"sortition based deliberative democracy" - I'm not certain how exactly such a system should be called in English. I mean a political system in which instead of making a general election or referendum, one selects a random group of citizens, then provides them with detailed data about some issue, lets them think and talk about it and at the end gets their opinion, which reflects the average persons views, but also is done by well informed people. Seems that on wikipedia the closest idea is: https://en.wikipedia.org/wiki/Deliberative_opinion_poll
Nevertheless, such an idea sounds quite nice. But there is a matter of legitimacy of the system. Let's say 80% of population supports idea A, while 20% B. After selecting random citizens, giving them data from experts, long discussion, drinking coffee, they mostly changed their mind and the result is 30% A and 70% B, which by rules make the country choose B.
Quite possibly the selected decision is reasonable. Nevertheless, what message was sent to public opinion? (If you had read more about the issue you'd change your views?)
Already in a standard representative democracy, there are people puzzled how on Earth it is possible that someone wins, who had opposite views to them and most of their acquaints. Not mentioning that for example in the US it became a politically controversial issue how many people were on the photo of the presidential inauguration. (Sorry Americans for choosing an example from your country, but embarrassing stuff from my country is luckily not so well publicized in world media).
Then in such a sortition based deliberative democracy there are even more issues where the system can be slightly manipulated, or even worse, just look like such.
Sample selection (I'm not asking how to do it correctly from statistical perspective, but how to do it in a convincing way)
Expert selection (mainstream scientist? Both sides? Or maybe there are quite a few sides? Or maybe there is realistically quite clear scientific consensus, and the real debate should be about technically dealing with the issue)
Setting selection, etc.
Secrecy or total publicity? (Problem of people being afraid of making themselves idiots in front of milion people and problem of being afraid of revenge or expecting reward for openly voting in one way or another. (including just being ostracized by your own community))
OK, so how can I make such a system look legitimate? I mean a system in which an average person prefers option A, was selected option B, still may have doubts whether B is really such a good choice, nevertheless grudgingly accepts that everything was being done correctly and that there is no vast conspiracy?