a model of robust positions in social structure matt bothner edward bishop smith harrison c. white...
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A Model of Robust Positions in Social Structure
Matt BothnerEdward Bishop Smith
Harrison C. White
University of ChicagoColumbia University
The Nortons: Spring & Summer 1937
The Nortons: Spring & Summer 1937
Bowling Finishing Rank
Sta
tus
in N
ort
on
s S
tre
et
Ga
ng
2 4 6 8 10
0.8
1.0
1.2
1.4
1.6
Danny
Doc
Long John
Mike
Joe Carl
Frank
Alec
Bowling Finishing Rank
Sta
tus
in N
ort
on
s S
tre
et
Ga
ng
2 4 6 8 10
0.8
1.0
1.2
1.4
1.6
Danny
Doc
Long John
Mike
Joe Carl
Frank
Alec
Alec’s Attack on Long John
“He seems to have the Indian sign on me.” -- Long John
“It is significant that, in making his challenge, Alec selectedLong John instead of Doc, Danny, or Mike. It was not that LongJohn's bowling ability was uncertain. His average was about thesame as that of Doc or Danny and better than that of Mike. As amember of the top group but not a leader in his own right, it washis social position that was vulnerable.” – Whyte
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
The Nortons: Spring & Summer 1937
The Nortons: Early Spring 1937
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
α,β α+βi j ijj
S S X
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
α,β α+βi j ijj
S S X k 1
k=0
α,β α β k
S X 1
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Methodological Contribution: Using Nutsy’s Descent (Early Spring 1937)
Nortons’ Status Scores: Early Spring 1937
Alec .67
Angelo 1.06
Carl .75
Danny 1.23
Doc 1.79
Frank .90
Fred .82
Joe .75
Long John .90
Lou .71
Mike 1.23
Nutsy .90
Tommy .67
status
The Nortons: Early Spring 1937
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 .5
[2] Angelo .5 0 .5 .5 .8 .5 .9 .5 .3 .8 .5 .5 .5
[3] Carl .5 .5 0 .1 .3 .5 .5 .5 .3 .5 .1 .5 .9
[4] Danny .5 .5 .5 0 1 .5 .5 .5 1 .5 1 .5 .5
[5] Doc 1 1 1 1 0 1 1 1 1 1 1 1 1
[6] Frank .8 .5 .5 .3 .5 0 .5 .9 .3 .5 .3 .5 .5
[7] Fred .5 .5 .5 .1 .5 .5 0 .5 .3 .9 .1 .5 .5
[8] Joe .9 .5 .5 .1 .3 .5 .5 0 .3 .5 .1 .5 .5
[9] Long John .3 .3 .3 .9 .9 .3 .3 .3 0 .3 .9 .3 .3
[10] Lou .5 .5 .5 .1 .3 .5 .5 .5 .3 0 .1 .5 .5
[11] Mike .5 .5 .5 1 1 .5 .5 .5 1 .5 0 .5 .5
[12] Nutsy .6 .2 .4 .6 .6 .7 .4 .8 .1 .4 .6 0 .4
[13] Tommy .5 .5 .5 .1 .1 .5 .5 .5 .3 .5 .1 .5 0
Measuring Fragility (and Robustness)
simple two-step transformation: normalize each entry by its row sum andsquare the proportions
Measuring Fragility (and Robustness)
simple two-step transformation: normalize each entry by its row sum andsquare the proportions
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.01
[2] Angelo 0.01 0.00 0.01 0.01 0.01 0.01 0.02 0.01 0.00 0.01 0.01 0.01 0.01
[3] Carl 0.01 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.03
[4] Danny 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.02 0.00 0.02 0.00 0.00
[5] Doc 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
[6] Frank 0.02 0.01 0.01 0.00 0.01 0.00 0.01 0.02 0.00 0.01 0.00 0.01 0.01
[7] Fred 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.03 0.00 0.01 0.01
[8] Joe 0.03 0.01 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.01 0.01
[9] LongJohn 0.00 0.00 0.00 0.03 0.03 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00
[10] Lou 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.01 0.01
[11] Mike 0.00 0.00 0.00 0.02 0.02 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00
[12] Nutsy 0.01 0.00 0.00 0.01 0.01 0.02 0.00 0.02 0.00 0.00 0.01 0.00 0.00
[13] Tommy 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.00
, +i j ijj
F a b a bF Z
Measuring Fragility (and Robustness)
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.01
[2] Angelo 0.01 0.00 0.01 0.01 0.01 0.01 0.02 0.01 0.00 0.01 0.01 0.01 0.01
[3] Carl 0.01 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.03
[4] Danny 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.02 0.00 0.02 0.00 0.00
[5] Doc 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
[6] Frank 0.02 0.01 0.01 0.00 0.01 0.00 0.01 0.02 0.00 0.01 0.00 0.01 0.01
[7] Fred 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.03 0.00 0.01 0.01
[8] Joe 0.03 0.01 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.01 0.01
[9] LongJohn 0.00 0.00 0.00 0.03 0.03 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00
[10] Lou 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.01 0.01
[11] Mike 0.00 0.00 0.00 0.02 0.02 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00
[12] Nutsy 0.01 0.00 0.00 0.01 0.01 0.02 0.00 0.02 0.00 0.00 0.01 0.00 0.00
[13] Tommy 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.00
, +i j ijj
F a b a bF Z k 1
k=0
, ka b a b
F Z 1
Measuring Fragility (and Robustness)
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.01
[2] Angelo 0.01 0.00 0.01 0.01 0.01 0.01 0.02 0.01 0.00 0.01 0.01 0.01 0.01
[3] Carl 0.01 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.03
[4] Danny 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.02 0.00 0.02 0.00 0.00
[5] Doc 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
[6] Frank 0.02 0.01 0.01 0.00 0.01 0.00 0.01 0.02 0.00 0.01 0.00 0.01 0.01
[7] Fred 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.03 0.00 0.01 0.01
[8] Joe 0.03 0.01 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.01 0.01
[9] LongJohn 0.00 0.00 0.00 0.03 0.03 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00
[10] Lou 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.01 0.01
[11] Mike 0.00 0.00 0.00 0.02 0.02 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00
[12] Nutsy 0.01 0.00 0.00 0.01 0.01 0.02 0.00 0.02 0.00 0.00 0.01 0.00 0.00
[13] Tommy 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.00
, +i j ijj
F a b a bF Z k 1
k=0
, ka b a b
F Z 1
Measuring Fragility (and Robustness)
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[1] Alec 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.01
[2] Angelo 0.01 0.00 0.01 0.01 0.01 0.01 0.02 0.01 0.00 0.01 0.01 0.01 0.01
[3] Carl 0.01 0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.03
[4] Danny 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.02 0.00 0.02 0.00 0.00
[5] Doc 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
[6] Frank 0.02 0.01 0.01 0.00 0.01 0.00 0.01 0.02 0.00 0.01 0.00 0.01 0.01
[7] Fred 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.01 0.00 0.03 0.00 0.01 0.01
[8] Joe 0.03 0.01 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.01 0.01
[9] LongJohn 0.00 0.00 0.00 0.03 0.03 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00
[10] Lou 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.01 0.01
[11] Mike 0.00 0.00 0.00 0.02 0.02 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00
[12] Nutsy 0.01 0.00 0.00 0.01 0.01 0.02 0.00 0.02 0.00 0.00 0.01 0.00 0.00
[13] Tommy 0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.01 0.00 0.01 0.00
b c c is a parameter capturing thecoupling of nodes in the network
Nortons’ Fragility Scores: Autumn 1937
Alec .67 1.03
Angelo 1.06 .91
Carl .75 1.06
Danny 1.23 .94
Doc 1.79 .85
Frank .90 .97
Fred .82 1.02
Joe .75 1.06
Long John .90 1.17
Lou .71 .99
Mike 1.23 .94
Nutsy .90 .99
Tommy .67 1.03
status fragility
The Nortons: Autumn 1937
Predicting Status Growth in Newcomb’s Fraternity
, 1 1 , 1i t it it i t i tS S F
Models Predicting Status, t+1 in Newcomb’s Fraternity
1 2 3 4
Status 0.56545 0.53436 0.32897 0.32897
(0.03475)** (0.04444)** (0.08848)** (0.08848)**
Fragility (decoupling assumed; c=0) -0.05100 0.17340
(0.04548) (0.12635)
Fragility (coupling assumed; c=.99) -0.17216 -0.09097
(0.09056)** (0.03283)**
Constraint 5.62474
(1.78250)**
Sychophant -0.00696
(0.00217)**
Constant 0.48865 0.57128 0.44281 -0.58196
(0.04246)** (0.08503)** (0.08576)** (0.43804)
N 238 238 238 238
R2 Within 0.5688 0.5714 0.5788 0.6032
Standard errors in parentheses
* significant at 5%; ** significant at 1% (one tailed)
Fixed effects for individuals and time periods included but not shown
Models Predicting Status, t+1 in Newcomb’s Fraternity
1 2 3 4
Status 0.56545 0.53436 0.32897 0.32897
(0.03475)** (0.04444)** (0.08848)** (0.08848)**
Fragility (decoupling assumed; c=0) -0.05100 0.17340
(0.04548) (0.12635)
Fragility (coupling assumed; c=.99) -0.17216 -0.09097
(0.09056)** (0.03283)**
Constraint 5.62474
(1.78250)**
Sychophant -0.00696
(0.00217)**
Constant 0.48865 0.57128 0.44281 -0.58196
(0.04246)** (0.08503)** (0.08576)** (0.43804)
N 238 238 238 238
R2 Within 0.5688 0.5714 0.5788 0.6032
Standard errors in parentheses
* significant at 5%; ** significant at 1% (one tailed)
Fixed effects for individuals and time periods included but not shown
Models Predicting Status, t+1 in Newcomb’s Fraternity
1 2 3 4
Status 0.56545 0.53436 0.32897 0.32897
(0.03475)** (0.04444)** (0.08848)** (0.08848)**
Fragility (decoupling assumed; c=0) -0.05100 0.17340
(0.04548) (0.12635)
Fragility (coupling assumed; c=.99) -0.17216 -0.09097
(0.09056)** (0.03283)**
Constraint 5.62474
(1.78250)**
Sychophant -0.00696
(0.00217)**
Constant 0.48865 0.57128 0.44281 -0.58196
(0.04246)** (0.08503)** (0.08576)** (0.43804)
N 238 238 238 238
R2 Within 0.5688 0.5714 0.5788 0.6032
Standard errors in parentheses
* significant at 5%; ** significant at 1% (one tailed)
Fixed effects for individuals and time periods included but not shown
Models Predicting Status, t+1 in Newcomb’s Fraternity
1 2 3 4
Status 0.56545 0.53436 0.32897 0.32897
(0.03475)** (0.04444)** (0.08848)** (0.08848)**
Fragility (decoupling assumed; c=0) -0.05100 0.17340
(0.04548) (0.12635)
Fragility (coupling assumed; c=.99) -0.17216 -0.09097
(0.09056)** (0.03283)**
Constraint 5.62474
(1.78250)**
Sychophant -0.00696
(0.00217)**
Constant 0.48865 0.57128 0.44281 -0.58196
(0.04246)** (0.08503)** (0.08576)** (0.43804)
N 238 238 238 238
R2 Within 0.5688 0.5714 0.5788 0.6032
Standard errors in parentheses
* significant at 5%; ** significant at 1% (one tailed)
Fixed effects for individuals and time periods included but not shown
Models Predicting Status, t+1 in Newcomb’s Fraternity
1 2 3 4
Status 0.56545 0.53436 0.32897 0.32897
(0.03475)** (0.04444)** (0.08848)** (0.08848)**
Fragility (decoupling assumed; c=0) -0.05100 0.17340
(0.04548) (0.12635)
Fragility (coupling assumed; c=.99) -0.17216 -0.09097
(0.09056)** (0.03283)**
Constraint 5.62474
(1.78250)**
Sychophant -0.00696
(0.00217)**
Constant 0.48865 0.57128 0.44281 -0.58196
(0.04246)** (0.08503)** (0.08576)** (0.43804)
N 238 238 238 238
R2 Within 0.5688 0.5714 0.5788 0.6032
Standard errors in parentheses
* significant at 5%; ** significant at 1% (one tailed)
Fixed effects for individuals and time periods included but not shown