Statisticians or electoral process specialists - question on polling

[Arnold Winkelried]

I am planning on opening a poll to vote on the proposed smilies (see thread in ATMB for more details.) The vBulletin polling process allows 10 choices. We have 50 submissions. I plan on having 5 polls with ten smilies each, and the top 10 from those 5 polls will form the final poll.
My options are: pick the top two from each of the five polls, or pick the 10 most-voted-for smilies.
Example:
Poll 1: Smiley 1A gets 40 votes, Smiley 1D gets 30 votes, Smiley 1G gets 20 votes, etc...
Poll 2: Smiley 2J gets 15 votes, Smiley 2H gets 10 votes, Smiley 2E gets 5 votes, etc...
Poll 3: Smiley 3F gets 30 votes, Smiley 3C gets 29 votes, Smiley 3B gets 25 votes, etc...


If I pick the top two from each poll, I would have 1A, 1D, 2J, 2H, 3F, 3C as finalists.
If I pick the top vote-getters (and assuming I limit the number of finalists to 6), the finalists would be 1A, 1D, 3F, 3C, 3B, 1G.
Which is the "correct" method? In poll 2, 2J was the winner, but less people voted in poll 2. If I have 5 polls, people might start voting in polls 1 and 2, but then get bored and skips polls 3, 4, 5 (for example.) Does this mean that the winner of poll 5 should be skipped, and instead I should include the smiley in third or fourth position in poll 1, if that smiley has more votes than the top vote-getter in poll 5?