To me, Sergey, the question is, does the process allow the intent of the contest to be achieved?
As the rules stand today, it could happen. The problem is not due so much to the essayer's ratings of others' essays,or that apparently one can vote for himself, but it is due to the fact that the results depend on the non-essayers judges adherence to the very specific rules under which they must judge the essays.
The most interesting entries must be those of concepts consistent with known facts and which are falsifiable. They must be written in layperson's terms as much as possible for non-professional fans of science to better understand.
The only value given to essayer's ratings should be no more than a grain of salt simply because, IMO, I immediately saw many that appeared to be posted just to show they garnered great interest from friends.
That Man is corruptible is an undeniable fact of life. For the intents of the contest to emerge as desired, we must hope the judges can select the many that adhere strongly to the rules first, then from those, select the ones most likely to represent reality.