Take two political extremists, one believes that taxation is theft, the other that property is theft. The difference could make Kamala and Donald seem like twins. Sortition is a way for either to become decision makers by chance. Whichever is more objectionable to you, could you really endorse a process that would put them in power, as opposed to a traditional election where the extremes tend to winnow out? That seems like a large increase in the risk of getting an extreme result.
Now take a representative body with 100 members. You get, say, five extremists on the left and seven on the right. The other 88 members basically leave those 12 extremists on the margins, and the extremists become irrelevant.
Now, if extremists (total of all flavors) exceed 50% of your population, you're in trouble. But you were probably in trouble in a democracy, too...
I think that's right. The point of sortition is for the body to look (statistically) like the wider public. The smaller the number of people in the body, the more likely it is that they are not representative.
I'm sure statisticians could give a better answer than I can about where the line should be. I think it is basically a statistical question.
But for a one-person executive? No, probably not a good idea.
