The $NORM for the day the vote was cast seems a good value. While this will involve quite a lot of calculations, something like:

my $weighted_norm = 0;
foreach (@days) {
 $weighted_norm += $norm_of_the_day * $amount_of_votes_on_this_day / $
+total_amount_of_votes ;
}
[download]

could calculate the weighted norm. I'm afraid this will be too big a burden (CPU-time) to implement.