This reminds of a dialogue I saw on TV between a muslim 'clan' leader and a muslim woman journalist.
She asked him how one could discern between two people's interpretations of the Koran, and he replied 'follow the true Islam'. To which she asked 'What If I say my Islam is the true one?, why should I follow your interpretation?' (paraphrased). At which point he got up, and left, along with his clan.
The question here is, in the event of schism, how is it then sorted out?
From where I stand, the Orthodox have no tradition, hierarchical or logical structures to base their answer upon since each is either contradictory to their faith (the pope), logically inconsistent (Old Believers vs 1054) or too varied to form a solid answer (early schisms vs Chalcedon vs 1054 vs Old Believers etc...).
In contrast, the Catholic position is simple and easy to define, and I suspect, often presented in a triumphalist manner. This in turn causes aggravation, and discussion turns into a shouting match, with no one learning anything.
This is probably because the initiative behind the OP's question is designed to highlight the lack of ability (by the Orthodox) to deal with schism (abstractly). Although I agree with the point it is addressing, previous experience has left me with no doubts as to actually how non-effective it is in terms of trying to prove a point, and winning agreement.
Glory to Jesus Christ!