We introduce the theoretical principles that underlie the design of a software tool which could be used by judges for making decisions about litigations and for writing judgements. The tool is based on Binary Decision Diagrams (BDD), which are graphical representations of truth-valued functions associated to propositional formulas. Given a type of litigation, the tool asks questions to the judge; each question is represented by a propositional atom. Their answers, true or false, allow to evaluate the truth value of the formula which encodes the overall recommendation of the software about the litigation. Our approach combines some sort of 'theoretical' or 'legal' reasoning dealing with the core of the litigation itself together with some sort of 'procedural' reasoning dealing with the protocol that has to be followed by the judge during the trial: some questions must necessarily be examined and sometimes in a specific order. That is why we consider extensions of BDD called Multi-BDD. They are BDD with multiple roots corresponding to the di erent specific issues that must necessarily be addressed by the judge during the trial. We illustrate our ideas on a case study dealing with French trade union elections which has been used throughout our project with the Cour de cassation. We also introduce the prototype developed during our project and a link with restricted access to try it out.