Update:
Narumi Misuhara
Nope, there's no skewing or anything special done to the selection. All avatars should have roughly the same number of view
Aka you should see a avi that has never got a upvote as much as a avi which only gets upvotes, any time you see one avi multiple times its should be by chance as a result of truely random selection. Observational bias will heighten the "non-random seeming" of the randomness.
So, as Kailin
posted
We have a new museum feature which lets us see how many votes we got.
In the Halfatar contest
1st place = 1224
2nd place = 1223 (Close much?)
5th = 1203
16th = 1155
19th = 1146
21st = 1132
From this is "seems" clear that it is purely a "upvote" count which decides who places where. (as opposed to a ratio).
This would explain why you often see "trending" avis a lot more than other avis, because when top ranks are as close as this, they would need more votes to assure position. Aka why the "randomizer" seems not random for certain avis. (Though we cannot technically rule out that all 4 of these may have been "viewed" say 1500 times, and this is their scores out of 1500). But
observational bias does seem to favor trending avis. Prehaps something to check on at the ATA.
If you got top 5 in any contest feel free to share your vote count (if you were first three, or know you were 4/5th). (Or if you didnt place, but want to anyways thats cool too)
For your vote counts
Red,
npc,
half,
beach
wander,
colour splash,
blue,
green,
yellow,
red,
orange,
monster,
town pride,
night on town,
New york,
business casual 
150
100
400
