The problem with picking slip-jigs on the mandolin comes from the fact that your hand needs to be picking on alternate down and up strokes (to keep the tune going fast enough), while the timing of the tune requires notes to be played in threes. Each bar of the music can be represented by the phrase "diddley, diddley, diddley" (hence the pejorative term for some of this music?) The emphasis is not as represented in the reply above, but more like
D-u-d/U-d-u/D-()-u/ (diddley. diddley. diddley)
D-u-d/U-d-u/D-u-d/
D-u-d/U-d-u/D-()-u/
D-u-d/U-d-u/D-u-d

As was pointed out above, many tunes are phrased so that there's a long or double-value note [D-()] somewhere. This allows you to keep starting each bar on the down-stroke without having to hit two downstrokes together (very tiring) more than occasionally. The trick is to get past the hurdle of emphasising the Up-stroke on the second "diddley" (or wherever it's required). It's just ingrained into your muscle memory that down-strokes provide the emphasis. However, if you tried consistently to play
D-u-d/D-u-d/D-u-d/ etc, you would soon find it a real pain in the arm.

Couldn't find any mandolin examples, but there's this:-
Youtube - Jean Carignan playing Foxhunter's Jig
(By the way, none of the above phrasing would work for Foxhunter's - you're on your own now!)

Ross