The paper presents an evolutionary model illustrating the dynamics that give rise to discriminatory social norms i.e. such rules of behaviour that fulfi l two conditions: (1) they treat differently actors having the same abilities and technical options, but differing in some arbitrary sense (2) they are supported by socially enforced sanctions. In the presented model both discrimination and social norms are necessary to solve a coordination problem that arises when the situation requires different actors to perform different tasks. The properties of behavioural rules relying on discrimination and leading to various degrees of inequality are analysed. It is demonstrated that in general norms ensuring equal payoffs are easier to stabilize, but unfair norms can also be stable.

In fair distribution of a set of indivisible goods it is problematic to provide basic equality if the goods differ in value. One of the most popular solutions to the problems are lotteries. The paper presents seven selected probabilistic procedures: random distribution, lexicographic procedure of equal chances of satisfaction, random serial dictatorship, core from random endowments, probabilistic serial, top trading cycles from equal division and
random priority with infi nite k factor. Some of these procedures always lead to the
same result as some other procedure, therefore these procedures are equivalent. The formal features of the procedures are also analysed in the paper: ordinal efficiency, ex post efficiency, and both strong and week version of: envy-freeness, proportionality, equitability, and individual strategy-proofness.

Statistical tests are used in science in order to support research hypotheses (theory, model). The Bayes Factor (BF) is a method that weighs evidence and shows which out of two hypotheses is better supported. Adopting the BF in statistical inference, we can show whether data provided stronger support for the null hypothesis, the alternative hypothesis or whether it is inconclusive and more data needs to be collected to provide more decisive evidence. Such a symmetry in interpretation is an advantage of the Bayes
Factor over classical null hypothesis signifi cance testing (NHST). Using NHST, a researcher draws conclusions indirectly, by rejecting or not rejecting the null hypothesis. The discrepancy between these decisions and the researcher’s needs, often leads to misinterpretation of signifi cance test results, e.g. by concluding that non-signifi cant p-values are evidence for the absence of differences between groups or that variables are independent. In this work we show the main differences between the Bayesian and
the frequential approach to the understanding of probability and statistical inference. We demonstrate how to verify hypotheses using the BF in practice and provide concrete examples of how it modifi es conclusions about empirical fi ndings based on the NHST procedure and the interpretation of p-values. We discuss the advantages of the BF – particularly the validation of a null hypothesis. Additionally, we provide some guidelines on how to do Bayesian statistics using the freeware statistical program JASP 0.8.