Here is my idea. Assuming that: 1) we still want democracy (not despotism or authoritarianism), 2) Arrow impossibility condition exists, 3) Plato's philosopher Republic is simply not attainable, then we may want to consider, I am proposing two possible alternatives:
- Random assignment. A lottery is assign to (s)elect leaders or representatives. All eligible citizen will have equal probability to be leaders or representatives.
- Take turns. Just like (1), but do a random assignment only once in the beginning. Then design a mechanism where each will take turn every a certain period. (Oh wait, who will have the authority to design the system?)