So who determines if a post should be re-opened?
It seems that anyone can close a question, but re-opening is a different story.
Voting to reopen works in more or less the same way as voting to close: five users with 3k+ reputation are enough to reopen any closed question, and moderator votes are binding (as are gold-tag-badge-holder votes when it comes to duplicate questions).
This is covered in the help centre:
What if I disagree with the closure of a question? How can I reopen it?
Stack Exchange is collaboratively built, maintained, and moderated by the community. If you see a question and you disagree with the stated reason of its closure, you should first try to edit the question to improve it as much as possible. Read the close notice and any comments carefully to address concerns raised there. Closed questions that receive edits within the first 5 days of closure are automatically put into a review queue to be considered for reopening.
Additionally, you can:
- Leave a comment on the question itself calling for it to be reopened. Be detailed: explain why the question shouldn't have been closed. Be constructive: name-calling is as likely to drive folks away as it is win them to your cause. Remember, anyone on the site with at least 3,000 reputation points can vote to reopen a question - even if a moderator closed it.
- Be sure that you've read the close notice and any comments on the question so you can address any concerns raised there. Addressing the concerns often means editing the post, which any user may do.
- Flag the question for moderator attention. Again, explain why it should be reopened. There is more than one moderator, and moderators do reconsider their decisions.
- If you have at least 3,000 reputation points, vote to reopen yourself.
If you're simply unsure about the validity of the closure, the best place to ask is on the community's meta site. Asking in the meta site allows those who took the action to comment, and will help others to learn about the issues being discussed. You can find a link to a site's meta in the two place in every site's top bar: under the "help" menu in the upper right, and in the Stack Exchange site switcher in the upper left.
Reopening a question follows the same process as closing a question.
Users with 3,000 reputation can cast up to 24 reopen votes per day. When a question reaches 5 reopen votes, it is no longer closed, and new answers may be submitted. You may only vote to close or reopen a question once. To cast a reopen vote, click the "reopen" link beneath the question.
Moderators may close or reopen any question with a single vote.