Well, they certainly won't all contradict. The more votes you have for a particular matchup, the more reliable the outcome is. That is, the more you can feel secure that the outcome is correct, and not just one person's honest opinion (which is subjective, and YES, all votes are subjective) at best, and off-the-wall goofiness at worst.
When you have a loop as you describe, which could (and most likely will, given the huge number of pics you have and the geometrically larger number of potential matchups) happen, you can do several things, or a combination of them. In no significant order:
A) assign more votes to be taken to raise or lower confidence, to resolve the situation by establishing which matchup is incorrect. If two of the three are strong, you can guess that the third is an anomaly, and concentrate extra votes there.
B) you can check their records against opponents in common, to see if a pattern emerges.
C) if the matches were all close, you can guess that the pix are a dead heat.
If I wasn't clear before, the tree is transitory. It is a way to establish an initial sort order. Then pix are assigned into your rating pools. There is one pool for each possible pic rating. Once the pools are established, the tree goes away. So, with the loop above, the three (or 4 or 5 or whatever pics) can just be placed in the same starting pool. After that, they will move up or down based on whatever new data comes in, as long as confidence in matchups is kept high. Only make solid decisions on strong data, that is how you maintain confidence that your ratings are correct.
Be clear that there will be a LOT of pics in each rating pool, I've discussed this elsewhere, dividing your 1.2 million pics amongst a limited number of possible ratings.
Pics within a pool are considered tied, until one or more either shows inferiority to the pool, or shows up as outstanding. Then they move one or more pool locations based on how strong or weak their records. They will get a new group to be tested against, to see if they have reached their more or less final resting place (they may creep up or down a little, but when you get their number right they will tend to stay put, running around 50% in future pool matches, appropriately higher or lower out of pool.