I purchased this little dust pan at the grocery store. I have seen them at Walmart as well. It is made to clamp onto the broom handle, I would guess tight enough to stay in place which makes the dust pan very convenient. When you use a broom, you usually need a dust pan.
I have a Stanley broom that is ??? old. I have had it for years and love it. Well, the broom handle is a little too small for the dust pan to fit properly and it slides down to the bottom of the handle when I put the broom in the closet.
Steps:
Using the elastic is a good idea and I'll use it next time if I need a quick fix.
What I did was make a thick bead around the broom handle using a glue gun.
The rubber band also holds the dust pan in place and keeps it from turning. I just figured this tip out last week and have been putting up with it sliding since I purchased it several months ago.
The glue sounds like a good tip as well however, I have a bunch of these celery rubber bands. They have come in handy for a lot of things. I'm sure it will need to be replaced eventually.