Three papers came out on new technique at almost the same time. What order do I cite?
This could be a very delicate diplomatic issue. There might be three groups arguing over the paternity of the original idea. I strongly suggest citing all three.

As for the order, first of all check the journal guidelines. In my field, typically citations are numbered in alphabetical order in the bibliography; if it's the same in yours, then I suggest you to cite them ordered by their citation number (thus alphabetically), i.e., put them in the same bracketed list [a,b,c], with a&lt;b&lt;c.

Ordering the references like this is a good habit to adopt exactly because of these attribution issues.