When Efficient Communication Explains Convexity

Much recent work has argued that the variation in the languages of the world can be explained from the perspective of efficient communication; in particular, languages can be seen as optimally balancing competing pressures to be simple and to be informative. Focusing on the expression of meaning -- semantic typology -- the present paper asks what factors are responsible for successful explanations in terms of efficient communication. Using the Information Bottleneck (IB) approach to formalizing this trade-off, we first demonstrate and analyze a correlation between optimality in the IB sense and a novel generalization of convexity to this setting. In a second experiment, we manipulate various modeling parameters in the IB framework to determine which factors drive the correlation between convexity and optimality. We find that the convexity of the communicative need distribution plays an especially important role. These results move beyond showing that efficient communication can explain aspects of semantic typology into explanations for why that is the case by identifying which underlying factors are responsible.