All I know about Arianism is that it denied the divinity of Christ, and it was kinda sorta related to Gnosticism. I didn't know it was ever a majority "faith".
When I said "popularity", I think I was mainly referring to within the Church. I know I have been told that any individual, or even any individual Father, could have and did think and write things that are now considered wrong. However, if enough of the clergy got together and agreed that something was right, then it could be declared either infallible, or dogma, doctrine, or discipline. (I think maybe you taught me that. :) Anyway, I was just saying that because I have a different view of the authority of the Magisterium, that I thought that not only is any one man capable of error, but that also any one group of men is also capable of error.
The point is that majoritarian decisions have nothing to do with it either way. The Chruch has the promise of Christ that the gates of hell shall not prevail over it. There is also a promise to St. Peter from Christ, that He will protect Peter personally from error. Based on that, the Chruch believes that however her decisions are reached, by consensus, majority, or papal infallibility in absence of consensus, she is protected from error by the Holy Spirit. It is not a belief akin to what one might have about the American justice system, for example, that because of its juruducal constitutional structure, it is self correcting. It is a mystical belief in the promise of Christ.