I think it'll be difficult to find a fair system for such a small group of voters.
While it's true that one person's vote can have a large influence on
the order of victory, it isn't obvious to me that that is inherently
bad. Isn't the point of voting that each person be heard? Under that
theory isn't it a good thing that one person can make a difference?
All right. Let's apply it to a presidential election. Would you say a voting system is good if no matter what everyone does, I can decide with my vote who actually wins? Would you say it's fair?
Will you still think it's fair if next competition I tell 10 friends to vote randomly but making sure my game is on top (hell, maybe not even 10 are needed, maybe with a couple it's enough)? The potential for exploiting the system in such a small group of voters is too big.
I think I'd change the competition to something very different. A period of time where the games are played, feedback is given the community on any and all the games. This way we see what games generate more/less interest. We see what the experiences playing the games are, etc... Then maybe after a while, each person says what game they enjoyed the most. But instead of concentrating on the ranking results, I'd say we concentrate on what's actually useful. Playing and giving feedback to the games. If you can't trust the ranking system to be fair, then what's the point?