I am a mathematician. I enjoy solving puzzles, chatting with others, and making art (poorly).
When I judge rounds, I will assume the burden of proof is split evenly, unless explicitly stated otherwise in R1. The winner is the one who makes the most compelling arguments, regardless of how I feel about the topic or how "silly" the topic is. I don't vote on semantics unless the semantic argument is compelling. This largely applies to the case when someone accepts a debate with the clear intent of debating something other than what was intended by the issuer of the debate.
I will not vote on topics that I don't understand well enough to make a sound judgement on the quality of each debater's arguments. And while my judging style above does not necessitate clash, I do very, very much prefer to see it.