This wasn't an example of blind voting. These Aes Sedai have been fighting the Black Ajah together. They are comrades at arms so to speak -- like troops in a platoon. They stepped into a meeting to which they weren't invited, and they saw their ally standing for a motion. They would trust her with their life, so why not for this vote, when her comments indicated clearly that, in her opinion, they should stand?

If I showed up to a tense situation and one of my closest friends, who I trust implicitly, advised me to do something, I would do it without question. Blind voting implies that they didn't know at all what they were voting for. That's not the case. Rather, they were voting along with their ally. They had every reason to be confident that, if they knew all of the facts, they would stand too. They didn't need to waste time learning of them.

Moreover, by voting in this way, they made it clear to everyone that they were a team, supporting Egwene. It was funny and powerful at the same time. Not random or stupid. A great moment.