The main topic of the paper is to reformulate some elements of traditional algebraic measurement theories so that statistical testing is possible. This leads to probabilistic measurement theory where the axioms are expressed in terms of choice probabilities. The aim to use probabilistic theory for testing needs some considerations about the geometry of the parameter space (Section 3). The authors show that the ML-methodology may be used for this purpose: they prove the existence and uniqueness of an ML-estimator to an empirical data structure (preferences), but they do not give any general formula leading to such an estimator as it seems of rather high complexity. Instead, two special cases are studied in more detail - test of weak stochastic monotonicity (Section 4.1) and of quadruple condition (Section 4.2).