I've found that with a lot of people.. some bikers included... when you say "On your left" they tend to move to their left. Either looking over their shoulder and inadvertently tracking left or sometimes get jumpy and move to the left. It's not specific to bike paths an MUP's. It happens all the time on the slopes, too.

So I usually announce "Passing". I seem to get a better reaction that way. And I always say thanks as I pass. I think anyone over 16 is used to cars passing on the left as a standard in a vehicle on the road, so the idea isn't complete foreign, but "on your left" may very well be.