The Emperor convoked each ecumenical council, declaring its time, place, and purpose, and invited all the bishops of the Empire. After the partition of the Empire and the barbarian invasions, the Emperor only had jurisdiction over the East. In order for the bishops of the West to be represented, the Emperor would send an invitation to the Pope, who had patriarchal authority over all Latin bishops, and could act on their behalf. If a doctrine of the faith was in dispute, the Pope would prepare a definition of the faith, either on his own initiative or in consultation with the Latin bishops. Ecumenical councils took place in or near the imperial city of Constantinople, so it was generally feasible only for the bishops of that patriarchate to attend. The patriarchs of Alexandria, Antioch, and Jerusalem attended in person or by proxy. The Pope never attended in person, but sent his legates with specific instructions on doctrinal matters.
Once an ecumenical council was convened, the papal legates presided over the synod on behalf of the Pope. The issues at hand were discussed among the bishops, and the pope's definition of faith was read to the assembly. The council would then give its assent to the definition, and use it as a basis for constructing its dogmatic constitutions, which define the faith, determine which persons or writings have fallen into heresy, and prescribe ecclesiastical penalties. The bishops could also issue disciplinary canons. At the close of a general council, the constitutions and canons were submitted to the Emperor so he could promulgate them throughout the Empire, while storing the original documents in the imperial archive. In this way the Emperor acts as guardian of the faith. Since the Pope did not attend in person, and he only authorized his legates to proclaim his definition of the faith, any further acts of the council needed papal ratification. After the council closed, the constitutions and canons were sent to the Pope for his signature. Only with papal approval could the acts be binding in the West, thereby giving the council true ecumenical status. The Pope sometimes elected to exclude or qualify some of the constitutions or canons in his ratification. Any decree or canon excluded by the Pope would not have ecumenical authority, but would at most be binding in the ecclesial jurisdictions of the East.
How accurate is this definition?
Originally it was only a council of the Orient; the arguments of Baronius (ad an. 381, nos. 19, 20) to prove that it was called by Pope Damasus are invalid (Hefele-Leclercq, Hist. des Conciles, Paris, 1908, II, 4). It was attended by 150 Catholic and 36 heretical (Semi-Arian, Macedonian) bishops, and was presided over by Meletius of Antioch; after his death, by the successive Patriarchs of Constantinople, St. Gregory Nazianzen and Nectarius.
In 379 Meletius held a council of 150 bishops in order to assure the triumph of orthodoxy in the East, and published a profession of faith which was to meet the approval of the Council of Constantinople (382). The end of the schism was near at hand. Since the two factions which divided the Antiochene Church were orthodox there remained but to unite them actually, a difficult move, but easy when the death of either bishop made it possible for the survivor to exercise full authority without hurting pride or discipline. This solution Meletius recognized as early as 381, but his friendly and peace- making proposals were rejected by Paulinus who refused to come to any agreement or settlement. http://www.newadvent.org/cathen/10161b.htm
So, papal legates running a council that is presided by a holy Bishop not even in communion with Rome? Don't think so.