Sure, have a "yes/no": check box, but after it, a text box where the voter gives their reasoning behind their vote. No reasoning, then the vote can be appropriately weighted. A whole bunch of votes with identical boilerplate "reasoning" pasted in, also weighted appropriately.
This proposal seems sort of OK ... he's not constrained to vote whatever way the internet polling goes. I'm very much against internet voting for real votes, though -- unless some scheme can be devised to guarantee the secret ballot. It is absolutely essential that a person is not only able to cast a vote where no one can tell how he voted -- it *must* be impossible for anyone to prove to a third party how he voted to prevent vote buying/extortion schemes. Absentee ballots are a violation of this, but probably necessary. I'd sure like to see their use restricted to people who are actually absent, or have mobility issues with getting to a polling place.
Perhaps some way a person can change their vote later, up to the deadline? There should be a way with one-way hashes and encryption to make that possible, while not making it possible for anyone on the inside to determine how they voted, either time.