We address two major issues of Waves, a collective learning protocol that has been recently proposed. The protocol aims at enhancing individual agent learning in an agent society organized in a network in which agents may interact with their neighbors. When considering a turn-based setting, Waves guarantees that at the end of a turn each agent has a model consistent with all observations present within the society. This guarantee is obtained thanks to exchange of observations and hypotheses between neighbors. All interactions are performed in parallel and the protocol may lead to redundancies and some lack of diversity in the hypotheses revised by the agents. The first issue concerns the redundancy that follows from the generation and transmission by agents of hypotheses equivalent to hypotheses previously encountered. The second issue is the lack of diversity that may result in losing the accuracy increase, with respect to an isolated agent, observed whenever all agents freely interact with each other.