You want to organize your group to do something. There's 15 people in this group - each with equal voting power. Three of them are loud big talkers who sound utterly confident in their ideas except the ideas they have are very bad. The rest of the group seem to be ready to choose them to lead.
Your a quiet talker who likes verifying an idea to see if there's a chance it will work. Nobody is paying attention to you and the three loud talkers are always interrupting you.
Most of the other members of the group are just those who'll follow whoever is in charge but they get to choose who is in charge.
What do you do?
If you want to be the #1 then as soon as they mention a bad idea, immediately suggest reasons why & if you can't think of a bad reason, select the weakest point of the idea and heavily focus on it.
Once you have done this, they will probably try and act smart and say "what's your big idea then?" then you have your time to convince everyone & as soon as any of the 'loud talkers' interrupt, don't let them by speaking louder and keep going they'll shut up and as soon as they do, rework parts of what you said whilst they were speaking gibberish back into your speech by saying "as I mentioned earlier but was interrupted by person X, Y and Z alongside..." and carry on speaking.
Seriously, you can either sit in a corner or you can come out fighting so to speak, assert your authority and take the top spot.