On some consequences of the permutation paradigm for data anonymization: Centrality of permutation matrices, universal measures of disclosure risk and information loss, evaluation by dominance

Recently, the permutation paradigm has been proposed in data anonymization to describe any micro data masking method as permutation, paving the way for performing meaningful analytical comparisons of methods, something that is difficult currently in statistical disclosure control research. This paper explores some consequences of this paradigm by establishing some class of universal measures of disclosure risk and information loss that can be used for the evaluation and comparison of any method on most data, under any parametrization and independently of the characteristics of the data to be anonymized. These measures lead to the introduction in data anonymization of the concepts of dominance in disclosure risk and information loss, which formalize the fact that different parties involved in micro data transaction can all have different sensitivities to privacy and information.