This is a variation on a Card Sort, but instead of cards you just have list items. This is an excellent technique for learning user priorities, preferences, or hierarchies of value. Once the user has the order to their liking, you would ask them to send you a screen cap if you weren't in the room observing.
If you have a web-based use for this tool, download the file locally and edit the HTML. You just change the words Item 1, Item 2, etc. and leave everything else alone.
Drag and drop the items in the list.