This is a concept that I've been playing with as a thought experiment for a while now. It emerges out of my frustrations with party politics in Canada, and the way that our elected representatives now put party ahead of constituents, ideology and political "points scoring" ahead of governance and statecraft.
Fundamentally, I'm starting from the assertion that democracy in Canada is broken. The rot is clearest here in Alberta where things have degenerated to a single party state with 22% of the eligible voters determining over 80% of the seats in the legislature. The politics of divisiveness and mendacity being played by the HarperCon$ are steadily pushing the rest of the country the same direction.
The concept of "random democracy" is simple - put responsibility for government back in the hands of the citizens in the most direct and absolute way possible. In this case, we change things from having a slate of candidates put forward by the various political parties to a process where prospective MP names are selected randomly from the electoral rolls. In other words, we make being an MP a responsibility that all citizens are subject to - in a manner similar to how jury selection works today.
Since the majority of citizens are non-partisan today anyhow, this will return political parties to what they should be in the first place - advocacy and lobbying organizations with their hands removed from the direct levers of power.
Looking a step beyond this, and into the process of creating an executive from these MPs, we must rely on the fundamental principle that an MP is sent to serve in parliament to form a meaningful government. The easy solution to this is to form small committees for each area of government ministry from the elected MPs. These committees are formed from the pool of MPs in a similar random fashion to what was used for selecting the MP in the first place. The committee then selects its "chair" for the next year or 18 months who will act as the "Minister" for that committee's area of responsibility. Committees will be broken up and reshuffled every 2 1/2 years - this will avoid any one committee becoming someone's personal fiefdom.
The Prime Minister would also be selected at random as well - for a term no longer than half the duration of the parliament.
Serving as an MP is an obligation on the part of the individual, but on behalf of the greater good. So, in such a circumstance, the MPs should be adequately remunerated during their time in office. As such, like with Jury duty, employers would have to guarantee that the individual selected to serve as an MP must be able to return to their jobs at the end of their term without penalization of any sort.
This does several things that I think are desperately needed in Canada's democracy now:
(1) It breaks the stranglehold power that political parties have over the situation.
(2) It obliges MPs to in fact gather feedback from the citizenry.