This paper outlines a formal model of socially motivated language change which unites insights from identity-oriented theories of language change with formal theories of language use and understanding. We use Gärdenfors\u27s (2000) Conceptual Spaces framework to formalize socially motivated ideological change and use signaling games with an iterated best response solution concept (Franke, 2009; Frank and Goodman, 2012) to formalize the link between ideology, linguistic meaning and language use. We then show how this new framework can be used to shed light on the mechanisms underlying socially-motivated change in French grammatical gender