Towards a simple mathematical model for the legal concept of balancing of interests

Frederike Zufall*, Rampei Kimura, Linyu Peng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. 11 EUCh. These competing rights are denoted by (i1) right to privacy and (i2) access to information; mathematically, their indices are respectively assigned by u1∈ [0 , 1] and u2∈ [0 , 1] subject to the constraint u1+ u2= 1. This constraint allows us to use one single index u to resolve the conflict through balancing. The outcome will be concluded by comparing the index u with a prior given threshold u. For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome u by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for u, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data.

Original languageEnglish
Pages (from-to)807-827
Number of pages21
JournalArtificial Intelligence and Law
Issue number4
Publication statusPublished - 2023 Dec


  • Balancing of interests
  • Mathematical model
  • Right to access
  • Right to the protection of personal data
  • Weight formula

ASJC Scopus subject areas

  • Law
  • Artificial Intelligence


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