I seems pretty consistent that it is the order that I added them to the list. I have to select them one at a time and save it each time, but then it stays in that order in the 'edit' modal. I can even see the order that I selected them in the JSON values in the database table. If I reorder the content in the content tree, it stays in the original order in the JSON until I republish the page.
I was hoping to create an A/B test with different widget values. Will have to think of a different way to do it.