Thank you for posting what I have been thinking of posting for weeks but have not for fear of being downvoted into oblivion (seriously).  This would be a culture shift, but I have thought about this for some time, trying to make a strong case for it, and here is how I would suggest it should work:

As a trial, and since feature requests seem the most prone to problems, this is for feature requests.  (Maybe it need only ever be for feature requests, but having different voting methods for different question types would certainly be confusing.)

A good starting point would be to start phrasing questions *as questions*, to exercise the normal SE instinct people have.  That is, only down questions if they show no research effort, are unclear, or are not useful.  A feature request could be presented as a question outlining the problem *and* an answer with the actual feature request in it.  The question could be of the form "What can we do to deal with [perceived problem]?" (or just "Dealing with [perceived problem]?")

 - An advantage of this is that *other* feature requests that would same the *same* problem in the question.  Alternate solutions to the problems inherent in feature requests are not captured especially efficiently in the present system.
 - Another advantage of this is that the questioner would have to think a little harder about *what* exactly the underlying problem is.  This should cut down on proposals with little backing them up, but the main advantage would probably be the first one again:  generating a wider array of possible solutions.
 - Of course, we would probably chase away fewer new users of Meta (and have to deal with less complaining and explaining that "voting is different") due to perception of established Meta users be mean.  Voting need not be different.
 - What I would consider the **main advantage** of the new system would be *adding information*.  We could distinguish between voting on *the problem* and *the proposed solution*.  It seems to happen very often that good problems get dragged down by poor proposed solutions, when really those problems should be addressed.

Downvoting could be made free, by the way, for answers, in order to keep those free-flowing.

For some problems that really only admit of one solution (true single feature requests), it might look strange to fit it into the mold I am talking about, but I think it would be worth it.