ICPSR - Complex Systems Models in the Social Sciences - Lecture 6 - Professor Daniel Martin Katz

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ICPSR - Complex Systems Models in the Social Sciences - Lecture 6 - Professor Daniel Martin Katz

  1. 1. Complex Systems Models in the Social Sciences (Lecture 5) ! daniel martin katz illinois institute of technology chicago kent college of law @computationaldanielmartinkatz.com computationallegalstudies.com
  2. 2. How Complex is a Particular System?
  3. 3. This is an Important Question Considered in the Field
  4. 4. For an Overview See Chapter 7
  5. 5. Lots of Potential Candidate Measures
  6. 6. http://web.mit.edu/esd.83/www/notebook/Complexity.PDF
  7. 7. “1. How hard is it to describe? 2. How hard is it to create? 3. What is its degree of organization” Questions Typically Considered:
  8. 8. 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)
  9. 9. 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.)
  10. 10. Metric Entropy Fractal Dimension Excess Entropy Stochastic Complexity Sophistication Effective Measure Complexity True Measure Complexity Topological epsilon-machine size Conditional Information Conditional Algorithmic Information Content Schema length Ideal Complexity Hierarchical Complexity Tree-subgraph diversity Homogeneous Complexity Grammatical Complexity 3. Degree of organization (a) Effective Complexity
  11. 11. Algorithmic Mutual Information Channel Capacity Correlation Stored Information Organization 3. Degree of organization (B) Mutual Information
  12. 12. http://vserver1.cscs.lsa.umich.edu/~crshalizi/ notabene/complexity-measures.html
  13. 13. Measuring Complexity: An Applied Case
  14. 14. Measuring the Complexity of Legal Systems
  15. 15. Optimal Precision in Legal Rules Kaplow (1995) Tullock (1995) The Complexity of the Law is Canonical Question Applied Scholarship -- Tax, Environmental Law, Admin Law, etc. Legal and Political Theory Justifications for Law and the State
  16. 16. 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
  17. 17. 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
  18. 18. 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
  19. 19. This is the United States Code
  20. 20. 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
  21. 21. The 50 titles in US Code
  22. 22. 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?
  23. 23. How Large is the United States Code?
  24. 24. How Large is the United States Code?
  25. 25. How Large is the United States Code?
  26. 26. How Large is the United States Code?
  27. 27. ~Title 29 - Labor How Large is the United States Code?
  28. 28. How Large is the United States Code?
  29. 29. This is the United States Code
  30. 30. 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
  31. 31. Computational Approach to the Measurement of Complexity (2) Generate a Measurement Strategy for that Object (1) Provide a Mathematical Representation for an Object
  32. 32. A Mathematical Approach to the Study of the United States Code 389 Physica A 4195 (2010 Forthcoming)
  33. 33. Additional Treatment Available Here
  34. 34. 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)
  35. 35. 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/
  36. 36. + Hierarchical Structure Citation Network
  37. 37. + Hierarchical Structure Citation Network
  38. 38. Linguistic Content United States Code Features 13 Million tokens +
  39. 39. Measuring the Complexity of the United States Code http://link.springer.com/article/10.1007%2Fs10506-014-9160-8
  40. 40. Knowledge Acquisition Framework Knowledge Acquisition Subfield at Intersection of Computer Science and Psychology Interested in protocols used by subjects as they acquire, store and analyze information
  41. 41. 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
  42. 42. 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
  43. 43. The Complexity of Knowledge Acquisition 3 Factors Influence Complexity of Executing the Protocol Structure Language Dependence
  44. 44. Proxy for an Information Acquisition Process (1) Work Through a Hierarchy (2) Look up any Citations you encounter (3) Confront Language of varying length and diversity
  45. 45. The Complexity of Law The sheer difficulty of searching for and assimilating the information content of a relevant body of legal rules Distinct from other important features: Ambiguity Uncertainty
  46. 46. Structure The Unnormalized Measure: Structure Vertices (Nodes)
  47. 47. Structure The Unnormalized Measure: Structure ! Vertices (Nodes)
  48. 48. Net Flow Dependence The Unnormalized Measure: Net Flow
  49. 49. Composite Measure through Weighted Ranks (A) For each factor - Measure each of the 49 Active titles (C) Apply a Weight to each of these factors (Simplest Case is to Average) (B) Then, rank each title from (1) Most to (49) Least
  50. 50. Toward a Composite Measure Structure LanguageDependence Composite Measure
  51. 51. Two Forms of Weighted Ranks Unnormalized Measure Considers the Complexity of reviewing a full title Does not Control for Title Size Normalized Measure Considers the Average or Emblematic Provision within the Title Thus, we control for title size
  52. 52. The Unnormalized Measure Structure LanguageDependence Unnormalized Measure EntropyNet Flow Vertices (Provisions)
  53. 53. The Unnormalized Measure: Structure ! Structure Vertices (Provisions)
  54. 54. The Unnormalized Measure: Structure Structure Vertices (Provisions)
  55. 55. Net Flow Dependence The Unnormalized Measure: Net Flow
  56. 56. The Unnormalized Measure: Net Flow Net Flow Dependence
  57. 57. The Unnormalized Measure: Language Language Entropy !
  58. 58. The Unnormalized Measure: Language Language Entropy Uniform Random
  59. 59. The Unnormalized Measure: Language Language Entropy Uniform Random Dog, Dog, Dog, Dog, Dog, Dog, Dog, Dog, Dog, ... snug pizza pasture it observation hand how of dare ...
  60. 60. The Unnormalized Measure: Language Language Entropy Title 42 - Public Health & Welfare Leprosy Social Security National Flood Insurance US Synthetic Fuels Corp Intl Child Abduction Remedies Entropy ≈ Diversity
  61. 61. The Unnormalized Measure: Language Language Entropy
  62. 62. The Unnormalized Measure Structure LanguageDependence Unnormalized Measure EntropyNet Flow Vertices (Provisions)
  63. 63. The Unnormalized Measure
  64. 64. The Normalized Measure Structure LanguageDependence Normalized Measure Mean Depth Entropy Net Flow Per Section Tokens Per Section Language
  65. 65. The Unnormalized Measure
  66. 66. Offered a framework designed to Measure the complexity of the legal rules 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

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