I was trying to explain to a very non-techy person why I had chosen to use a "/" rather than "http://example.com" to go to his home page. I like root relative URLs because they make switching from dev to test to live simple as it can be (which may or may not be simple, depending).
Anyway, I realized immediately that wasn't going to work, so I dubbed the root relative URL "the Vegas Method" because what happens in Vegas, stays in Vegas.
So of someone (i.e. me) happens upon the test server, I stay on the test server. Whereas if I had hardcoded absolute URLs, I would be whisked away to the live site.
I know there are other arguments for absolute URLs (RSS and scrapers for example), but this is more about my proud new (to me) neologism for explaining root relative linking to a non-tech person, which may come in handy for you. Even if you were arguing against it you could say "The problem with that is that it's the Vegas method - what happens on that site stays on that site. So if a scraper steals youe page, all the links keep you on his site, but if we use the full URL and he doesn't take the time to update them, the full links take the user back home to your site."
As it turns out "root relative linking" is a much more intimidating phrase than "the Vegas method."