There are a couple of ways to approach this one. Using the last contest as an example, only about 30% of bracket makers actually voted in this poll:
http://www.gamefaqs.com/poll/index.html?poll=4068
I didn't include the ones that voted for "Not yet, but I'll do it before the deadline", because not all of those voters would have filled out a bracket. So based on the total votes for the first 2 options in today's poll, we could be looking at around 15000 brackets.
Another way to think about this is to compare the total number of brackets from the last contest to the total number of battle picks for the first match. There were 19920 battle picks for the first match and 31314 total brackets. Then I found out this link is actually revealing the the total number of battle picks so far: http://www.gamefaqs.com/features/rivals_battle_stats.html
If you keep refreshing, it will switch between 13118, 13091, 13079, and 13020. So with 13118 battle picks, a proportion can be set up with the known data. 19920/31314 = 13118/?????
The missing number that goes in the "?????" spot would be 20621. Realistically, I probably expect between 15000 and 22000 brackets.
So for my guess, I'll go with...
18742
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Luster Soldier - Popular at school. ~Shield Bearer~ | ~Data Analyst~