this year we really fought to have an honest pizza contest, with clear rules and so that everyone has the same chance
The chances can never be equal: a chef has a higher chance of winning this competition than a student who, at most, cooked instant noodles. 
And regarding clear rules, I already wrote above:
- I reserve the right to decide at my own discretion whether your baked goods are pizza or not.
psychological subjection, if theymos makes a pizza, many will be tempted to vote for theymos' pizza even if it's not the most beautiful pizza
That's why he doesn't participate in this contest. But your message is clear: popular and recognizable users on the forum will have a psychological advantage.
A hack for winning this competition: if Laszlo cooks the pizza, he will take all the prizes pool.
to have voters who vote objectively, in my opinion, we need to publish the pizzas anonymously so people can really vote for the one they like
This would certainly increase the objectivity of the assessment when voting for the participants’ baked goods.But it seems that this condition of Bitcoin Pizza Day competition will not be introduced until next year (best case scenario).