The site is in private beta and there are only few active users so it's likely to upvote many posts of one user. Does a script run to detect serial up/downvoting during the private beta?
Yes, but there's not going to be sufficient votes in the system for anything meaningful to come up. This is a part of a site's life where the focus is writing good questions and up-voting every single thing you think is worthy, while down voting every single thing you feel isn't good for the site or the topic.
Until there's more than 'a few hundred or so' votes in the system as a whole, irregular patterns aren't meaningful, not this early on. Every single one of you looks like a sock puppet for the other right now, since vote distribution is so narrow.
If, during a private beta you suspect that someone might have targeted you specifically with down votes out of revenge or something - you can flag it, we'll have a look - we don't like that kind of community hostile behavior at any stage, especially this critical one.
Don't worry about it during the private beta, there's far better / more interesting things to worry about :)