Asymmetry degree as a tool for comparing interestingness measures in Decision Making: the case of Bayesian Confirmation Measures

Bayesian Confirmation Measures are used to assess the de- gree to which an evidence E supports or contradicts a conclusion H, making use of prior probability P(H), posterior probability P(H|E) and of probability of evidence P(E). Many confirmation measures have been defined till now, their use being motivated in different ways depending on the framework. Comparisons of those measures have already been made but there is an increasing interest for a deeper investigation of relationships, differences and properties. Here we focus on symmetry properties of confirmation measures which are partly inspired by classical geometric symmetries. Measures which do not satisfy a specific symmetry condition may present a different level of asymmetry: we define an asymmetry measure, some examples of its evaluation providing a practical way to appraise the asymmetry degree for Bayesian Confirmation Measures that allows to uncover some of their features, similarities and differences