A-Style mandolin players are forced to make a tough decision in regards to how they put a strap on their mandolin. F-Style players have the ability to loop the strap around the scroll, which works quite well. A-Style players are basically left with 3 options...
Looping the strap around the body, beneath the fretboard extension.
This works, though it presents a few issues. First, it is not the most attractive option. Second, it places the strap along the top of the body, which will in time wear through the finish.
Using a loop on the headstock, between the tuning pegs.
You will find many players who use this method and it works well for them. One consideration is that it can tend to get in the way of your left hand. Another is that it feels a bit imbalanced, especially for players accustomed to the feel of looping the strap around the scroll of an F-style mandolin. The mandolin can't move as freely as you may like, although this could be a plus for some players.
The Strap Button
This is perhaps the best option, so long as you are willing to have a hole drilled into the heel of your instrument. Collings mandolins utilize a mortise and tenon joint for attaching the neck, so you don't have bolts to worry about like on acoustic guitars. It does, however, need to be very carefully drilled and the placement is very critical so that it doesn't hinder access to the higher frets. Kym Warner and Tim O'Brien both have strap buttons on their A model mandolins.