Win over everyone with opposing views, from a coworker to a packed conference room, when follow a few psychologically convincing steps. Stay true to your viewpoint, but remain receptive to new ideas. Individually win over opposers one by one if possible. Present new ideas and back them up with social proof of other times the ideas have worked. And, perhaps most importantly, stay likeable and reinforce that your viewpoint is in the best interests of the group.
Being the odd one out or the one with an opposing viewpoint can be nerve-wracking at first, but once you apply some simple psychological rules, you can easily win others over. Stay consistent in your viewpoint, without being stubborn. Don't wish-wash in your stance disagreement but do acknowledge and at least appear to consider new information when presented. Next make your move to persuade by dividing and conquering. Studies show we are more likely to stick to our guns when we have an ally. The best way to sway others who are against your viewpoint is one by one in order to diminish any sense of majority rule. Likeability is also key, and much more important than you may think. Staying friendly and specifically stating that your viewpoint is in the best interest of others (showing care, which is attractive) is essentially to getting your way. Finally, present new angles to a situation and back them up with social proof - giving examples of others who have taken your viewpoint and had success.