It's taken 1511 several years to "refine" the design process and they are still working on it
What we have found works best is before you even THINK about robot design, sit down, discuss all of the rules, and discuss all possible strategies. We then sit down in small groups and select a small subset of the strategies, present them and the reasons why that was chosen. These choices are tallied (I agree Voting is dangerous) just to get a sense of if the team is on the same page. If there is a wide variance, then we discuss more, if there is pretty much solid agreement, we decide what strategy we will go on.
This is the important part: SELECT YOUR STRATEGY BEFORE YOUR ROBOT DESIGN.
Another Important part: Heavily weight what you are capable of. FIRST is all about trying new things and experimenting, but pick no more than 1 part of the robot that "you have zero experience with". For example this year if you picked treads and a pneumatic kicker, and have no experience at either, you are likely to have issues across both and a poor robot. If you pick a drivetrain you have experience/feel comfortable with and a pneumatic kicker, then you have more time and energy to focus on the one you don't know. You learn something new and are much more likely to come out with something good.
Once you have a strategy, you can go into mechanism brainstorming, from the mechanism brainstorming, you build robot designs. From the robot designs, you do pros & cons & weighted objectives tables. Hopefully from that the robot that best meets your strategy objective is obvious. And while this sounds like a lot, 1511 is done with all of this by Kickoff Sunday.
I have to admit, while we have used them, I caution somewhat against just using WOTs unless you are very experienced. The problem with them is that the "weight" ends up being biased if its not done correctly. If you do the "weights" immediately after your strategy, but before you come up with any robot designs, its likely to be less biased. If you do it after your robot designs, it is likely to bias towards whatever one the person creating the weights wants...
And we have also found that sometimes in the end, the team leader just has to make a decision and push the group forward on this. I have done this, and to be honest, I feared the result... I was somewhat afraid everyone would be mad at me, and I was also afraid of making the wrong decision. But the reason I did it was because I realized if everyone continued to argue they would all be mad at eachother and would not function well together, and it might take forever to "all agree" on a design. With me making the decision, we had a plan by the end of kickoff weekend and were into real design by Tuesday, giving the team the full 6 weeks for design, build, test, tweak. But its important that this is done by a person respected and recognized to have the knowledge necessary to make this decision.
Also remember, build season is SHORT, and honestly I have found people only argue when they are passionate about something, and while it doesnt feel "good" at the time... it means that you have a lot of people that care what the outcome is. So just reason it out, pick a strategy, and pick a design that best accomplishes that strategy... Good luck!