Testing for symmetry about an unknown median is a problem that has attracted the attention of statisticians for decades. Many of the existing tests of symmetry are based on the asymptotic distribution of a skewness coefficient, which typically is asymptotically normal and centered around zero for symmetric distributions. Unfortunately, the asymptotic variance depends on the underlying distribution and differs from one symmetric distribution to another one. A possible way out is to estimate this asymptotic variance from the sample by means of the bootstrap. In this paper, we explore this approach for six different skewness coefficients existing in the literature. Extensive experiments are performed for comparing the performance of the six associated tests of symmetry to that of two state-of-the-art symmetry tests in terms of preservation of the significance level under several symmetric distributions, power under asymmetric distributions and robustness in the presence of outliers. Even though the results show no clear best test, we conclude by providing some guidelines for choosing a test of symmetry based on the needs of the user.

The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the choice of aggregation function is sometimes restricted to a desired value of orness (orness-directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.

The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, strong stochastic transitivity, the presence of a candidate that Borda dominates all other candidates, etc. Unfortunately, one could easily find a prominent ranking rule, for which the outcome does not agree with these relaxed conditions. In this study, we aim to identify a condition weaker than unanimity, but under which the social outcome is still obvious. This condition, defined as the conjunction of three properties already studied by the present authors and hereinafter referred to as acclamation, will be proven to be a meeting point for the most prominent ranking rules in social choice theory, and will be used for introducing an intuitively appealing ranking rule.