The opportunity prior: A simple and practical solution to the prior probability problem for legal cases

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


One of the greatest impediments to the use of probabilistic reasoning in legal arguments is the difficulty in agreeing on an appropriate prior probability for the ultimate hypothesis, (in criminal cases this is normally “Defendant is guilty of the crime for which he/she is accused”). Even strong supporters of a Bayesian approach prefer to ignore priors and focus instead on considering only the likelihood ratio (LR) of the evidence. But the LR still requires the decision maker (be it a judge or juror during trial, or anybody helping to determine beforehand whether a case should proceed to trial) to consider their own prior; without it the LR has limited value. We show that, in a large class of cases, it is possible to arrive at a realistic prior that is also as consistent as possible with the legal notion of ‘innocent until proven guilty’. The approach can be considered as a formalisation of the ‘island problem’ whereby if it is known the crime took place on an island when n people were present, then each of the people on the island has an equal prior probability 1/n of having carried out the crime. Our prior is based on simple location and time parameters that determine both a) the crime scene/time (within which it is certain the crime took place) and b) the extended crime scene/time which is the ‘smallest’ within which it is certain the suspect was known to have been ‘closest’ in location/time to the crime scene. The method applies to cases where we assume a crime has taken place and that it was committed by one person against one other person (e.g. murder, assault, robbery). The paper considers both the practical and legal implications of the approach. We demonstrate how the opportunity prior probability is naturally incorporated into a generic Bayesian network model that allows us to integrate other evidence about the case.


External organisations
  • University of London
  • University College London
  • Agena Ltd
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Law (excluding Law and Society)


  • Bayesian networks, Crime scene, Island problem, Opportunity prior probability, Prior probability, Time
Original languageEnglish
Title of host publicationProceedings of the 16th International Conference on Artificial Intelligence and Law, ICAIL 2017
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Electronic)9781450348911
Publication statusPublished - 2017 Jun 12
Publication categoryResearch
Event16th International Conference on Artificial Intelligence and Law, ICAIL 2017 - London, United Kingdom
Duration: 2017 Jun 122017 Jun 16


Conference16th International Conference on Artificial Intelligence and Law, ICAIL 2017
CountryUnited Kingdom