Jeff,
This is just my guess from what I've seen and not an Official IBCA answer and in fact i don't think that information is made public. First I'll state that we are never supposed to know if there was a tie because we aren't supposed to know any scores. However, when there has been a rumor of ties on brisket, it appeared that the brisket ranking was determined on the highest score in ribs then back to chicken if necessary.
However given the nature of the IBCA whole number scoring, it would seem to me that a fair process to break ties would be to start at Brisket and work back to chicken since brisket is the grand champion tie breaker. So starting with brisket final table ties, you would first revert back to the highest scoring on the preliminary table scores and if that doesn't settle it to go to the highest final table Ribs score, then to preliminary ribs score,the highest final table chicken then highest preliminary chicken then flipping a coin, playing rock paper scissors, guessing a number 1-10, drawing straws, having a foot race, playing a hand of poker, seeing who can hold their hand over hot coals or hold their breath the longest, having a staring contest, or any other form of random draw.
It would be nice if IBCA would make the actual scoring and tie-breaking information public, i just have never been able to find it if they did. Their method of not releasing final table scores or preliminary score to cooks is IMHO not a very good method since it doesn't allow cooks to use that data to try and make improvements but it is the way this sanctioning body operates. Since I make a choice to participate in their contests, i am also making a choice to play by their rules. Every year we can submit rule changes at the annual meeting. I've made two suggestions and am 0-2 in having any rule or method officially altered. To have IBCA BOD make a change seemingly would require that a significant majority of members sign a petition or some form of cohesive documentation to show that enough of their members want such a change and i don't know if anyone has ever attempted that. The only other options you have is to vote for new Board members at the next election who may support change.