“So then the EO has no infallible authority huh?”
Oh, we have an infallible authority, just no infallible individuals. Ecumenical Councils can and have declared infallibly Christian dogma. Interestingly, we know that declared dogma is true, however, only if the Laos tou Theou, the People of God, accept the dogma and live it out in their lives as Christians. We believe this because we do not believe that the Holy Spirit, given to The Church at Pentecost, will allow the Body of The Church to fall into error.
Here’s a link to the 1848 Encyclical of the Eastern Patriarchs in Reply to a Letter of Pope Pius IX. The letter is a reply to the Pope’s claim of absolute authority over the entire Church. They disagree. What you may find interesting is the discussion of dogmatic authority within The Church. It is rather more polemical than one would read today. So was the letter from the pope. But the principles enunciated by the Patriarchs are as true today as when they wrote them.
http://www.orthodoxinfo.com/ecumenism/encyc_1848.aspx
Based on WHAT
We believe this because we do not believe that the Holy Spirit, given to The Church at Pentecost, will allow the Body of The Church to fall into error.
Paul did not believe that, He warned against error and false teachers entering the church
2Cr 11:4 For if he that cometh preacheth another Jesus, whom we have not preached, or [if] ye receive another spirit, which ye have not received, or another gospel, which ye have not accepted, ye might well bear with [him].
2Cr 11:13 For such [are] false apostles, deceitful workers, transforming themselves into the apostles of Christ. 14 And no marvel; for Satan himself is transformed into an angel of light. 15 Therefore [it is] no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works.
Neither did Peter
2Pe 2:1 But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction.
John did not believe that
1Jo 4:1 Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.
Jude was very clear in his warning
Jud 1:3 ¶ Beloved, when I gave all diligence to write unto you of the common salvation, it was needful for me to write unto you, and exhort [you] that ye should earnestly contend for the faith which was once delivered unto the saints. Jud 1:4 For there are certain men crept in unawares, who were before of old ordained to this condemnation, ungodly men, turning the grace of our God into lasciviousness, and denying the only Lord God, and our Lord Jesus Christ. Jud 1:5 ¶ I will therefore put you in remembrance, though ye once knew this, how that the Lord, having saved the people out of the land of Egypt, afterward destroyed them that believed not. 6 And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day. 7 Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire. 8 Likewise also these [filthy] dreamers defile the flesh, despise dominion, and speak evil of dignities.Jesus warned us
Mat 24:5 For many shall come in my name, saying, I am Christ; and shall deceive many.
Mat 24:11 And many false prophets shall rise, and shall deceive many.
The EO may claim they do not have an infallible man ...but the men of those councils are credited with infallibility IF THEY HAVE NO FINAL INFALLIBLE MEASURING ROD for that doctrine.. it is nothing more than the doctrine of men