Hopefully(!) you'll be working with people who are intelligent, rational and willing to consider well reasoned arguments. Therefore, you should think carefully about /why/ you believe your approach is the best one, and come up with a persuasive, well reasoned and well supported argument expressing the reason or reasons. Then it is up to them to either find fault with your argument, to accept that you are right, or to block-headedly refuse to budge from their own view despite facing a convincing argument.
Obviously this is a simplification, as real people are far more complex, and a significant degree of diplomacy is vital (this is where being friends with your co-workers helps tremendously, as you can gauge much more easily how they will react in any kind of workplace confrontation).
It is also important to ask them to explain why they hold the views they do - ask them what they think are the benefits of their approach, try to understand as fully as possible their reasoning. Not only is this important for making sure that as a group you do make an informed and intelligent decision, but it also makes it clear that you are not trying to simply impose your will, but you are interested in assessing the merits of each idea, and that you want to consider carefully your colleagues' ideas.
I have to say though, the fact that you referred to it as "a battle of wills and who is most willing to concede first" is a little worrying. Surely as a consultant everything I've mentioned above should be pretty essential 'tools of the trade'?
