Daniel Martin Katz Michigan State University - College of Law Complex Systems Models in the Social Sciences (Lecture 8)
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 - Professor Daniel Martin Katz
Dec 08, 2014
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Daniel Martin KatzMichigan State University - College of Law
Complex Systems Models in the Social Sciences
(Lecture 8)
!
How Complex is a Particular System?
This is an Important Question Considered
in the Field
For an OverviewSee Chapter 7
Lots of Potential Candidate Measures
http://web.mit.edu/esd.83/www/notebook/Complexity.PDF
“1. How hard is it to describe?
2. How hard is it to create?
3. What is its degree of organization”
Questions Typically Considered:
Entropy
Algorithmic Complexity
Minimum Description Length
Fisher Information
Renyi Entropy
Chernoff Information
Dimension
Fractal Dimension
Lempel--Ziv Complexity
Code Length (prefix-free, Huffman, Shannon-Fano, error-correcting, Hamming)
1. Difficulty of Description(Typically measured in bits)
Computational Complexity
Time Computational Complexity
Space Computational Complexity
Information--Based Complexity
Logical Depth
Thermodynamic Depth
Crypticity
2. Difficulty of Creation(Typically measured in time, energy, dollars, etc.)
Metric EntropyFractal DimensionExcess EntropyStochastic ComplexitySophisticationEffective Measure ComplexityTrue Measure ComplexityTopological epsilon-machine sizeConditional InformationConditional Algorithmic Information ContentSchema lengthIdeal ComplexityHierarchical ComplexityTree-subgraph diversityHomogeneous ComplexityGrammatical Complexity
3. Degree of organization(a) Effective Complexity
Algorithmic Mutual Information
Channel Capacity
Correlation
Stored Information
Organization
3. Degree of organization(B) Mutual Information
http://vserver1.cscs.lsa.umich.edu/~crshalizi/notabene/complexity-measures.html
Measuring Complexity:An Applied Case
Measuring the Complexity
of Legal Systems
Optimal Precision in Legal RulesKaplow (1995) Tullock (1995)
The Complexity of the Law is Canonical Question
Applied Scholarship -- Tax, Environmental Law, Admin Law, etc.
Legal and Political TheoryJustifications for Law and the State
Aligns Incentives / Channels Behavior
Offers Focal Points / Coordination Mechanisms
Encourages Actors to Internalize Costs
Maintains Monopoly on Legitimated Violence
Protects Individual Rights and Liberties
Law as a Means of Solving Social Dilemmas
Complexity of Society & Complexity of the Law
Economic Exchange
What conditions must be met for law to Achieve these Ends?
Legal Rules Should Reflect The Nature of:
Social Interaction
Political Behavior
Applying the Tools of the ‘Big Data’ Era
A Perspective on the Scope of Law in a Modern Society
Using an Important Corpus of Written Law
This Paper is an Effort (Albeit Imperfect)to Measure the Complexity of the Law
That is Large and Cross Cutting
This is the United States Code
Compiled Version of Federal Statutory Law
This is the United States Code
Drawn from the U.S. Statutes at Large
Does not Include Fed Admin Regulations
The 50 titles in US Code
How Complex is the Code and its Components?
How has its Composition Changed Over Time?
Some Potential Questions
Can we understand if those changes Scale to changes in the complexity of broader Society?
How Large is the United States Code?
How Large is the United States Code?
How Large is the United States Code?
How Large is the United States Code?
How Large is the United States Code?
~Title 29 - Labor
How Large is the United States Code?
How Large is the United States Code?
This is the United States Code
The Case for a Computational Approach
The United States Code is Large ...
Computational Methods are Arguably Required
Need Tools and Methods that Scale to the Size and Scope of this Body of Information
Computational Approach to the Measurement
of Complexity
(2) Generate a Measurement Strategy for that Object
(1) Provide a Mathematical Representation for an Object
A Mathematical Approach to the Study of the United States Code
389 Physica A 4195 (2010 Forthcoming)
Additional Treatment Available Here
The US Code as a Mathematical Object
Hierarchical Structure
Title 26
Subtitle A
Chapter 1
Subchapter F
Part I
Section 501
Subsection (c)
Paragraph (3)
Citation Network
Example: Tax Evasion
Title 26 - Tax
Might Cite
Title 18 - Crimes &
Criminal Procedure
The US Code as a Mathematical Object
http://computationallegalstudies.com/2009/09/14/the-structure-of-the-united-
states-code/
+
Hierarchical Structure
CitationNetwork
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Hierarchical Structure
CitationNetwork
Linguistic Content
United States CodeFeatures
13 Million tokens
+
Measuring the Complexity of the United States Code
Knowledge Acquisition Framework
Knowledge Acquisition
Subfield at Intersection of Computer Science and Psychology
Interested in protocols used bysubjects as they acquire, store and analyze information
Interested in Mirroring the “Protocols”Used by a Hypothetical End User
Costs of Executing the Protocols Are Driven by the Complexity of the Object
We Consider an Individual Engaging in a Knowledge Acquisition Process
Measuring the Complexity of the United States Code
Protocol for United States Code Knowledge Acquisition
(1) Select an initial element of the Code corresponding to a concept of interest
(2) Beginning from this initial element, recursively assimilate the content of all sub-elements
(3) When a citation is encountered, apply this protocol recursively to the cited element
The Complexity of Knowledge Acquisition
3 Factors Influence Complexity ofExecuting the Protocol
Structure Language Dependence
Toward a Composite Measure
Multidimensional object--> Composite Measure Full Code and Individual Titles
Weighted RanksImperfect but a good start
A Positive Feature of weighted ranks (1) Change Weights(2) Add Additional Dimensions
Two Forms of Weighted Ranks
Unnormalized Measure
Considers the Complexity of reviewing a full title
Normalized Measure
Considers the Average or Emblematic Provision within the Title
Thus, we control for title size
The Unnormalized Measure
Structure Language Dependence
Unnormalized Measure
The Unnormalized Measure:Structure
Structure
Vertices(Nodes)
Structure
The Unnormalized Measure:Structure
Vertices(Nodes)
Structure
The Unnormalized Measure:Structure
!
Vertices(Nodes)
Net Flow
Dependence
The Unnormalized Measure:Net Flow
Net Flow
Dependence
The Unnormalized Measure:Net Flow
The Unnormalized Measure: Language
Language
Entropy
The Unnormalized Measure: Language
Language
Entropy Uniform Random
The Unnormalized Measure: Language
Language
Entropy
!
The Unnormalized Measure: Language
Language
Entropy Title 42 - Public Health & Welfare
LeprosySocial Security National Flood Insurance US Synthetic Fuels Corp Intl Child Abduction Remedies
Entropy ≈ Diversity
The Unnormalized Measure
Structure Language Dependence
Unnormalized Measure
Vertices EntropyNet Flow
The Unnormalized Measure
The Normalized Measure
Structure Language Dependence
Normalized Measure
Mean Depth Entropy
Net FlowPer
Section
Tokens Per
Section
Language
The Unnormalized Measure
Offered a framework designed to Measure the Complexity of the Law
Designed to open a dialogue regarding Legal complexity and its measurement
Demonstrated measurement principles that are potentially applicable to other classes of legal documents
Summary
Highlighted what computation might be able to offer to empirical legal studies
SupportingMaterials Available Online!
Thanks for Support
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