Many properties of gravity models are sole consequences of the quasi-symmetry condition or its avatars. We investigate here quasi-symmetry per se, in contrast to geographical tradition, which has been more focused on the exogenous socioeconomic and spatial conditions. In particular, the 'size - utility - accessibility' parameterization of migration counts turn out to rely exclusively upon the quasi-symmetry of flows. Various facets of quasi-symmetry are presented and put in correspondence with Markov chains theory, Bradley - Terry - Luce decision theory, the Weidlich - Haag model, and alternative classical statistical models (marginal homogeneity, symmetry, independence). Existing as well as presumably new estimation and model selection procedures (maximum likelihood, minimum discrimination information, maximum entropy, generalized power divergence, least squares and logarithmic least squares) are discussed in a way which unifies different traditions in gravity modelling.
