Learning to agree over large state spaces

We study how a consensus emerges in finite population of like-minded individuals who are asymmetrically informed about the realization true state world. Agents observe private signal and then start exchanging messages. Generalizing classical model rational dialogues Geanakoplos Polemarchakis (1982) its subsequent extensions, we dispense with standard assumption that space is probability do not put any bound on cardinality itself or information partitions. show class can be found always lead to provided three main conditions met. First, everybody must able send messages else, either directly indirectly. Second, communication reciprocal. Finally, agents need have opportunity engage transfinite length.