Imagine a country where the people are so slow that a 1990 science poll found that half the adults weren't sure whether the sun revolved around the earth or the earth revolved around the sun. Now imagine that this same country has a system of government that not only bases its policies on the things that those people say, but subtly encourages them to remain ignorant about important policy issues.
Surprise! It's Canada!
That's right. Think of it: our government, in its wisdom, hires a polling firm to find out what we think of (say) global warming. Joe Blo knows all the stats of his favorite sports team, but can't tell the difference between a methane molecule and a giraffe. The polling firm relates Joe's opinions back to the appropriate government minister, and then that minister thinks up some suitably lame policy based on it. No wonder our various Liberal and Conservative governments are only now starting to get serious about the issue.
Now imagine a country where the main media outlets occasionally collaborate to gather a random sampling of its citizens to a central location to discuss a policy issue in depth. We're not talking about a two hour focus group session; we're talking about hundreds of citizens looking at all the ins and outs of a particular issue for a whole week. They have access to "balanced" briefing materials and are allowed to question competing experts.
Prior to the whole exercise, a normal poll is taken, and then at the end another normal poll is taken. And (surprise, surprise) the result changes significantly.
(By the way, the country is Britain, and the media outlets are the BBC and the newspaper, The Independent.)
The exercise is called a "deliberative poll".
A Harvard website (one of the links listed below) describes the drawbacks of the current system:
"[status quo] opinion polls, which measure the snap judgments of an often inattentive and ill-informed public."
As well:
"Deliberative Polling seeks to create a social environment in which ordinary citizens will be motivated to overcome the tendency toward rational ignorance (the notion that because a single individual’s opinion is unlikely to cast much influence on political decisions it is entirely reasonable to spend little time and effort becoming informed)."
I think the major cause of society's problems can be blamed on sheer ignorance. Thus, anything which promotes deliberation and dialogue--and which can help to translate the results of such dialogue into policy--can only be positive. Of course, the final decisions will always rest with our elected representatives, but at least they won't be pandering to the lowest common denominator of opinion polls based on the output of a nation of couch potatoes.

And, of course, the other great benefit is that the general public will become a lot less apathetic and cynical about the whole political process. They will see that their input is being taken seriously, so they'll naturally start to take the output (ie, government policies) seriously.
A deliberative poll is only a small subset of Deliberative Democracy. A deliberative democracy is one in which dialogue by the citizenry on important issue is seen as a vital element in policy formation. This can range from a simple deliberative poll to an elaborate Citizen's Assembly (see the B.C. and Ontario example below).
Deliberative Democracy will also introduce a general change in the culture of politics. If people from all backgrounds can gather together in a deliberative poll and calmly discuss important issues, it's conceivable that our leaders may eventually copy the example. And then Question Period in the House of Commons will no longer be an embarrassment to watch.
It must also be emphasized that Deliberative Democracy is a very effective tool in promoting community cohesion. And we will need every bit of community cohesion we can muster in the difficult times ahead.