Why would you use document.location.protocol instead of plain // prefixed urls?

At least has one problem in IE because it causes double downloads: http://www.stevesouders.com/blog/2010/02/10/5a-missing-schema-double-download/

Indeed, it was not an oversight by the GA Team!
GA loader loads a script, so that's not affected by the double-download bug on a <link> or @import for a stylesheets in IE7/IE8.

They use the conditional (ternary) operator on document.location.protocol because of an edge-case bug in IE6 that causes a security-dialog to pop up under certain security settings when requesting from the non-'ssl' subdomain,

as explained by Paul Irish (who worked together with the Google Analytics javascript lead developer on this matter) on his blog: https://www.paulirish.com/2010/the-protocol-relative-url/ from which I quote below:

2011.01.23: But... what about using this on the Google Analytics snippet?

Yes of course, wouldn't that be nice... So I worked with the Google Analytics javascript lead developer (God, I love working at google) to see if we could do this... turns out we can't. There is an edgecase bug in IE6 that causes a dialog to blow up... under some security settings (unsure if they are default) when requesting from the non-'ssl' subdomain. screenshot here. So feel free to take 40 bytes off your GA snippet if you don't care about IE6.. otherwise you're gonna need that ternary operator. `:)`

2011.12.24. Eric Law (from the IE team) chimes on why IE6 doesn't play well GA...

The reason this doesn't work in IE6 is that the server is using SNI to deduce what certificate to return. XP (and thus IE6) doesn't support SNI in the HTTPS stack. See for details.