Firstly I must make it clear that I think the fortnightly challenge is a great idea and I wholeheartedly support it. It is the idea of voting for the next topic that I am questioning.
If we are exhaustively working our way through the tags as seems to be the case, we could choose the next in any order. For example alphabetically.
If we choose them by popularity then as we proceed, the remaining topics will become less and less popular until we are left with the 'dregs'.
If we really want to choose tags in popularity order, there is a very simple way. The popular tags page already arranges them in order of popularity - as chosen by the whole community.
Repeated voting means that people whose vote fails once simply have to keep voting until it succeeds. It would be simpler to have a one-off vote and proceed in order of votes. Then do the same again when the first list has been exhausted.
So that all tags get a turn, we could simply choose them in alphabetical order.
If popularity is the method, then do away with the vote and choose them from the sorted list that is already available.
If we want to encourage use of little-used tags then start at the end of the current sorted list.
What is the actual intended purpose of repeated voting?
Is it the most efficient means of achieving that purpose?