Articles, messages and many other items on The Code Project have associated with them a Vote Total (Vt), a Weight Total (Wt), and a number of votes (N). When a member votes, the system adds the weight of their vote (dependant on membership level) to Wt, and the rating itself multiplied by their weight to Vt. The rating of an item is then R = Vt / Wt.
If everyone has a weight of 1 then Wt = N, and R = Vt / N. Having differing weights, though, means that when a gold member (weight = 4) and bronze member (weight = 1) vote, the vote is weighted towards the gold:
Assume Gold votes 5 and Bronze votes 1:
Wt = 4 + 1 = 5
Vt = 4 x 5 + 1 x 1 = 21
R = 4.2
For a ridiculously indepth analysis please read Is CodeProject's Voting system really smart?