It's obvious what would happen.
Although 'campaigning' was banned, every group (churches, schools, Rotary Clubs, unions, workplaces, etc) would find a way to 'suggest' a slate of 9 voters, and 'encourage' their members to vote for those nine.
So the biggest and best organized group would be the ones in charge.
How could you prevent campaigning? Hell, Elections Canada couldn't even prevent spreading the election results across the country before the blackout was over.
Then we'd need to encourage a culture that would be turned off by campaigning. If my neighbour comes to me one day asking me to vote for him, even if I was thinking of voting for him before, I change my mind. Of course we'd need to teach such an attitude in the education system I suppose. And no it wouldn't be perfect, but it would reduce campaigning considerably.
As for the biggest groups being in charge, that would be ONLY if they could develop considerable loyalty. Remember, the larger the number of voters in the organization, the larger the number of candidates.
To take an example, if you have, just for example here, twenty million caucasians and ten thousand First Nations, you might think caucasians are guaranteed a win if they stick together (assuming there was racially inspired voting, God forbid), but their vote cold be scattered among them too. First Nations might be smaller in number, which would mean not only fewer voters, but fewer candidates too, so if they decided, again God forbid, to vote racially, their vote would be less scattered. So the chances of any single group winning would be totally proportional.
Again, we'd have to create a new culture that shuns campaigning in the education system for this to work.
And besied, unions can hint at people voting NDP or whatever too, no?