I'm working on a site that does exactly this! It learns pretty well what you want to read (based on voting up/down on everything). It's mostly based on correlating your preferences with those of other people.
My site is http://newsbrane.com and you can try it if you like. I'd appreciate feedback; click 'send feedback' at the top of the page (or post here - I'll read it).
It feels a bit awkward to use: three stories at a time, and they're all displayed so big! No idea how you're finding these readable stories.
The problem with this is that I feel no need to continue using it. No incentive. Part of that's because I know you'll keep giving me a stream of items, no matter what my limit for reading stories is.
I think it would be neat if this could determine what things attracted me to stories, and ONLY showed me ones that I'd be interesting in. A site willing not to give me content is one that I'd possibly become a diehard fan of.
Newsbrane is still in its infant stage, and your criticisms are entirely valid :). The first 10 minutes aren't very satisfying.
The site actually does exactly what you want it to do: it learns your tastes and shows you only the things you're interested in.
What you experienced was the "Explore" mode, which is designed to figure out your tastes, not give you the best stuff. Explore is the 3-at-a-time mode you start out in. Once you've done some voting, you can use the "Recommended" mode, which does what you want.
The site works great for people with 50 votes or more. We are still working on the new user experience, and we are ravenous for feedback like yours, so thank you.
I think relevance is a hard problem to solve when it comes to news. You need to trust the community that filters your news for you and if it is an open community then that leads to all sorts of FAIL. Lots of exciting things happening in the area though.
FriendFeed/Twitter allows you to specifically choose each individual that belongs to that group that gets you your news. I just don't feel like these two companies focus on this aspect of it enough.
My site is http://newsbrane.com and you can try it if you like. I'd appreciate feedback; click 'send feedback' at the top of the page (or post here - I'll read it).
Lincoln