The technical term is sortition. And it is my pet unorthodox political position. The legislature should be replaced with an assembly of citizens picked by lottery.
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From a practical point of view the selection process is a bit of a red herring though. The current controls break down because the feedback loop is simply way too long to meaningfully affect the process.
While I personally subscribe to the idea that sortition is a superior way of electing representatives I don't see people considering it seriously. However what everyone can understand is using the same process but with sampling with a higher frequency.