There are many times that you will need to get buy in for an idea, project, analysis, paper, presentation, etc. I have found that it is hard to get total consensus in a meeting when participants are coming in cold. It is important to give your colleagues a chance for a dialogue with you, a give and take so you can understand their position and they can ask you questions about yours. However this doesn’t usually unfold the way you scripted it in your head. So for critical decisions when multiple people are involved, I have found it very helpful to do one off prep meetings in person with those you need buy in from before the key decision meeting. It will take more time this way but think of this time as an investment in the outcome you are looking for, a way to improve your odds of gaining consensus in your round table meeting, which I would say is time well spent.