A Model of Robust Positions in Social Structure Matt Bothner Edward Bishop Smith Harrison C. White...

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