If anyone wants to become a moderator, he/she can tender their application then Theymos can access them by also looking at the reports they made to moderators because i learnt that if you make good reports to moderators, you can have a high chance of becoming one in the future so the administrator cannot just make appointments, what if he appoints someone and the person isn't willing to take the job despite that a payment is attached to it? As for approving a moderator via a voting process, it doesn't make any sense because just like you said, it will become bias, political and probably someone that is incompetent might be voted in.
True,
But as a corollary, it wouldn't even be necessary for anyone to apply as a moderator, as Theymos already has a pretty clear idea of the situation. Knowing how much each user cares about the board and has sufficient time, technical capabilities, and commitment to be a moderator.
I may be wrong but the approval of moderators in the past was done automatically by Theymos after assessing the level of commitment of a user in a particular board but in recent times, i found out that before a moderator can be assigned to a particular board they are being assessed through their commitments in making valid reports, and probably get backings from users who frequent on that particular board before Theymos will grant them as staffs of the forum.