You could defer decisions involving sensitive information to the top N delegates (i.e. those with the most voting power.) They'd be a sort of ad-hoc congress.
You may face problems with those delegates still leaking sensitive information, but then again, Congressional staff is already notorious for doing that both willfully and accidentally.
Not necessarily. The composition of this "congress" might vary depending on the topic under discussion. The group trusted on "trade with china" might differ from that trusted on "military action in Syria". And entry is derived from trust networks theoretically involving all people, not some electoral process where only career politicians are realistically candidates.
But it does mean I can't decide to delegate it to my friend who knows a lot about the trade situation with China. All the power would become consolidated in a few people again, and giving your vote to anybody else would be a waste of it unless they pass it on to one of those. Sure, the group could be different for each issue, but in practice it won't be. You'll need to campaign long and hard to be in that top N, and try to get a lot of people to trust you. That leads right back to career politicians and popularity contests.
You may face problems with those delegates still leaking sensitive information, but then again, Congressional staff is already notorious for doing that both willfully and accidentally.