When persuading groups, you don’t need unanimity or an overwhelming mandate to generate agreement; you need critical mass.
Consensus is something everyone can live with, not something everyone would die for. With that in mind, focus on the pragmatism of the numbers. That means that “being right” in your own mind isn’t sufficient. You may have all the facts and all the right conclusions, but that still doesn’t mean your idea will become reality in a group setting.
You must be cajoling and politically savvy. “Work” the system, just as you would “work” a room when you’re networking. You don’t want to meet everyone, just the people who can help you the most. (A politician wants to convince every voter to vote for him or her but is most interested in those voters who can deliver — through their own influence — thousands of additional votes. Hence, a union officer is more attractive to a politician than a union member.)
Groups are not sentient creatures as an entity, but they contain sentient creatures. The legal and marketing departments will have different views on your pitch than, say, the R&D and finance departments.
In other words, where others stand on an issue depends on the professional background they bring to the discussion and the impact a “yes” will have on their job, rank or career.
One of the weaknesses of group influence is that the task takes much longer because of such dynamics. You have to stay the course and, in some cases, outlast opponents who will eventually be transferred, promoted, retired, terminated, or otherwise obscured or overruled. Sometimes, no other way exists, so be prepared for a long-term persuasion arrangement in which you might need to create allies who recognize how they can prosper from your ideas.