Assessing the Italian tax courts system by weighted three-way log-ratio analysis

Deciding on what should be the most suitable reforms of a national judicial system, whether this means reorganising a courts' structure or offering incetives to judges, requires more empirical evidence. The efficiency of the public judicial system is important to any functioning democracy as it affects several aspects of citizens’ life. As a consequence, new statistical methodologies are required for further valuable insights into the issues that affect the effectiveness of a judicial system. The current study attempts to fill this gap by introducing a new statistical method to investigate the heterogeneity among Italian judicial courts. Here we propose a generalisation of log-ratio analysis for the analysis of the association between the variables of a three-way contingency table. Our focus of this investigation will be on the tax court system of the Italian judicial system. Log-ratio analysis presents many advantages, two of which are the computation and the visual representation of the odds ratios on which the analysis is based. For three-way tables, a conditional odds ratio reflects the likelihood that an event (say tax disputes) will take place in a particular geographical area (say North Italy) instead of an another (say South Italy) given a specific condition (type of justice court). Interestingly, the three-way log-ratio analysis presented in this paper allows one to visually describe these conditional odds-ratios in terms of point distances in a biplot between the types of justice court located in different geographical areas of Italy.