Comparison and choice

This paper develops the idea of a choice as a mapping of subsets of a set X into their respective subsets and the idea of the comparison, as a relation between elements of X, that is determined or revealed by a choice. It then studies how certain properties of a choice imply or are implied by certain properties, such as acyclicity, quasi-transitivity, pseudo-transitivity and transitivity, of the comparison revealed, finally giving a complete logical diagram of all the implications between these latter properties of the comparison.