https://developer.mozilla.org/en-US/docs/Web/HTTP/Reference/...
I wrote about it once; https://dijit.svbtle.com/trusting-the-user-they-know-what-la...
Outlook web actually respects this, which is refreshing.
I speak Dutch and English, but have English set as my preferred language, because most of the time that multiple languages are available, that is the original language. However, sometimes I'll be visiting a Dutch site that has a (usually badly-)translated English version available, and I'd rather get the Dutch version.
I would think the ideal prioritisation should probably be:
* Exact (en_GB)
* Exact (fr_CA)
* Soft (en_*) // Any variant of English you might have available
* Soft (fr_*) // Any variant of French you might have available
* Translated. (to first preferred)
for Accept-Language: “en_GB,fr_CA”
(Also note that I wasn't talking about automatically translated content necessarily. Manually translated content still often is of worse quality than the original language.)
You could probably also trick websites into serving the original language by setting a language they probably don't support (how many websites have a version available in Akkadian anyway?) but you'd need to pick something that the Google Translate widget found on many websites doesn't pick up and try to use.
(To be clear, with how widespread English is, and how often Dutch sites are Dutch-only, this is a minor issue - having English, then Dutch as my preference is usually good enough.)
If websites really need translation (which they very likely do not!), this should be the norm as well.