A small diaphragm condenser mic would be ideal for live mandolin given the instrument's range.
Edit: and just to add....I'd consider condensers in general, technically the most ideal, yet often the most overlooked acoustic instrument mic out there. Largely based on folks simply using what they've seen others use in the past. But...in the past, many folks avoided condensers unless absolutely neccesary (like for drum overheads) simply because of the added headaches and issues that used to come up with needing batteries, or an inline phantom power supply (per mic!!). Club owners and small/med sized PA companies simply resorted to the next best thing that didn't require added power, and typically had a mic case full of 57's and 58's. Today, every little $100 6-ch mixer has built in phantom power. It's no longer an issue, and in my honest opinion, condensers should probably be used in all acoustic stringed instrument applications. They definitely add that bit of sparkle, shimmer, and detail that a full range cardioid tends to flatten out. Plus they do a better job of picking up the instrument without getting in the way as they have a longer range field. A 57 needs to be right up on the instrument to hear it's full potential.