  Scenarios for the emergence or bootstrap of a lexicon involve the repeated
interaction between at least two agents who must reach a consensus on how to
name N objects using H words. Here we consider minimal models of two types of
learning algorithms: cross-situational learning, in which the individuals
determine the meaning of a word by looking for something in common across all
observed uses of that word, and supervised operant conditioning learning, in
which there is strong feedback between individuals about the intended meaning
of the words. Despite the stark differences between these learning schemes, we
show that they yield the same communication accuracy in the realistic limits of
large N and H, which coincides with the result of the classical occupancy
problem of randomly assigning N objects to H words.
