Appointment by lottery? Candidates would still either have to put themselves forward or be nominated, but a lottery will make it harder to rig the process, since there is only a percentage chance of being successful, rather than this being potentially guaranteed.

I actually think including randomness in many of our decision making processes will reduce corruption, as this is a limit as to how effective corruption could be - it will be capped by the random selection process. Of course, the random selection itself could be corrupted, but it is relatively easy make this transparent enough that it cannot be corrupted easily.