Taming the complexity of the law: modelling and visualisation of dynamically interacting legal systems [RENEWAL].
Lead Research Organisation:
King's College London
Department Name: Mathematics
Abstract
Following a successful first phase of my fellowship, this proposal has the aim of further understanding and curbing the complexity of legal systems, from a dual standpoint: on one hand, we will develop and add important features to our 'Graphie' visualisation interface, which allows users to navigate the UK legal corpus beyond the traditional purely 'textual' paradigm. On the other hand, we will deepen our theoretical investigation on what makes a legal text 'complex' -- from the point of view of how difficult it is for a generic reader to locate a piece of information hidden in a hierarchical structure (modelled as a complex network). The phases of the project entail data collection, visualisation/user experience design, theoretical modelling, and development of novel quantitative tools to assess the complexity of dynamically interacting and ever-evolving units of a network of provisions (for instance, the articles or chapters of a living Act). The 'legal complexity' problem is long-standing and hard-felt by legal scholars, practitioners, and even untrained users, and my project has the ambition to address it via an innovative and truly interdisciplinary approach, which leverages tools from complexity science as well as state-of-the-art techniques and frameworks for data visualisation. The final goal is to demonstrate that the current way legislation is produced, displayed, and offered to end-users is highly suboptimal, and that an alternative is possible. This cultural switch will rest on recent developments in network theory and complexity science, which for the first time mark a transition between 'qualitative' and 'quantitative' approaches to legal complexity.
One of the primary sources of legal complexity is the sheer volume of legal provisions in force at any given time. A rough estimate points to the existence of about 50,000,000 words of law currently in force in the UK legislative system (in comparison, there are only about 25,000 genes in the human genome) and 100,000 being produced or amended each month. Another issue concerns the way individual acts of parliament are written: the original structure as well as the subsequent amendments make it very difficult for a general reader to follow all the implications of a given provision, because multiple hops across different 'nodes' of the network are typically needed to form an exhaustive view of an act's content. The fact that legal provisions are continuously created, amended and repealed, and typically point towards other ones, either older or located elsewhere, makes the legal corpus a dynamical and highly intra-connected entity -- which is surprisingly still accessed via the same tools used for centuries: manual word searches and references to numbered paragraphs. 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, the options proposed there to curb the complexity of the corpus as a whole -- for instance in the standard Red Tape or 2-out-1-in initiatives -- are generally based on a naïve 'item-removing' strategy, which is not guaranteed at all to achieve the goal of keeping the intricacy of the law under control. Finally, a further issue contributing to the problem of legal complexity is the fact that lawyers and legal practitioners do not usually have the necessary training in complexity science and quantitative methods to be able to effect a meaningful change on the way their own professionals go about their daily business in a more efficient and rational way. My vision is that advanced network theory, digital tools and analytical techniques from Complexity Science -- as well as the creation of an interdisciplinary training programme blending law and basic science together -- should be combined in an unprecedented synergy to set new measurable standards in the drafting, accessibility, and user-friendliness of the law.
One of the primary sources of legal complexity is the sheer volume of legal provisions in force at any given time. A rough estimate points to the existence of about 50,000,000 words of law currently in force in the UK legislative system (in comparison, there are only about 25,000 genes in the human genome) and 100,000 being produced or amended each month. Another issue concerns the way individual acts of parliament are written: the original structure as well as the subsequent amendments make it very difficult for a general reader to follow all the implications of a given provision, because multiple hops across different 'nodes' of the network are typically needed to form an exhaustive view of an act's content. The fact that legal provisions are continuously created, amended and repealed, and typically point towards other ones, either older or located elsewhere, makes the legal corpus a dynamical and highly intra-connected entity -- which is surprisingly still accessed via the same tools used for centuries: manual word searches and references to numbered paragraphs. 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, the options proposed there to curb the complexity of the corpus as a whole -- for instance in the standard Red Tape or 2-out-1-in initiatives -- are generally based on a naïve 'item-removing' strategy, which is not guaranteed at all to achieve the goal of keeping the intricacy of the law under control. Finally, a further issue contributing to the problem of legal complexity is the fact that lawyers and legal practitioners do not usually have the necessary training in complexity science and quantitative methods to be able to effect a meaningful change on the way their own professionals go about their daily business in a more efficient and rational way. My vision is that advanced network theory, digital tools and analytical techniques from Complexity Science -- as well as the creation of an interdisciplinary training programme blending law and basic science together -- should be combined in an unprecedented synergy to set new measurable standards in the drafting, accessibility, and user-friendliness of the law.
People |
ORCID iD |
| Pierpaolo Vivo (Principal Investigator / Fellow) |
Publications
Mori F
(2024)
Cost of excursions until first crossing of the origin for random walk and Lévy flights: An exact general formula
in Physical Review Research
Bartolucci S
(2024)
Distribution of centrality measures on undirected random networks via the cavity method.
in Proceedings of the National Academy of Sciences of the United States of America
Gamberi L
(2024)
Price of information in games of chance: A statistical physics approach.
in Physical review research
Bartolucci S
(2025)
Correlation between upstreamness and downstreamness in random global value chains
in Journal of Economic Behavior & Organization
Bartolucci S
(2025)
Upstreamness and downstreamness in input-output analysis from local and aggregate information.
in Scientific reports
Aufiero S
(2025)
Phase transitions in debt recycling
in Journal of Economic Dynamics and Control
Vivo P
(2025)
CompLex: Legal systems through the lens of complexity science
in Europhysics Letters
| 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 | AI and Tax Law in Italy |
| Organisation | University of Turin |
| Country | Italy |
| Sector | Academic/University |
| PI Contribution | This collaboration aims at using tools and techniques from complexity science to inform policy recommendations concerning the Tax collection and court proceedings in Italy. |
| Collaborator Contribution | Two PhD students from Univ. of Turin have visited me for three months in 2023. We have set up the project, performed relevant calculations and modelling, and investigated data from the Italian Treasury to determine bottlenecks and policy improvements towards fairer proceedings for tax fraud and evasion. |
| Impact | Outputs (2 scientific papers) are being drafted right now. Seminar invitations are being circulated. |
| Start Year | 2023 |
| Description | Participation as discussant in QuanTo activity in Turin |
| 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 | Discussant and panel discussion on emerging AI technology and tax law. The presentation was given in front of law professor and PhD students, which sparked questions and discussion afterwards, and further networking opportunities |
| Year(s) Of Engagement Activity | 2025 |
| Description | Presentation to civil servants about legal complexity during the module "Embracing uncertainty" |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presentation given in the context of the module Embracing uncertainty aimed at civil servants of the main features of complex adaptive systems. The audience gave very positive feedback, stating that they could not suspect that mathematics could be so interesting and engaging. I have received many requests for the slides and further explanation, and the invitation has been extended to 2025 as well. |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://www.kcl.ac.uk/short-courses/embracing-uncertainty-policymaking-in-turbulent-times |