Quoting relevant pieces from the OP's question, emphasis mine:

> All I'm attempting to say is that with the right infrastructure, subjective questions do have a useful place in the exchange of ideas. In a way, such a site would be similar to Wikipedia; but it's content would be *organized by popular vote*.
>
> I know this is no little task, but is there value in doing so? I think there is. *Nothing is going to prevent people from asking ill-formed questions. Wouldn't it be nice to somehow accommodate these in an intelligent manner?* In this way both objective and subjective questions would have their own place. And people that like Stack Exchange the way it is would actually benefit. Lots of flagged-and-closed questions remain on this site. Such questions could be migrated to the sister site so that only the purely objective ones remained here.

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Responding to individual points:

> [Stack Exchange subjective] content would be *organized by popular vote*.

I think Grace Note did a good job explaining the issues with handling subjective questions on Stack Exchange in [this Arqade Meta post](http://meta.gaming.stackexchange.com/questions/997/handling-game-recommendations-how-can-we-solve-these-two-problems-of-quality); see the discussion about Repositories.

The problem with voting for subjective answers is that not everyone has the same criteria for the object being discussed... that's why these discussions are subjective.  For instance, Q: "What graphical design program should I use?"... 

Do I have to mention all the possible answers and religious battles about Gimp vs Adobe Illustrator vs Inkscape vs Visio...  The problem of course is that the question was bad, and voting for answers to bad questions often has questionable value... What do the votes really mean other than *"I like this software for what I think the (extremely vague) question intended"*.

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> I know this is no little task, but is there value in doing so? I think there is. Nothing is going to prevent people from asking ill-formed questions. Wouldn't it be nice to somehow accommodate these in an intelligent manner?

[Chat](http://chat.stackexchange.com/) is not a bad way to handle subjective discussions on Stack Exhchange.  If someone asks a subjective question, close it and point them to chat (assuming they have 20 points on the site).

It's not a perfect solution, and it doesn't have answer votes; however, I don't really think voting helps subjective questions.