One great way around this is to alternate rounds of sortition with rounds of election: - You pick 1000 random people to serve as the House of Representatives.

One great way around this is to alternate rounds of sortition with rounds of election: - You pick 1000 random people to serve as the House of Representatives. - They elect 100 people from among themselves to serve as the Senate. - You randomly divide them into 10 person committees. If you have enough rounds, there are some great effects: - The election means that only competent or representative people make it through to the next round. - The sortition makes it so that no one individual or small group is likely to make it all the way to the top.