Yes, it's a very good idea, although also obvious enough that I wouldn't pin your ego on claiming it as your own. I don't know how far back the idea's history goes, but I've discussed it before. People usually dismiss it as impractical for political reasons - politicians will never vote to implement a system for tracking the performance of politicians, because they know they aren't expert decision-makers. (I suspect many of them would say that the important point is not to predict what will happen, but to have the moral compass to say what should happen.)

IMHO, getting our governments to move in this direction is of an importance on a par with thinking how to avoid making AIs that go berserk. Our existing forms of government are not competent enough to handle the power they will soon have. Evaluating track records is the only way I know to improve the quality of decision-making.

Comments on the math:

Don't assume that each agent is correct more than half the time. As I showed in my simulation, things are easily tractable when agents are correct more than half the time. Agents may be right more than half the time on problems in their life in general, but the problems that are controversial enough to come up in Congress are ones where overall we have closer to random performance.

The scheme you have proposed results in choosing the worst of two options when the correct choice is obvious. That's because if you have 100 voters, and 99 of them choose option A while 1 who is an idiot and is right half the time chooses option B, the values of (1 - c_i) for the 99 voters, multiplied together, will be less than 1/2.

Upvoted, because this is important and you're trying to formalize it.