Our president may call special or emergency meetings. We haven't detailed whether or not we could hold "electronic" meetings or votes, but we have done it informally.
If it is a true emergency and the group cannot get together quickly to discuss it, then I would say it would be acceptable. I agree with Venzmama, though - that the email be sent to the group and each of you respond by "reply all" so that you can each see every response.
If it is becoming more the rule rather than the exception perhaps at your next board meeting you could suggest amending your bylaws to include a provision for this.
All votes and the voting party would be listed and sent to all. That way, everyone could confirm their vote AND other's votes. It doesn't sound like you trust your president, though, so I don't know that it would work for your group.
Help! Our president keeps forcing executive board votes over e-mail. The reason she cites is that "time is of the essence" and she needs an answer now. If you do not get back to her as quickly as she thinks you should (she gives no time frame) I think it is recorded as an abstention. She is the only one who receives the votes, and then decides if there is any more discussion needed although no one else on the board has participated in any type. If she feels like sharing the results of the vote she might, but it hardly ever happens.
This does not seem kosher to me. We have no discussion, no dissention, and no tracking of the vote, and any information we receive is filtered through her. THe last vote she held, I wrote that it should wait for our executive meeting which was two days away, and she refused and marked my reply as a vote. What do you think?