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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Now, the idea of electing a few thousand representatives and having sortition determine who is actually selected is something I could feasibly get behind.
- A randomly selected lower house with an elected upper house (or the reverse)
- policy juries which deliberate only on one specific piece of legislation, which then must be approved by a separate oversight jury before taking effect
- election by jury, where candidates are chosen by "elector juries" who interview and vet the candidates before selecting one
- multi-layer representative selection based on the Venetian model where randomly selected bodies elect representatives, of whom a random subset are chosen to then appoint officials
Right now the lottocratic/sortition-based bodies that exist are purely advisory, though in some places like Paris and Belgium they have gained a good amount of soft power.
It wouldn't be that hard to implement a conservative version of one of these in certain US states though. For example, add "elect by jury" to the ballot, where if it wins the plurality, a grand jury is convened to select the winner (counties in Georgia already use grand juries to appoint their boards of equalization, so there is precedent).