Not sure if this belongs here or meta.SO but should the Original Poster be allowed to vote to close or reopen his/her own posts? Or is it just because of the private beta?
As Rarity said in the comments, this is by design. The reputation requirement is different during private and public betas, but the principle is the same.
Since four other people (or a moderator) need to agree with the vote, there's little chance for abuse.