Complex societies and the growth of the law
Open accessAbstract
While many informal factors influence how people interact, modern societies rely upon law as a primary mechanism to formally control human behaviour. How legal rules impact societal development depends on the interplay between two types of actors: the people who create the rules and the people to which the rules potentially apply. We hypothesise that an increasingly diverse and interconnected society might create increasingly diverse and interconnected rules, and assert that legal networks provide a useful lens through which to observe the interaction between law and society. To evaluate these propositions, we present a novel and generalizable model of statutory materials as multidimensional, time-evolving document networks. Applying this model to the federal legislation of the United States and Germany, we find impressive expansion in the size and complexity of laws over the past two and a half decades. We investigate the sources of this development using methods from network science and natural language processing. To allow for cross-country comparisons over time, based on the explicit cross-references between legal rules, we algorithmically reorganise the legislative materials of the United States and Germany into cluster families that reflect legal topics. This reorganisation reveals that the main driver behind the growth of the law in both jurisdictions is the expansion of the welfare state, backed by an expansion of the tax state. Hence, our findings highlight the power of document network analysis for understanding the evolution of law and its relationship with society.
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The complexity of the law imposes real consequences for many individuals and organizations.
“The complexity of the law [12–15] imposes real consequences for many individuals and organizations [16,17].”
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Cites
Maps of random walks on complex networks reveal community structure
Rosvall, M., & Bergstrom, C. T. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0706851105 · Cited by 4,583 · see citing works
Statistical physics of social dynamics
Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119 · see citing works
Quantifying social group evolution
Palla, G., Barabási, A.-Ĺ., & Vicsek, T. (2007) · Nature · doi:10.1038/nature05670 · Cited by 1,679 · see citing works
Consensus clustering in complex networks
Lancichinetti, A., & Fortunato, S. (2012) · Scientific Reports · doi:10.1038/srep00336 · Cited by 898 · see citing works
Rosvall, M., Axelsson, D., & Bergstrom, C. T. (2009) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2010-01179-1 · Cited by 829 · see citing works
Network Analysis and the Law: Measuring the Legal Importance of Precedents at the U.S. Supreme Court
Fowler, J. H., Johnson, T. R., Spriggs, J. F., Jeon, S., & Wahlbeck, P. J. (2007) · Political Analysis · doi:10.1093/pan/mpm011 · Cited by 271 · see citing works
A network analysis of committees in the U.S. House of Representatives
Porter, M. A., Mucha, P. J., Newman, M. E. J., & Warmbrand, C. M. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0500191102 · Cited by 211 · see citing works
Armour, J. H., Deakin, S. F., Lele, P. P., et al. (2009) · The American Journal of Comparative Law · doi:10.5131/ajcl.2008.0017 · Cited by 134 · see citing works
Measuring the complexity of the law: the United States Code
Katz, D. M., & Bommarito, M. J. (2014) · Artificial Intelligence and Law · doi:10.1007/s10506-014-9160-8 · Cited by 117 · see citing works
Self-citationRuhl, J. B., Katz, D. M., & Bommarito, M. J. (2017) · Science · doi:10.1126/science.aag3013 · Cited by 94 · see citing works
Self-citationEbrahim, A. (2020) · Stanford University Press eBooks · doi:10.1515/9781503609211 · Cited by 71 · see citing works
A mathematical approach to the study of the United States Code
Bommarito, M. J., & Katz, D. M. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.05.057 · Cited by 68 · see citing works
Self-citationNetwork analysis in the legal domain: a complex model for European Union legal sources
Koniaris, M., Anagnostopoulos, I., & Vassiliou, Y. (2017) · Journal of Complex Networks · doi:10.1093/comnet/cnx029 · Cited by 55 · see citing works
How Long is the Coastline of the Law? Thoughts on the Fractal Nature of Legal Systems
Post, D. G., & Eisen, M. B. (2000) · The Journal of Legal Studies · doi:10.1086/468085 · Cited by 55 · see citing works
Computational Methods in Legal Analysis
Frankenreiter, J., & Livermore, M. A. (2020) · Annual Review of Law and Social Science · doi:10.1146/annurev-lawsocsci-052720-121843 · Cited by 55 · see citing works
Cabrelli, D. L., & Siems, M. (2015) · The American Journal of Comparative Law · doi:10.5131/ajcl.2015.0004 · Cited by 53 · see citing works
Large-Sample, Quantitative Research Designs for Comparative Law?
Spamann, H. (2009) · The American Journal of Comparative Law · doi:10.5131/ajcl.2008.0023 · Cited by 43 · see citing works
A network approach to the French system of legal codes—part I: analysis of a dense network
Boulet, R., Mazzéga, P., & Bourcier, D. (2011) · Artificial Intelligence and Law · doi:10.1007/s10506-011-9116-1 · Cited by 40 · see citing works
The Direction of Intra-Societal Diffusion
Bowers, R. V. (1937) · American Sociological Review · doi:10.2307/2084362 · Cited by 38 · see citing works
The cultural evolution of national constitutions
Rockmore, D. N., Fang, C., Foti, N. J., et al. (2017) · Journal of the Association for Information Science and Technology · doi:10.1002/asi.23971 · Cited by 38 · see citing works
The evolution of European Union law: A new data set on the Acquis Communautaire
Fjelstul, J. C. (2019) · European Union Politics · doi:10.1177/1465116519842947 · Cited by 34 · see citing works
Lee, B., Lee, K.-M., & Yang, J. (2019) · PLoS ONE · doi:10.1371/journal.pone.0209844 · Cited by 15 · see citing works
Inferring mechanisms for global constitutional progressPreprint
(2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 14 · see citing works
Creating Context Networks in Dutch LegislationPreprint
Winkels, R., Boer, A., & Plantevin, I. (2013) · SSRN Electronic Journal · doi:10.2139/ssrn.2368852 · Cited by 11 · see citing works
The Quantitative Study of Social Dynamics and Social Change
Bogue, D. J. (1952) · American Journal of Sociology · doi:10.1086/221042 · Cited by 8 · see citing works
Coupette, C. (2019) · Mohr Siebeck eBooks · doi:10.1628/978-3-16-157012-4-appendix · Cited by 7 · see citing works
Self-citationHusa, J. (2016) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780199935352.013.26 · Cited by 6 · see citing works
The Structure and Organization of EU Law in the Field of Direct Taxes
Schaper, M. (2013) · Doctoral series. · doi:10.59403/1ksbttj · Cited by 4 · see citing works
Inferring mechanisms for global constitutional progress
Rutherford, A., Lupu, Y., Cebrián, M., Rahwan, I., LeVeck, B. L., & García–Herranz, M. (2018) · Nature Human Behaviour · doi:10.1038/s41562-018-0382-8 · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 7
- [3]Tuma NB Social Dynamics Models and Methods 1984 Amsterdam Elsevier
- [9]Epstein L Martin AD An Introduction to Empirical Legal Research 2014 Oxford Oxford University Press
- [12]Livermore, M. A. & Rockmore, D. N. Law as Data: Computation, Text, & the Future of Legal Analysis (Santa Fe Institute Press, Santa Fe, 2019).
- [24]Sweeney, P. M. et al. Network analysis of manually-encoded state laws and prospects for automation. In Winkels, Lettieri & Faro (eds.) Network Analysis in Law 53–77 (Edizioni Scietifiche Italiane, Napoli, 2014).
- [42]Zweigert, K. & Kötz, H. An Introduction to Comparative Law (Clarendon Press, Oxford, 1998).
- [45]Glenn HP Reimann M Zimmermann R Comparative legal families and comparative legal traditions The Oxford Handbook of Comparative Law 2019 Oxford Oxford University Press
- [47]Winkler, W. E. String comparator metrics and enhanced decision rules in the Fellegi–Sunter model of record linkage. In Proceedings of the Section on Survey Research, American Statistical Association 354–359 (1990).
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Katz, D. M., Bommarito, M. J., Gao, S., & Arredondo, P. (2024) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2023.0254 · Cited by 420 · see citing works
Self-citationLexGLUE: A Benchmark Dataset for Legal Language Understanding in English
Chalkidis, I., Jana, A., Hartung, D., Bommarito, M. J., Androutsopoulos, I., Katz, D. M., & Aletras, N. (2021) · SSRN Electronic Journal · doi:10.2139/ssrn.3936759 · Cited by 111 · see citing works
Self-citationL'acte administratif algorithmique
Stepanov, A. (2026) · doi:10.70675/adc05be3za62ez4b4fz81e7zabf744e60dbf
- Authors
- Katz, D. M., Coupette, C., Beckedorf, J., & Hartung, D.
- Affiliations
- Illinois Institute of Technology (US)
- Max Planck Institute for Informatics (DE)
- Heidelberg University (DE)
- Bucerius Law School (DE)
- Corresponding author
- Katz, Daniel Martin
- Venue
- Scientific Reports
- Published
- 2020-10-30
- Volume
- 10
- Issue
- 1
- Pages
- 18737-18737
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC7599339
- OpenAlex
- W3025095288
- Cited by
- 55
- References
- 29
- Citations by year
- 2026: 10 · 2025: 10 · 2024: 10 · 2023: 10 · 2022: 8 · 2021: 7
- FWCI
- 21.58
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Bucerius Law School Interdisciplinary Legal Research Programé
- Topics
- Social Sciences › Political Science and International Relations › Artificial Intelligence in Law
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Legal and Constitutional Studies
- Social Sciences › General Social Sciences › Computational and Text Analysis Methods
- Keywords
- legal networks, document networks, legislative text analysis, welfare state expansion, law and society
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