1) Pick people for congress the way we pick juries. Sure, we'd have a number of dunces in the bunch. But without motivation for corruption, I trust the general honesty and character of the average American more than members of Congress.
2) Copy the legislature of New Hampshire, which has a huge number of members, and increase the number of Congress members by an order of magnitude, or more. The reason is that members would be elected from very small areas, where it's almost guaranteed you will personally know your Congressman. It would be much harder for interest groups to use influence, because they would have to influence so many people. Lobbying would become more like spam, and ignored by members. Any corruption big enough to work, would have so many co-conspirators as to be guaranteed to be exposed.
Sure, we'd have a number of dunces in the bunch.
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Very likely that there would be fewer!