Voting & Alliances
 

I know this is a VERY late answer, but if you happen by here someday wondering if anyone ever replied to you (or if you're someone else looking for an answer to the question)...

Yes, senate votes are secret; I don't know if they make a difference, if the AI uses some intelligence to infer that it was probably your vote that put them in office or not (I suspect not). Papal votes are open, though, so the AI would see those.

I've offered pacts to the AI many times, but only once or twice did I get someone accepting it. I don't know just what does it; all I can figure is to try to be harmless, at least toward them: don't get their senators hung, don't assassinate their people, and certainly don't burn their warehouses. Also don't attack their caravans. As I recall I had sent the AI a bunch of money before trying the pact, so that probably has a lot to do with it.

I don't know about announcing your candidacy for Pope or Doge. I would assume the AI checks each computer player's opinion of you and votes accordingly (likely with a random factor added), but I don't know for sure.