Read the fine print. Its only good for 1 ticket:
During the week of July 20, 2009, the Baltimore Orioles will send eligible participants an e-mail containing a ticket redemption code which may be used online only. Limit one (1) redemption code per e-mail address. Redemption code will be valid for one (1) non-prime game ticket in Oriole Park Upper Reserve seat seating after the All-Star break, subject to availability. Free ticket offer not available at the box office, by phone, or by postal mail.
So if you go as a family either everyone in the family must vote 25 times (and have an email address) or you go by yourself!