You probably don't want ratings to appear by the songs in the current battles because it might affect future votes.
However...
I think it would be nice to have a column included: "You rated this song..." and display my personal rating for each song beside the song name and the star (if I have rated it, of course). That way, I can go back to "Browse/Dec Battle" and see how my fav songs are doing vote wise.

Agreed - I tend to check out the top voted songs first & may not get around to those with 1 or 0 votes. This slants the voting & then we'll end up like the UK Charts (if I hype up a single, it gets the snowball effect). Nah not really but you get the point.

ummm...maybe I need to clarify myself. I'm not quite sure what he is reffering to.
I was referring to the list of songs in the current month's battle under the browse tab. There it lists the songs, those with less views on top and a star beside the song if I've rated it. I thought it'd be cool to add an extra column to this page that displayed what rating I have given each song, not the current average rating of it.
I've just re-read Arroseuk post and I understand it now, sry.