  In the process of collectively inventing new words for new concepts in a
population, conflicts can quickly become numerous, in the form of synonymy and
homonymy. Remembering all of them could cost too much memory, and remembering
too few may slow down the overall process. Is there an efficient behavior that
could help balance the two? The Naming Game is a multi-agent computational
model for the emergence of language, focusing on the negotiation of new lexical
conventions, where a common lexicon self-organizes but going through a phase of
high complexity. Previous work has been done on the control of complexity
growth in this particular model, by allowing agents to actively choose what
they talk about. However, those strategies were relying on ad hoc heuristics
highly dependent on fine-tuning of parameters. We define here a new principled
measure and a new strategy, based on the beliefs of each agent on the global
state of the population. The measure does not rely on heavy computation, and is
cognitively plausible. The new strategy yields an efficient control of
complexity growth, along with a faster agreement process. Also, we show that
short-term memory is enough to build relevant beliefs about the global lexicon.
