History-Independent Distributed Multi-agent Learning

How should we evaluate a rumor? We address this question in a setting where multiple agents seek an estimate of the probability, b, of some future binary event. A common uniform prior on b is assumed. A rumor about b meanders through the network, evolving over time. The rumor evolves, not because of ill will or noise, but because agents incorporate private signals about b before passing on the (modified) rumor. The loss to an agent is the (realized) square error of her opinion.