Taming the complexity of the law: modelling and visualisation of dynamically interacting legal systems.

Lead Research Organisation: King's College London
Department Name: Mathematics

Abstract

This project aims at modelling and quantifying the complexity of legal systems and devising innovative ways to visualise and navigate the UK legal corpus beyond the traditional 'textual' paradigm. The phases of the project entail data collection, visualisation/user experience design, numerical modelling and development of novel quantitative tools to assess the complexity of dynamically interacting and ever-evolving units of a dense network (for instance, the articles or chapters of a living Act). I will address the long-standing and high-impact problem of the volume and intricacy of the UK legislative production by proposing a fresh departure from traditional ways of conceiving, connecting and 'measuring' legal documents. The framework I propose is timely, innovative and truly interdisciplinary. My ambition is to change the way legislation is produced, displayed, and eventually exploited by end-users, while claiming at the same time that recent developments in network theory and complexity science can and should induce a cultural switch between 'qualitative' and 'quantitative' approaches to legal complexity.
This project is rooted in the observation that many disciplines - ranging from finance to biomedical sciences - have recently witnessed a 'data explosion'. Network-based tools have greatly advanced our understanding of large intra-connected systems as diverse as stock markets and the human genome. The UK legal system has faced similar challenges in terms of accumulation of information: there are perhaps about 50,000,000 words of law in force in the UK legislative system (in comparison, there are only about 25,000 genes in the human genome) and 100,000 are produced and amended each month. Surprisingly, though, few quantitative approaches have been undertaken so far to model, visualise and tame the complexity of legal systems. The legal corpus is still accessed via the same tools used for centuries: manual word searches and references to numbered paragraphs. In reality, legal provisions are continuously created, amended and repealed, and typically point towards other ones, either older or located elsewhere, making the legal corpus a dynamical and highly intra-connected entity. Understanding a single provision often requires awareness of the 'big picture', and 'localised' interventions may indeed produce undesired or unforeseen "long-range" consequences. In 2013, the Office of the Parliamentary Counsel launched the ''Good law" initiative "with a shared objective of making legislation work well for the users of today and tomorrow". However, it is not at all clear whether a naive item-removing strategy (as proposed in the standard Red Tape or 2-out-1-in initiatives) is the only viable option - or, better, if it is a viable option at all - to keep the intricacy of the law under control. My vision is that advanced network theory, digital tools and analytical techniques borrowed from Complexity Science and Information Theory can and should be combined in an unprecedented synergy to set new objectively measurable standards in the drafting, accessibility and user-friendliness of laws.

Planned Impact

A positive outcome of my project will attract considerable attention from and prove highly beneficial to a wide array of stakeholders. First and foremost, policy-makers, MPs and parliamentary officers will be offered an innovative set of digital and quantitative tools that should radically change the way they approach the drafting phase of a new bill and the planning phase of interventions (amendments/repeals) on existing ones. My ambition is that - by the end of the Fellowship - the new visualization interface developed by my team is made available (if only as a prototype) on the official government website legislation.gov.uk. The superiority of this tool in terms of user experience with respect to the currently available 'text-only' option should rapidly trigger more initiatives aimed at charting broader sectors of the legislation. After an initial training phase, the individuals responsible for making and keeping the law alive will reach a deeper level of awareness on the importance of considering - right at the beginning of the legislative process - 'complexity' and 'structural' issues from a 'visual' and 'quantitative' standpoint too, this way addressing in very concrete and practical terms a key societal issue of our times. The flexible and long-term nature of this Fellowship will give me enough time to familiarize with the most practical aspects of how the UK legislative process currently works and to gather unique insights into practical ways to reduce its intricacy, thanks to dedicated training activities detailed in my P2I, and to regular channels for discussion and interaction with this specific category of stakeholders that my enterprise will open.
The idea of producing navigable digital charts of the UK laws within a network-based framework should also be very appealing to startups and enterprises operating in the fast-growing LawTech sector: I am certainly eager to explore with some of them the possibility to apply the same concept and vision as an aid for private and commercial transactions. Indeed, the same philosophy and underlying methodology could well be adapted to the digitalisation and visualisation of private contracts and other legally binding documents in the private sector, whose complete oversight with traditional methods is hindered by their sheer volume, size, or inherent intricacy. I have planned a series of short visits to London-based startups (named in the JoR), as well as invitations to the one-day launch event (as detailed in the P2I) to encourage a faster and more widespread uptake of my project's outputs by this community. In terms of economic impact, an increased level of clarity and transparency of legal provisions, as well as the generalised adoption of network-based visualisation tools and complexity indicators among private-sector stakeholders is expected - within a time-horizon of roughly ten years - to generate savings for the UK economy in the range of hundreds of millions of Pounds (see P2I for details).
The visualization interface and the 'digital laboratory' will also offer an invaluable support tool to legal practitioners and end-users from the general public who may be occasionally interested in consulting the law (for instance, due to their involvement in litigation), as well as secondary beneficiaries - such as groups lobbying for sector-specific changes in the law. The introduction of the new digital framework I am advocating will promote a cultural shift in the UK society, eliminating the most frustrating aspects in the accessibility of services, which usually constitute a primary source of distrust towards the government and public offices. My planned dissemination activities (detailed in the P2I) intend to demonstrate that their institutional mission to serve the needs of the population can be best accomplished by playing the role of true 'innovation engines', this way improving the public perception and the quality of services they provide.

Publications

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Bartolucci S (2019) A Percolation Model for the Emergence of the Bitcoin Lightning Network in SSRN Electronic Journal

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Bartolucci S (2023) Ranking influential nodes in networks from aggregate local information in Physical Review Research

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Evan Tzanis (2023) Graphie: A network-based visual interface for UK's Primary Legislation in Graphie: A network-based visual interface for UK's Primary Legislation

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Förster Y (2022) Information retrieval and structural complexity of legal trees in Journal of Physics: Complexity

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Gamberi L (2021) Maximal modularity and the optimal size of parliaments. in Scientific reports

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Gamberi L (2022) Rationalizing systematic discrepancies between election outcomes and opinion polls in Journal of Statistical Mechanics: Theory and Experiment

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Vivo P (2024) A complexity science approach to law and governance. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

 
Title Legal data parsing and visualisation 
Description Scope: We aim to advance the readability of Legal documents. We wish to deliver an infrastructure where we unlock legal information on behalf of a wide range of legal stakeholders, satisfying their user needs. For achieving this, we are looking to establish a pipeline (mostly automated) where parsed legal data feed corresponding front end visualisations. [Parsing] Define a cross Legal - Act data model, representing different Actions with respect into a unifying data structure. A cross Act parsing according into a specific data model. Import the parsed data into front end layers (say, D3JS based network visualisations) or other third-party data clients (in Python or R). [Visualisation] Evaluate different front-end solutions for tree and graph-network visualisations. Prototype cross platform visualisations using these libraries. Advance the above visualisations introducing more user driven graph interactions (considering node/lines colouring, nodes size, node filtering and etc) We have considered two different visualisations. Act driven trees and Act driven networks. In an Act Tree, all the contents (sub contents) of an Act are displayed as a tree. Tree leaf nodes might contain a reference into an outbound Act. Given a specific Act, Act driven networks, show with how this Act is interconnected with other Acts - where those references are further displayed as extra network nodes. We call an Act Tree, as a Zoom In technique. Contrary, we call an Act-Network graph as a Zoom out approach. We now wish to marry these two approaches within the same front-end experience. Where users could switch from a tree graph into a network graph and vice versa. This is a challenging task, that might require the development of a new web network library. [Other Topics] In a more theoretical direction, we wish to associate each node with a quick textual or keyword summary about the content of its sub-nodes. We aim to apply natural language methods across the full text of an Act. We hope that such information, will help interested readers to look for their searched information faster. [Appendix] Data Model Given an Act, we are being able to store its information into a Python Object according to the following order: Parts, SubParts, SubPartItems, Items and etc. [Future Development] Over the next 6 months we aim to deliver the following: To develop our own web network library for representing information found on legal documents. To package all our development findings into a web service. 
Type Of Material Data analysis technique 
Year Produced 2023 
Provided To Others? Yes  
Impact The impact is not fully developed, but in the course of the following six months we will make snippets and a toy interface publicly available to external stakeholders to navigate the legislation and provide feedback on the user interface. 
URL https://github.com/kclquantlaw/graphie
 
Description Academic collaboration with Olga Siemers and Daniela Serban from International School for Government at King's College London 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact We have started an academic collaboration with the International School for Government at King's College London in order to apply quantitative methods to the study of governmental policy-making under uncertainty and the interpretation and functioning of local governments as complex adaptive systems. This collaboration is aimed at producing academic outputs and grant applications, creating a synergy between traditional methods of public policy analysis, and more quantitative tools (data collection and analysis, complex systems modelling) for which my expertise can provide added value.
Year(s) Of Engagement Activity 2020
 
Description Academic dialogue with Dr Rebecca Helm from University of Exeter 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact I have started an academic dialogue with Dr Rebecca Helm, a fellow FLF member, who is a Lecturer in Law at Exeter. Rebecca conducts research using quantitative methodology and behavioural biology to examine and evaluate the operation of legal regulation in practice, and the extent to which legal regulation reflects modern scientific understanding. This has included examining the failure of legal regulation to address psychological and social pressures that can lead innocent defendants to admit guilt, the relationship between the regulation of compensated and uncompensated surrogacy and human rights, and the appropriate treatment of witness testimony in adjudication. The purpose of this collaboration is to establish mathematical models and perform supporting data analysis to investigate decision-making processes under uncertainty, in particular concerning the behaviour and selection of juries in criminal trials, for which my expertise could provide added value.
Year(s) Of Engagement Activity 2021
 
Description Blog post on Machine Lawyering website 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I wrote a blog post on the prestigious Machine Lawyering, handled by Hong Kong University, which reaches academics and professionals interested in the application of software, technology, and mathematical techniques to issues orbiting around the legal landscape.
Year(s) Of Engagement Activity 2020
URL https://www.legalanalytics.law.cuhk.edu.hk/post/percolightning-what-network-theory-can-say-about-bit...
 
Description Invited expert talk at Complexity Masterclass led by Dr Olga Siemers 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Policymakers/politicians
Results and Impact This was a talk + conversation with a group of civil servants taking part in a Master's programme led by Dr Olga Siemers at King's College London (module name: Embracing Uncertainty: Policymaking in turbulent times at the International School for Government (ISfG)). I was asked to present a 20' talk on the issue of 'legal complexity' and lead the ensuing discussion on the topic of how decisions can be made in a complex world. After my talk and discussion, Dr Siemers wrote to me: "I would like to thank you for speaking for our module at King's last week! Your talk was really insightful and informative. We received encouraging and positive feedback from the module participants. They enjoyed your session and they have learned a lot from it."
Year(s) Of Engagement Activity 2021
 
Description Invited talk at Legal Tech Essentials 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Participation in a presentation/panel on Legal Data Science, with the focus on "Quantitative and computational methods are on the rise in legal academia. Some scholars, who are at the forefront of their fields, will share their latest results and explain their impact on the legal world of tomorrow. This session requires no prior knowledge but some solid curiosity." The PI delivered a presentation on their QuantLaw team activity, which sparked interesting discussion and offered many networking opportunities with like-minded scholars and stakeholders. It was a great opportunity to increase visibility of the PI's team and their contribution to knowledge and societal issues.
Year(s) Of Engagement Activity 2022
URL https://legaltechessentials.com/
 
Description Law School Guest Lecture 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact I was invited by Prof Nicola Palmer (Deputy Director of Post-Graduate Research at the Law School) of the Dickson Poon School of Law at KCL to give an online Guest Lecture on 30/11/2020 for their current PhD law students on the topic 'use of quantitative methods in legal research.'
Year(s) Of Engagement Activity 2020
 
Description Organisation of online conference "The Physics of the Law Legal Systems Through the Prism of Complexity Science" 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The 2020 Physics of the Law Conference took place online on November 12 and 13, 2020 and was linked to the Research Topic "The Physics of the Law" of Frontiers in Physics. The Conference was aimed at contributors to the special issues, practitioners and students active at the interface between legal studies and complexity science.

In recent years, a growing body of research understands the interaction of law and society as a complex adaptive system. There has been growth in social, political and economic complexity which has in turn manifested in legal complexity. In support of this view, in extant academic literature, scholars have leveraged techniques and tools from statistical physics, complexity and computational social science to both characterise and predict the behaviour of various legal institutions.

In part to confront the scale and complexity of the law, the commercial sphere has seen significant growth in the advent of Legal Tech and use of applied disciplines such as processing engineering and design.

In sum, how interactions between individuals are shaped by norms, and what are the emerging ("collective") phenomena in the highly interconnected "legal" landscape - interpreted in the broadest sense - constituted the core questions that this Research Topic and Workshop addressed.

Overall, reception was very positive, and many people added comments in a detailed feedback form that we made available after the event. The average overall satisfaction was an 8.65/10 for attendees and an 8.30/10 for panelists. We have a Net Promoter Score of 84.38 for attendees (panelists: 60). The detailed feedback can be accessed at https://docs.google.com/spreadsheets/d/1yaRIXS3iDkapUU8AN3-BbxFgg2S5FYAR-8uoM0PBm1o/edit#gid=1959550017
Year(s) Of Engagement Activity 2020
URL https://www.physicsoflaw.com/
 
Description Participation as panelist at Anthropology, AI and the Future of Human Society Virtual Conference 6 -10 June 2022 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The PI took part in "Is that AI judging us?", which was a 5-experts panel concerned with automated decision-making in the legal domain. The workshop was attended remotely by ~150 participants. Other participants in the panel included anthropologists, lawyer, and NGO representatives. The panel sparked many questions and discussion afterwards, and the panelists receive very comforting feedback from participants.
Year(s) Of Engagement Activity 2022
URL https://therai.org.uk/conferences/anthropology-ai-and-the-future-of-human-society
 
Description Participation in Legal Geek conference 2019 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact I participated in the Legal Geek conference, a networking event held in London on 16th Oct 2019. I met several practitioners and startup representatives working in the emerging LawTech field, and sowed the seed of future engagements with the Quantitative and Digital Lab I lead at KCL.
Year(s) Of Engagement Activity 2019
 
Description Participation in STEM for Britain 2022 at Westminster 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Policymakers/politicians
Results and Impact My PhD student Luca Gamberi, affiliated with the Quantitative and Digital Law Lab, is presenting a poster on the topic of the Bradley effect (discrepancies between votes cast and opinions publicly expressed in polls) at the event STEM for Britain 2022, held at Westminster on 7th March 2022. This will be a great occasion to showcase our research and advertise our Team to politicians, policy makers, MPs and other stakeholders, as well as fellow postgraduate students.
Year(s) Of Engagement Activity 2022
URL https://stemforbritain.org.uk/
 
Description Participation in STEM for Britain at Westminster 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Policymakers/politicians
Results and Impact My PhD student Luca Gamberi, affiliated with the Quantitative and Digital Law Lab, is presenting a poster on the topic of Parliamentary Representativity and Legal Complexity at the event STEM for Britain 2020, held at Westminster on 9th March 2020. This will be a great occasion to showcase our research and advertise our Team to politicians, policy makers, MPs and other stakeholders, as well as fellow postgraduate students.
Year(s) Of Engagement Activity 2020
 
Description Participation in conference 'Computational Legal Studies: past, present, and future' (CLS2022, Singapore) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This is an international and highly reputable conference in the field of computational legal studies. After my (invited) talk, I received a message from the lead organiser stating: "Many thanks for the talk. Really fascinating ideas."
Year(s) Of Engagement Activity 2022
URL https://cclaw.smu.edu.sg/events/computational-legal-studies-2022
 
Description Preliminary meeting with the Office of the Parliamentary Counsel 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Policymakers/politicians
Results and Impact I visited the Office of the Parliamentary Counsel on 23rd October 2019, where I met Hayley Rogers (who led on the Good Law project). I gave a 30' introductory presentation on the newly founded Quantitative and Digital Law Lab at King's College London, and I collected suggestions and feedback. I gathered that there is much interest in what my team is trying to achieve, and we agreed that I will update them regularly on our progresses, by setting up further informal and formal opportunities for fruitful exchanges.
Year(s) Of Engagement Activity 2019