Collective learning considers how agents, in a community sharing a learning purpose, may benefit from exchanging hypotheses and observations to learn efficiently as a community as well as individuals. The community forms a communication network and each agent has access to observations. We address the question of a protocol, i.e. a set of agent's behaviours, which guarantees the hypotheses retained by the agents take into account all the observations in the community. We present and investigate the protocol WAVES which displays such a guarantee in a turn-based scenario: at the beginning of each turn, agents collect new observations and interact until they all reach this consistency guarantee. We investigate and experiment WAVES on various network topologies and various experimental parameters. We present results on learning efficiency, in terms of computation and communication costs, as well as results on learning quality, in terms of predictive accuracy for a given number of observations collected by the community.