Monotonicity and the value of a language

In Alcalde-Ulzu et al. (Journal of Economic Theory, 2022), a novel model to measure the value of a language is developed, and a family of value functions is axiomatically characterized. These functions assign the value of a language by looking at the groups that can communicate with that language. Each group is assigned a fixed value that depends on its size. If a group can communicate in a language, that language gets assigned the value associated to the group, divided by the number of languages commonly spoken by the group. We show that this family crucially depends on the monotonicity axiom used, and that a di¤erent interpretation leads to a vastly different family of functions, in which the value of a language is a simple function of its number of speakers. Specifically, the difference in the monotonicity axioms boils down to the following question: If a group shares a common language, is there any value in being able to communicate in another language? Our version, that we call Language inclusion monotonicity, says that there is. It leads to different policy implications, not necessarily favoring the majority languages.