Taminad
I have four salient features of the TDG the early builders have to design their local TDG around. One of those features is "voting for good character and capacity for governance."
So at this point, I can't see how voting by lottery works with this salient feature. But maybe there will be some inventive early TDG builders.
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There will be more people involved in governance with the TDG. In my book, I have created a fictitious city of 100,000 people. I estimated that about 650 citizens will serving in government.
Most of these representatives will be at the lower level. They will be mostly volunteers, serving about 20 hours a month. If they are good at the low level, they might rise to the higher levels.
Some will serve in the TDG for many years. Some will just get one or two years and then the TDG will elect someone else.
Many more people will get some life experience in the TDG. Our current democratic structures do not provide this opportunity. In this manner, the TDG may have a bit of lottery as you have imagined.