One that I'm not worried about, however, is the "popularity contest" problem. Given the requirements to get your vote, it's an enlightened electorate we're talking about creating. Not the hoi polloi. Given that they will care a lot, I think that we're looking at a group that'll create a good response.
Put another way, I can give the exact same instructions (or rather better instructions) to each voter next year as I gave to the judges who volunteered this year. And I think it'll work out just as well or better.
You and others do have a point about the loudest (or "namest") design getting the most attention potentially. That is, it's possible that somehow some good game won't get read or talked about and then no votes will be cast for it. What I think would be good would be to ensure that one review at least got done for each game so that no game would get lost this way. That is, I think this is a small enough event that even one good review will indicate if a game is worth reading to the other voting participants.
This is actually cool because if you get done with your entry earlier, you'll have more choice in what to judge. But you won't be seeing the whole field yet. So even the later entrants who would be forced to pick from a potentially smaller field, would have newer games to choose from.
That's a bad paragraph. Here's what I'm seeing. Entrant A submits first, and has to wait for something to review. Entrant B submits, and can instantly choose to review A's game. A can choose to review B's game. Or they can wait and see what pops up later. But you can't review a game that's already been reviewed (at least not for credit). At some point, however, they have to get in some acceptable review, or they can't win. If somebody reviews your game, this is some incentive to make sure that you review somebody else's. If you do review somebody's game, and they don't ever do a review, you'll be forced to do another review, yes. So you should try to select the game of somebody that you think will do their review.
In any case, submitting your game, and then doing a review of a game who's creator has done a review, gets you your vote(s). Evan, I like your idea, but I think perhaps it might be simpler to give out 3 votes or something, and vote for your three favorites. I'm kinda on the fence there. Your method might work, too, but it would be problematic with the below (unless we came out with a sliding scale of points that you get to give).
I'm also thinking that anyone with emeritus status from participating in a previous year can also do an additional review (which doesn't count against the limit to a designer from this year using it as their game for review), and thus get a vote. And perhaps everyone gets additional votes for more reviews. Yes, this is how I'd intend to keep my finger in the pie. But it also means that y'all are all in, too!

In any case, we haven't settled on Peer Review for sure. It's just sounding very attractive to us judges right now.

Matthijs, apollogies to you and Paul and Evan. The last thing I should be doing is squashing discussion. Saying that something didn't work well is not the same thing as saying we judges are bad people. Please do criticize.
Ben, compared to what we do now, having to do a little administration like you and I are suggesting is eminently doable. I think that the Chairman's role, like in Iron Chef, should really fade away from having anything to do with picking a winner.

Hey, look, even Delta even agrees with me that I'm the one to blame!

Rather, he makes the excellent point that we simply need to have some of these things better worked out ahead of time next year. Very sound advice.
Mike