Test Writers, Test Preppers,

Lottery, Censors,

Lottery Cults, Electoral Parties,

Philosophers to advise the sorted and write and teach for the tests. nominated by schools, universities, political parties.

Tribunes to guard specific groups, rights,

Ambassadors from associating hives, strats, unions.

Commissioners to oversee departments trying to bring about specific programs.

..

Ministry of Rites—oversee the exams, foreign policy, state religion,

https://www.reddit.com/r/Sortition/s/lEgHhzhAMr

This is why I am in favour of a 2 house system where 1 house of government is chosen through democracy and 1 house is chosen by sortition. The democratic house would write the legislation and the sortition house would then approve or deny the bills, acting as a check on the power of the democratic house.

How does this solve your problems:

1. They don't need the competency to write the laws they just need to be able to understand the bill after it is written and then they would receive arguments from the democratic house for and against a bill. In the same way the jury in a court does not need to understand the intricacies of the law, they just need to listen to the lawyers and make a final decision. (This also gives a bonus in that the democratic house needs to write laws that are understandable to the intelligence of the common person).

2. This system provides accountability to the politicians who are elected. In theory, politicians are accountable to their electorate but in practice, as we see all around the world this isn't often the case. The sortition house provides accountability to the democratic house.

3. The legitimacy comes from the laws of probability, assuming the house of sortition has enough members we can assume that society is equally represented. It won't be perfect but it will be far more representative than the current democratic systems that can be influenced by the electorate's biases which are in turn influenced by corporations, media and the political parties. Furthermore, legitimacy comes from the fact both houses can block each other, keeping each other in check.

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I have a different take, but similar to your two house solution.

The upper house will comprise of experts (PhD and masters holders) from various disciplines, or people who took the test for the position and scored really high on it, they will be selected by sortition. The upper house reserves the right to pass legislation and make executive directives. These allows for a more technocratic government.

The lower house will comprise of randomly selected citizens that are representative of the general population, they will serve as an advisory board. But have the power to dissolve the upper house if they come to a super majority consensus that the upper house has failed in its responsibility.

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a technocracy like that would favor those political groups who could afford the best education as well as those writing the tests.

essentially government by SAT score.

that could actually be a very interesting dystopia to write, but I don't think I would want to live there.