Why are certain properties of binary relations relatively more common in natural language?

The aim of this paper is to explain the fact that certain properties of binary relations are frequently observed in natural language while others do not appear at all. Three features of binary relation are studied: (i) the ability to use the relation to indicate nameless elements; (ii) the accuracy with which the vocabulary spanned by the relation can be used to approximate the actual terms to which a user of the language wishes to refer; (iii) the ease with which the relation can be described by means of examples. It is argued that linear orderings are optimal according to the first criteria while asymmetric relations are optimal according to the second. From among complete and asymmetric relations (tournaments), those which are transitive are optimal according to the third criterion.