Robot Design: If there isn't a vote, who makes the decisions?

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Trade studies!!
Always use tools like the weighted design matrix (or figure of merit) to justify the designs. If there's not a clear winner out of this method, you can always add more parameters or, if you have the resources, build both systems and make it modular.
Last year my team made 2 completely different variations of a climber, and we kept it relatively modular so it can be swapped out. It turned out we used one design in the first regional, the other in the second, and tossed both out in favor of a 3rd for championship. That's how these things go, but it should never just come down to a popularity contest.