Partial orders and measures for language preferences

Relative own-language preference depends on two parameters: the publication share of the language, and the self-citing rate. Openness of language L with respect to language J depends on three parameters: the publication share of language L, the publication share of language J, and the citation share of language J among all citations given by language L. It is shown that the relative own-language preference and the openness of one language with respect to another one, can be represented by a partial order. This partial order can be represented by a polygonal line (for the relative own-language preference) or a three-dimensional solid (for openness), somewhat in the same spirit as the Lorenz curve for concentration and evenness. Any function used to measure relative own-language preference or openness of one language with respect to another one should at least respect the corresponding partial orders. This is a minimum requirement for such measures. Depending on the use one wants to make of these measures other requirements become necessary. A logarithmic dependence on the language share(s) seems a natural additional requirement. This would correspond with the logarithmic behavior of psychophysical sensations. We give examples of normalized functions satisfying this additional requirement. It is further investigated if openness partial orders can lead to measures for relative own-language preference. The article ends with some examples related to the language use in some sociological journals.