Cyprian: Epistles XXVI-XXVIII
In these Epistles we get the first clear(ish) view of Cyprian's polity, and it is one that does not completely stand up to Biblical scrutiny, albeit without completely falling either. Again, the question is what to do with the lapsed who are requesting readmission to the church. Some in this category are asking with humility and patience, had good reputations before the persecution as believers, and come with the support of the confessors. Their patience ought to be rewarded, even if we ought to find out which "confessors" are supporting them and ask that they stop taking action on behalf of the whole church.
But what is that whole church? Cyprian cites Matthew 16:18-19 ("thou art Peter, and upon this rock...") and then notes that:
Through the changes of times and successions, the ordering of bishops and the plan of the Church flow onwards; so that the Church is founded upon the bishops, and every act of the Church is controlled by these same rulers. Since this, then, is founded on the divine law, I marvel that some, with daring temerity, have chosen to write to me as if they wrote in the name of the Church...All this, of course, is simply false and an interpretation of Matthew 16:18-19 that does not account for the context of the rest of Matthew 16 or Matthew 18, where we see that the "keys" in question are tied respectively to the leadership (elders, pastors, bishops, whatever name that takes), the confession of Christ, and the congregation of believers. The church rests ultimately on Christ and the confession of Him as Messiah by believers, but within that umbrella both leadership and the congregation have a role to play in the government of the church. One does not have final authority over the other, but both have roles to play. (For more on that, check out these books.)
With that said, even Cyprian doesn't demand the absolute dominance of the leaders of the church, he goes on:
...in the name of the Church; when the Church is established in the bishop and the clergy, and all who stand fast in the faith.Even Cyprian sees a broader base for church government than those who would later abuse his writings in establishing a solid ecclesiastical hierarchy.
In Epistle XXVII Cyprian commends the leaders who have withheld communion from those individuals who have claimed to speak for the whole church, despite repeated warnings not to do so. Until the church can "by the Lord's mercy... begin to assemble together" no decision should be made and patience, care, and caution ought to be the order of the day--not haste and reconciliation based on sympathy for potentially false words. Cyprian is not claiming to have final authority himself ("Of which thing I cannot make myself sole judge, since many of the clergy are still absent..."), and notes that really the issues have not even been looked into. Epistle XXVIII sends a brief of this to the church in Rome, wanting to be sure that there is a "common plan for the advantage of the administration of the Church." Not that he is asking for guidance from Rome, just that he is keeping them in the loop.