The appeals process is to write to hn@ycombinator.com (Contact link in the footer.)
Go ahead and downvote me, doesn't make what I'm saying wrong.
If you don't like the moderation, apply to be a moderator.. or start your own forum.
The moderation is 100% transparent and you can see a log of every comment/submission that a moderator has removed. Furthermore, each subforum can control their own moderation team through a voting system. Moderators should serve their users, not rule over them as dictators.
I've already seen a few times where content demeaning YC companies mysteriously got disappeared... and then summarily blamed on automated removal. Who's right? No clue. But being able to see that log as it happens would be a significant good faith action.
I mean HN could publish a ranking algorithm and claim that that is what they use. But then we still wouldn't know
(1) if that is really what's running in the background,
(2) if that is really receiving user inputs that lead to the observed outcome.
I'm guessing for most people here the programming assignment "create a fake log including these real inputs so that this story is suddenly dropped according to the ranking algorithm" isn't that hard.
I think that in the end, you end up trusting something. (Eg. Is the log fake or real?) IF that is so, you might as well design the system around a predetermined root of trust... here, the moderators.