Though I would just directly fill up parliament with a few hundred MPs picked at random from among volunteers.
Parliament can then make laws and pick leaders for the executive (like in Germany or the UK).
As a slight complication, I would allow people to pre-declare proxies that would sit in parliament for them. Proxy declaration season would be akin to traditional election season.
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In the UK or Germany, this way you could keep most of the existing political architecture intact. You'd just change how MPs get selected. Compared to your proposal, you also get the benefit of the law of large numbers, and you don't have to have a judge etc.
I would argue against picking a singular leader at random, just because the variation is too high. But in the US, you could re-use much of the existing system: fill up the electoral college at random.
Though I would just directly fill up parliament with a few hundred MPs picked at random from among volunteers.
Parliament can then make laws and pick leaders for the executive (like in Germany or the UK).
As a slight complication, I would allow people to pre-declare proxies that would sit in parliament for them. Proxy declaration season would be akin to traditional election season.
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In the UK or Germany, this way you could keep most of the existing political architecture intact. You'd just change how MPs get selected. Compared to your proposal, you also get the benefit of the law of large numbers, and you don't have to have a judge etc.
I would argue against picking a singular leader at random, just because the variation is too high. But in the US, you could re-use much of the existing system: fill up the electoral college at random.
You could take inspiration from the 'National Popular Vote Interstate Compact' https://en.wikipedia.org/wiki/National_Popular_Vote_Intersta... for how to accomplish that gradually.
The US house of representatives and senate probably have enough members that you could bank on the law of large numbers.