I could start a power down with account @david on Sunday, make a post on Tuesday, upvote it on Wednesday, get my SP liquidated to Steem on Sunday. Power up the Steem to @goliath, vote on second Monday. The payout happens on second Tuesday, with effectively two votes for the same SP holding.
That said, this could be probably be prevented by disabling voting for the stake powering down. So if you power down 75% of your SP holding, it'll all be liquidated in one week, but for that week you would only be voting with the remaining 25% of your SP.
The idea of disabling voting on powering down stake was previously brought up, but the problem is due to the long drawn schedule it never made sense. However, if someone wants to liquidate their SP holding anyway, I don't think anyone would mind not voting for 1 week.
[Edit - snowflake has a better solution. Just do away with Steem Power, and let Steem be votable after 7 days held in an account]
Doesn't the SP delegation feature have something similar, the reverse way? I.e. when a delegation is canceled, it'll be one week before the delegator can vote again.
I'd definitely like to see this implemented. A 1 week power down period sounds much better.
Check my answer to smooth above. A system where steem power is removed and where only the steem that has been in an account for 1 week can upvote would also solve the problem you mentionned.