Based on what Theymos is saying, it seems most practical to attempt to finish nominations within a few days or a week at most, and thereafter create a thread to conduct a vote - maybe a 3-4 days voting period. Someone who is not running could probably run the vote.
Has someone started keeping a list of potential candidates? Can people nominate themselves or do you have to necessarily nominate someone else or both? Who gets to vote? Why?
In other words: Easier said than done.