I've tried to learn how to deal with "Jeffs" over the last couple of years. It's something I've struggled with, but I think I've found a solution this year; the good part is it's a solution to a bunch of other (potential) problems as well:
This year is the first that the team I'm working with has attempted to implement some type of engineering design process. While this has succeeded to varying degrees, it's still a success to me because we're infinitely better than last year. One of the critical aspects to this has been enforcing a fact-based approach to design analysis. We still discuss the various ideas, and people are free to express their opinions, but when it comes down to making decisions, we're trying to stick to rational arguments. If someone says they think that one design is better than the others, the immediate next question is "why did you come to that conclusion?" The response to this should be something of the form "when we prototyped this grasping mechanism, we found that it was more effective at grabbing innertubes while the robot is moving than any of the other designs we've tried." Part of this process is first generating a list of criteria that everyone agrees on, and then ranking them, as this gives a concrete to decide which one is really "the best," instead of just trying to impose one person's subjective opinion on the rest of the team. For a good methodology with this, you can check out JVN's
Weighted Objective Table paper. I tried to use the formal table with my team, and found it to be a bit constraining, just because of the learning styles of the students that are on my team, but it provides a nice example of what I'm talking about.
Find a process that works for your team, but I would suggest that the ultimate solution to someone with a baseless argument is use irrefutable facts.