Possibly of interest regarding named anchors...
For a while, back in 2009, for some large sites, Google serps returned onpage fragment identifiers as mini-sitelinks. These were links to named anchors, usually in large reference sites like Wikipedia and Internet Movie Database. We discussed these here...
Page Fragment Navigation in Mini Sitelinks - and snippet! Aug-Sept 2009 http://www.webmasterworld.com/google/3977406.htm [webmasterworld.com]
I'm not seeing these any more in the serps, which suggests that either Google found that this type of sitelink wasn't that helpful to users... and/or it might mean that named anchors on large reference sites have gone out of fashion.
Wikipedia is still using named anchors as a navigational tool, and they are still genuinely useful. Certain types of Wikipedia pages that were divided into named anchor sections, though, now seem to be split up into multiple pages... perhaps because pages were getting too large. Ditto, I'd say, with IMDB... though IMDB is often using javascript to hide or reveal page sections.
As for same-page links just for ranking, conceivably anchor text on a page might have some tiny effect, but this feels a lot like trying to pull yourself up off the ground by tugging on your shoelaces. This is not where I'd put my energies, particularly if it also creates a bad user experience.
In case you're wondering how I did this, I found a plugin which scans for keywords and turns them into links but since the keyword is on the page it was linked to, there is a link on that page which links back to itself.
I'd avoid this kind of navigation like the plague. YMMV.