[munin]

What if you accept applications for 30 days, then write the name of each applicant on a card, put the cards into a deck, shuffle the deck, then draw cards off the top of the deck and make offers until you run out of open positions?

It isn't merit based, but it's hard to argue that it favors one candidate over another! And maybe it's mimicking the effectiveness of your current system!

[sraf]

This has the added benefit that you only hire lucky people. Noone wants to hire an unlucky person.

[grue2]

This has a certain genius to it. The same genius as sleep sort.