FWIW, HN is implicitly biased towards YC companies, because posts by YC founders show up in a different color to other YC founders, which is an implicit voting ring of sorts.
This may no longer be the case; it was the case a few years ago to my knowledge.
YC alumni see each other's usernames in orange. That plus the job post on the front page are the two YC-specific things that HN has. Both have been in place for a long time, and moderators try to be meticulous about not giving special treatment beyond that. (I say "try to be" because no one is the best judge of their own biases. But we do try hard, sometimes to the point of overcompensating.)
I don't think the colored usernames affect voting ring activity much. YC alumni and startups certainly are not exempt from the penalties we put on such activity, and frequently get hit by them. The first thing we always tell YC founders is not to solicit upvotes for posts because that backfires.
Maybe, but I'm pretty sure the effect is small. For example, there aren't any posts by YC founders on the front page right now. And votes by YC founders mostly wouldn't be enough to move a story in ways that would escape the ring detector.
I'm pretty sure that the only privileged positions YC holds on HN today are the top-left link and the job posts that are not eligible for votes or comments.
And writing the algorithms. And setting policies. And employing the moderator. And ...
Whether this privileged position leads to different treatment for YC companies is a different question -- as Dan says, they try not to be biased and potentially even overcompensate. Still, the privileged position is certainly there.
You're exactly right—it's a privileged position, and a delicate one. Without the trust and the interest of the community, HN wouldn't be worth much, so those are the two things we care about most.
This may no longer be the case; it was the case a few years ago to my knowledge.