I'd love to simply write my thoughts on "deliberative democracy," but several others have written better explanations of it than I could hope to write, so it's best to lead you to them first. Blogonomicon, The Foundation for Economic Education, and The Liberty Sphere all have some good reading on the subject.
I'll still give you my thoughts on the subject, of course.
This is the ultimate expression of collectivism ruled by an elitist group. After all, the thought is that all people contribute to the debate, not the decision. Even if the people make the decision, we face tyranny by majority, but the fact that there's no vote-counting allows the ruling elite a lot of power. After all, if you've had the chance to speak, you feel you've been listened to. If the outcome doesn't match your choice, you probably guess that others made stronger points. In reality, of course, the lawmakers decided what they'd do long before anyone said a word.
A lot of psychologists simply listen to people spew their thoughts and opinions, which is really all the person wanted. Deliberative democracy hinges on a similar principle. Once you've given your opinion, as long as you feel you've had your time, you feel better about the outcome, even if it's completely opposite what you wanted. You contributed, or at least think you did, and that counts for something, at least psychologically.
The biggest inherent danger, of course, is the "hive mind." Once everyone has contributed, the outcome must be the best choice, right? So you start to see it as such. Pretty soon, everyone is certain that government choices are always best. This leads to a lack of intellectual debate, as well as an inherent trust in an inherently untrustworthy group of people.
Of course, to the Left, the idea of such collectivism looks great. They believe it will placate the public, which is their goal. If they can keep us placated, they can control us. If they can control us, they think it'll improve us. It's not an improvement, even if it does work. And it doesn't. There'll always be wolves to prey on the sheep you've made comfortable. And there'll always be a few independent thinkers the government will have to "quiet."
I'll stick with a constitutional republic. It's a lot better for those of us who may not want to assimilate ourselves into the hive mind.