Transcript Minimizing Rules

Complexity as a Methodology, Point
of View, Theory
Bruce Kogut
EIASM and Oxford University
June 2006
What Complexity Seems
to Mean In Practice
Interdisciplinary sharing of knowledge and creating a larger community
of scholarship.
Appreciation of the ‘a-linear’ view of the world
The importance of ‘events’ for triggering change.
Analyzing the statistical properties of large datasets
Understanding local interactions by micro-rules whose effects depend
on topology (structure) but whose interpretations rely upon
contextual knowledge.
More attention to what Elster and Hedstrom call ‘mechanisms’ as
opposed to ‘causes’
Research Strategies: 1. Some Old one, 2. Some
opportunistic ones, 3. Some new ones.
1. Greco-Latin Squares to Charles Ragin’s
comparative methods
2. Borrowed simulation ‘structures and
topologies’
3. Graph dynamics relying on new
estimation techniques
Example of (1): Old Method
Rethought
• In economics and management, we would like to
determine the complementarities, or
interactions, that compose ‘best practices’ to
improve performance.
• Economics gave us an elegant analysis of
complementarities but poor methods.
• The empirical problem of complementarities is
saturating an experimental design. (This is
identical to the theory of monotone comparative
statics: the power set of combinations has to be
tested for its effect on performance.)
Example of (2): a useful opportunistic strategy is
the NK model applied to complementarities
•
Consider a NK model in which a technological landscape is hardwired (the number of
nodes is given, they are connected, k-the interactions-are given: but … N and K can
be varied. Fitness values are randomly assigned to nodes and hence to their
combinations).
–
Random boolean nets have been useful in biochemistry in which there are rules of ‘and’, ‘or’,
‘not and’. (However, from genes to phenotypic expression, there are many things that
intervene: RNA, proteins. And fitness can be ‘endogenous’: my fitness can depend on how fit
is your fitness in a given space.)
–
We know a priori the central results from simulations in other fields: there are finite multiple
optima that for some k (such as k=2) has known expected values. We also know much about
search time to optima (this has received a lot of attention in science and little in social
science: is the rate by which we have gotten to where we are ‘explainable’?.
–
The apparatus sneaks in a language: long jumps, landscapes, iterations, that imply firms are
engaged in search over a technological terrain that awaits to be discovered. (This is not
social construction.)
–
Unfortunately, it is hard to feed data to the model.
Example of (3) is the application of graphs to
understanding data
1.
We now have a much appreciation that static representations of networks cannot
easily isolate ‘endogeneity’ (I smoke because I am weak or because you smoke)
but more importantly cannot easily identify ‘social rules’.
2.
We have though a better understanding even for static graphs that some
properties are consistent or inconsistent with important social behaviors.
•
For example, we know that the absence of a power law in degrees is inconsistent with
‘preferential attachment’. Since preferential attachment is a reasonable way to represent
such concepts as ‘prestige’ and ‘reputation’, a non-finding is important.
We still have a long way to go regarding ‘estimations’:
3.
•
•
4.
our models are convenient (even if very hard: exponential random graph models)
It is hard to rule out other explanations not specified.
Exciting space (for me) is the combination of estimation and simulation to arrive at
better understandings of the ‘possible’ interpretations.
•
Formal models will also be critical.
Return to Example (1): What can
old methods say to complexity?
Consider a question:
What are good corporate and labor
institutions for generating growth?
Some argue that there are two prototypes:
Coordinated (e.g. Germany) and market
(e.g. US) and each are good for growth (?)
Here are data from Hall and Gingerich who want to
show there are 2 best configurations for setting policy
COUNTRY
Growth
Degree of wage
coordination
Level of wage
coordination
Labor
turnov
er
Shareholder power
Stock market
size
Dispersion of
control
Austria
1
1
1
1
1
1
1
Germany
1
1
1
1
1
1
1
Italy
1
1
0
1
1
1
1
Belgium
1
0
1
1
1
1
1
Norway
1
1
1
1
0
1
1
Finland
1
1
1
0
1
1
1
Portugal
1
0
1
1
1
1
1
Sweden
0
0
1
1
1
0
1
France
0
0
1
1
1
1
1
Denmark
1
1
1
0
1
1
0
Japan
1
1
1
1
0
0
0
Netherlands
0
0
1
1
1
0
1
Switzerland
0
1
1
1
1
0
0
Spain
1
0
0
0
0
1
1
Ireland
1
0
0
0
0
1
0
Australia
0
0
0
0
0
0
0
New Zealand
0
0
0
0
0
0
0
Canada
0
0
0
0
0
0
0
United Kingdom
0
0
0
0
0
0
0
United States
0
0
0
0
0
0
0
The coordination dichotomies are all coded in the same direction, with a score of 1 signaling conformity with “coordinated”
market economies and a score of 0 signaling conformity with “liberal” market economies.
Observations on the Data
• N of 20 countries and yet 6 variables, hence 64 possible
combinations (2^6).
• Of these 64, only 15 are uniquely observed.
• We are making inferences based on a poorly populated
space.
– Sparseness may reflect the operation of a maximizing hand that
rules out inefficient (?) combinations.
– It may reflect “path dependency” and hence the paths not taken
(even if perhaps better).
– It may reflect cultural preferences that rule out certain
institutions, such as stock markets historically in some countries.
Approach One: Crisp Logic:
We can try to find good causal ‘combinations’ by
borrowing from electrical engineering.
Using three logical gates (join, meet, null), what are the minimal circuits
you need, or what are the fewest elements you need to ‘cause’
performance.
Absorption: A+ AB = A
Reduction:
AB + Ab = A(B+b) = A(1) = A
Advantage of this method: it is simple and intuitive.
Problem is that with too much sparseness, we won’t get much
simplicity.
Solution for High Growth/Low Initial GDP per
capita, without simplifying assumptions:
1. degreewc levelwc turnover sharehld STOCKMKT +
2. DEGREEWC LEVELWC turnover SHAREHLD
STOCKMKT +
3. DEGREEWC LEVELWC TURNOVER STOCKMKT
DISPERSN +
4. DEGREEWC TURNOVER SHAREHLD STOCKMKT
DISPERSN +
5. LEVELWC TURNOVER SHAREHLD STOCKMKT
DISPERSN +
6. DEGREEWC LEVELWC TURNOVER sharehld
stockmkt dispersn
Simplifying Assumptions
Consider the case where there are two solutions:
ABC + ABc
No reduction is possible.
If we permit two assumptions, we can achieve a simplification:
Y = ABC + aBc + ABc + aBC
= (ABC + aBC) + (aBc + ABc)
= (BC) + (Bc)
=B
This is a type of simulation, but done by intuition –called theory– on unobservables.
It is a theory that explicitly reduces the complexity: It posits, ‘let’s imagine that if we had
the data or if nature had been more experimental, we would indeed observe two
cases with positive outcomes. These cases are aBc and aBC. Once we do this, we
arrive at B.
This is very similar to Michael Hannan’s recent work in propositional logic in which
premises are fed to a computer program that derives logical propositions. We
simply say: let’s use nature as far as we can to ‘infer’ propositions and then add in
theory to derive more simple expressions.
Solution for Low Growth/High Initial GDP per
capita,
C. without simplifying assumptions:
1. degreewc levelwc turnover sharehld stockmkt dispersn +
2. DEGREEWC LEVELWC TURNOVER SHAREHLD stockmkt
dispersn +
3. degreewc LEVELWC TURNOVER SHAREHLD stockmkt
DISPERSN
D. with simplifying assumptions:
1. degreewc stockmkt +
2. SHAREHLD stockmkt
Let’s do better by understanding more
clearly the Limited Diversity in data
Table 6: Mapping Limited Diversity and Assessing Simplifying Assumptions*
Configurations of Labor Institutions
Configurations
of Corporate
Institutions
dlt
dlT
dLt
Dlt
dLT
DlT
DLt
DLT
psc
5
0
0
0
0
0
0
1
psC
0
0
0
0
0
0
0
0
pSc
1
0
0
0
0
0
0
0
Psc
0
0
0
0
0
0
0
1
pSC
1
0
0
0
0
0
0
1
PsC
0
0
0
0
2
0
0
0
PSc
0
0
0
0
0
0
1
0
PSC
0
0
0
0
3
1
1
2
Corporate Institutions (upper case denotes corporatist elements):
P = low shareholder power; p = high shareholder power
S = small stock market; s = large stock market
C = low dispersion of control; c = high dispersion of control
Labor Institutions (upper case denotes corporatist elements):
D = high degree of wage coordination; d = low degree of wage coordination
L = high level of wage coordination; l = low level of wage coordination
T = low level of labor turnover; t = high level of labor turnover
*Shaded portion of the table shows cells covered by the equation for high growth.
Logical exploration of the Not-Observed
1. Reconsider the result for low growth:
low_growth = degreewc*stockmkt + SHAREHLD*stockmkt
2. We did not though combine our knowledge of what determines ‘low
growth’ with that for what determines ‘high growth’. We can do this
by…
Apply De Morgan’s Law by reversing the outcome, changing all uppercase to lower-case, and vice verse, and then also changing
intersection to union, and vice versa:
high_growth = (DEGREEWC + STOCKMKT)*(sharehld +
STOCKMKT)
We have arrived now at the maximal saturation of our experimental
design, filling in as many of the 64 cells that we can.
After maximal saturation…
3. Finally, simplify the terms using Boolean algebra:
[hg=D*sh + DS + Ssh + SS.
By absorption rule and since SS= 1*1= 1=S,
high_growth = STOCKMKT + DEGREEWC*sharehld
4. And if we are not happy with two explanations, we can theorize what we
should observe by simplifying assumptions and reduce further.
This is a combination of an incomplete saturated design methodology that
analyzes complex non-linear interactions by a combination of logic, theory,
and simulation using DATA.
Example Two Reviewed: NK model
• NK models impose a large penalty on experimentation:
– Landscapes are rugged and organizations easily get trapped.
– Long-jumps are random.
• Consider Fontana’s idea of Neutrality (and the
implementation by Lobo, Fontana, and Miller)
– Fitness is discretized into bands such that organizations are inert
to small changes in fitness caused by experiments in
complements.
– However, for large changes in fitness, experiments can lead to
adoption of new configurations.
Simulating Neutrality in the Kauffman/Levinthal NK
Model (Amit Jain Implementation and Simulation)
Simulation run for neutrality in rugged landscapes
N= 10
K=2
Number of organizations = 100
Number of time periods = 100
Number of runs = 50
Only local search
Landscape does not change (p=0)
Runs made for M=? (in program this is M=0) (standard N-K), 10, 25, 100
Time periods in graph
1-100
Standard N-K run (M = ? /0)
100-200 M=10
200-300 M=25
300-400 M=100
Four simulations are run: first panel is the
standard, the next 3 vary neutrality from fitness
bands of 10%, 25%, 100%: that is, change only if
change in fitness hits the band.
Under Neutrality, Organizations
Discover ‘Ridges’ Between Peaks
Comparing results:
1. Fitness value is higher under neutrality (for these number of simulations).
In other words, local traps are less confining.
2. More organizational forms are ‘viable’ over the short-run.
3. We believe, but are checking, to show that there is more exploration of possible space
if N=10, then we have 1024 combinations. But with only a 100 organizations, how
many combinations are actually explored in a period of time. Here we are returning to
the type of questions: how long should it take to see a possible universe realized?
4. We still don’t how, nor do we think we know how, to fit data to this simulation.
Neutrality is a reasonable concept by which to capture the capability of firms to learn by
trial and error before engaging in massive ‘retooling’ or ‘reengineering’.
It also captures the idea of ‘institutions’ and ‘institutional transplants’: many institutions
can cross borders because they are ‘neutral’.
Example (3): Topologies, Graphs,
Data, Inferences
1.
2.
Science of the complexity should be engagement of
theory, data, estimation, simulation, imagining the
possible.
To understand ‘large complex systems’, we need a lot
of data.
1.
3.
A lot of what we do uses small data sets from which we try to
make claims about asymptotic significance.
Alternatively, we can see social action as agent driven
who are interacting by rules.
1.
We would like to liberate them from strong topological
impositions (e.g. regular graphs, or NK landscapes) but still
come to understand the relation of local and macro structures
on behavior, and vice versa.
Analyses of large data sets:
Venture Capital In US
•
•
•
We know little about entrepreneurial
activities in terms of network dynamics.
Many good studies on venture capital,
but we have no global picture.
We have no studies on dynamics.
Theories on VCs
Two common hypotheses:
1.
VCs do deal to signal prestige: this should lead to prestigious getting
more rich. Graph prediction: power law in degree.
2.
VCs do deals to find ‘complements’ in expertise. Graph prediction: power
law in ‘weighted link strength’.
Implication of (1) for components and clusters:
Venture capital is ‘clustered’ in geographies and a few prestigious companies
come later to bridge them.
Implication of (2) for components and clusters:
VC firms will seek new partners when new expertise is required and we will
thus see ‘repeated ties’ for investments in known areas and ‘new ties’ for
investments in new areas.
Thus we will have a dynamic between the conservational rule of relying on
proven expertiese and the diversity rule of seeking new partners.
Deal structure
• Over 150,000 transactions over 40 years.
• Several thousand VC investors, targets
• Let’s start by posing a simple question:
– Do regional markets grow and then become
integrated?
– Or is Braudel right: regions develop in relation
to global (national) dynamics.
Deals distribution among Firms
100%
90%
70%
60%
50%
40%
30%
20%
10%
Percentage of Firms
%
0%
10
95
%
90
%
85
%
80
%
75
%
70
%
65
%
60
%
55
%
50
%
45
%
40
%
35
%
30
%
25
%
20
%
15
%
10
5%
0%
0%
Percentage of Deals
80%
Number of Deals
Num Deals per Firm
02
20
99
19
96
19
19
19
19
19
19
19
19
19
19
19
19
19
93
0
90
-
87
1
84
5,000
81
2
78
10,000
75
3
72
15,000
69
4
66
20,000
63
5
60
25,000
Number of deals per Firm
Number of Deals
Number of Deals
High number of
deals per Firm
6
30,000
Year
Technological breaks create opportunities for new entrants.
National Component Grew Early and Connected
Regions and Sectors: So much for Clusters
100%
90%
Percentage of Nodes
80%
70%
60%
50%
Sectors Covered by the Giant
40%
Geographies Covered by the Giant
30%
Size of the Giant Component
20%
10%
0%
1962
1965
1968
1971
1974
Year
1977
1980
1983
1986
We do not find a power law in degrees: VC syndications don’t seem to
be the product of ‘preferential attachment’
378.742
Freq75
Freq80
167.387
1
1
1
1
61
140
K
K
3416.19
Frequency90
Frequency
1527.65
.223825
.694947
1
1
623
1104
K
K
Inference by adduction: the dog did not bark, the graph does not have power
law in degree, hence the culprit of rich get richer is innocent and released.
We do have Power Laws in Strength:
Incumbents like to rely upon trusted partners
• Most Deals are Incumbent
to Incumbent
10000
• Hence we find power laws
in repeated ties.
• Trusted expertise based
on experience, not
signalling of prestige,
seems to matter.
Frequency
1000
100
10
1
1
10
100
1000
10000
Strength s
VC networks have far more repeated ties than Guimera Uzzi et al Broadway
netorks.
100000
Percentage of Deals Where ‘Local’
cluster is greater than global
60%
50%
Percentage of deals
Geography
Sector
40%
30%
20%
10%
0%
1961 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004
Year
In other words, clusters are stronger globally than ‘within’ region or sector.
New Links are Formed when…
• A VC company goes
to a new geography
or sector
– that is, when it needs
new expertise.
New geography
New sector
Interaction
Firm degree
Target degree
• VC firms are drawn to
successful targets.
Constant
VC
Target
Year
Diversification Degree
Degree
Effects
-1.577
-1.504
-1.559
-1.57
-0.023
-0.023
-0.023
-0.024
-1.723
-1.613
-1.663
-1.669
-0.029
-0.029
-0.029
-0.029
1.502
1.449
1.483
1.499
-0.043
-0.043
-0.043
-0.044
0.002
0.002
0.002
0
0
0
-0.046
-0.056
-0.002
-0.002
1.398
1.24
1.487
23.439
-0.015
-0.018
-0.02 26,313.25
Conclusions to Example 3
•
What we showed:
•
1.
Looking at dynamics of graph
properties rules out certain
micro behaviors.
2.
Clustering and giant
component analysis confirms
the Braudel hypothesis:
clusters develop in relation to
the national graph.
1. A formal model of the choice
between new and old tie that
is the equivalent to the
Simon/Barabasi model of
preferred attachment.
2. Agent based models that test
more precisely the micro rules
employed.
What we did not show:
1. Why not shown: I don’t think
we have a good empirical
model yet.
2. We are out of time.
Caveats
• Social systems are harder than physical systems if we play only by
the rules of the latter.
– We don’t ask an electron ‘where y’a been and when were y’a d’ere?’
– We can ask people this question.
• Physical systems have given topologies:
– forests are reasonably viewed as 3 dimensional lattices.
– American suburbs are often 2 dimensional lattices, but Paris is not, and
people move around.
– Geographical space is not always the same as social space.
• Engineers often like to get rid of people because the problem is hard
enough.
– Systems are most often, even today, socio-technical.
– Machines and people inhabit the same graph.
Interactions in physical systems. High Power Items - Jet Engine
Adding in People makes this much harder
Function is physical
and cannot be represented
logically and symbolically
High power
Severe backloading
Interfaces must
be tailored to fct
Main fct carriers
can’t be standardized
From Whitney, MIT.
Side effects are
high power
and can’t be isolated
Module behavior
changes when
combined into system
Modules must be
designed anew
specifically for
their function
Modules display
multiple behaviors
in multiple energy domains
Modules are indep
in design
The design can be
converted to a picture
The picture
is an incomplete abstract
representation of the design
Modules must
be validated physically
Separate module and system
validation steps are needed
A construction process
exists that eliminates
most assembled interfaces
Systems cannot be designed with
good confidence that they will work
A conclusion
• Complexity is a point of view that the pursuit of
plausibility is more rewarding than certainty.
• Social sciences needs to move to an open science
model, where we spend more time in projects, less time
collecting data.
• Simulations and estimation should be seen as part of the
interpretative methodology to identify plausible
mechanisms as opposed to verify causes.
• Interactions, rules, non-saturated designs, simulations,
estimations, graph theory are the words in the new
vocabulary.
• But the going will not be easy… Consider Wings and
Engines and ….. People
Appendix: If Time Permitted: Extend This Method of
Experimental Design and Simulated and Real Data to
Complementarities in Manufacturing
• Consider activity systems that describe how auto companies
manufacture efficiently with quality, including the work teams and
social organization.
• Can we identify better ‘prototypical’ strategies that are robust across
settings?
Strategy and Prototypes
Consider strategy as the problem of choosing capabilities
and markets, that is the sets C and M are the givens to
the decision choose CxM such that S* = argmax(C,M).
This can rarely if ever be solved, so that people think
heuristically instead by prototypes that represent the
“best configuration”: differentiate, cut cost, have religion.
This formulation is close to the theory of complementarities
a la Milgrom and Roberts.
The empirical question is: Can we pick out the best
configurations from the data?
Fuzzy Sets:
• Data are no longer “crisp”.
• Important consideration is coding and functional
transformations.
• Rules are set theoretic: a necessary condition means
that the outcome is a subset of the condition; a sufficient
means that the condition is a subset of the outcome.
• Values are calculated for combinations using fuzzy set
algebra. These values are compared to value of the
outcome. If outcome value larger, then indicates
combination/element is sufficient; if smaller, then
combination/element is necessary.
Benchmarking the fuzzy
configuration against Data
1 .0
1.2
Actual Quality
Actual Productivity
1.0
.8
.6
.8
.6
.4
.4
.2
.2
0.0
-.2
0.0
.2
.4
.6
.8
Predicted Productivity
1.0
0 .0
- .2
0 .0
.2
.4
.6
.8
Predicted Quality
The data are 70 or so auto plants around the world and consist of
observations on teams, technologies, work processes, scale, etc.. These
practices were analyzed to find unique combinations of ‘minimal’
practices sufficient to achieve performance.
1 .0