## E109_Tur97 1 14 1 1 9 9

## E110_U_S97 12 1 55 31 32 0

## E111_U_S97 12 1 31 31 19 0

## Rehnquist 13 9 32 19 60 11

## Stevens 0 9 0 0 11 40

## O_Connor 15 0 32 19 29 14

## Scalia 11 0 23 15 18 1

## Kennedy 13 10 33 19 33 24

## Souter 0 11 34 19 39 23

## Thomas 15 0 41 26 29 4

## Ginsberg 0 0 24 0 25 21

## Breyer 8 9 0 0 21 18

## O_Connor Scalia Kennedy Souter Thomas Ginsberg Breyer

## E078_Abr97 8 7 8 0 11 0 0

## E079_Ago97 8 7 8 0 11 0 0

## E080_Ass97 57 35 52 57 53 39 34

## E081_Bab97 57 35 52 57 53 39 34

## E082_Bog97 0 4 7 5 7 0 0

## E083_Boa97 8 7 8 0 11 0 0

## E084_Cam97 11 0 11 11 0 0 11

## E085_Cha97 42 18 43 41 28 35 31

## E086_Cit97 0 8 14 0 14 12 0

## E087_Cit97 34 23 30 30 34 0 19

## E088_Com97 27 0 35 34 21 28 0

## E089_De_97 36 0 43 48 0 40 40

## E090_Gen97 57 35 52 57 53 39 34

## E091_Gli97 11 0 11 0 0 11 11

## E092_Har97 19 15 19 19 26 0 0

## E093_Ida97 8 7 8 0 11 0 0

## E094_Jef97 57 35 52 57 53 39 34

## E095_Kan97 8 7 8 0 11 0 0

## E096_Lam97 0 7 8 8 11 0 0

## E097_Law97 0 0 0 11 0 9 8

## E098_Lin97 11 0 0 11 0 11 11

## E099_Mar97 26 17 0 26 24 17 15

## E100_Met97 0 0 23 26 0 22 20

## E101_McM97 8 7 8 0 11 0 0

## E102_O__97 8 7 8 0 11 0 0

## E103_Old97 0 0 11 11 0 11 11

## E104_Pri97 8 7 8 0 11 0 0

## E105_Rai97 32 23 33 34 41 24 0

## E106_Ric97 11 0 0 11 0 11 11

## E107_Sar97 0 0 23 26 0 22 20

## E108_Tim97 15 11 13 0 15 0 8

## E109_Tur97 0 0 10 11 0 0 9

## E110_U_S97 32 23 33 34 41 24 0

## E111_U_S97 19 15 19 19 26 0 0

## Rehnquist 29 18 33 39 29 25 21

## Stevens 14 1 24 23 4 21 18

## O_Connor 71 24 38 46 35 30 32

## Scalia 24 36 19 20 36 12 12

## Kennedy 38 19 76 43 33 33 28

## Souter 46 20 43 80 32 38 34

## Thomas 35 36 33 32 57 20 12

## Ginsberg 30 12 33 38 20 60 24

## Breyer 32 12 28 34 12 24 52

xHierarchicalClustering(BC%*%t(BC), Input="Similarities", Method="average")

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