I was told, from my Congressman, that I tied for the principal nomination to the Naval Academy. I was wondering if that has happened before and how the Academy chooses which candidate to offer the appointment to?
It's REALLY hard to know what this means. "Tied" suggests at least two people were named the principal on the same slate. That actually can't be the case, as above posters said. There is only one principal nominee, hence the term "principal."
So, this
could mean that the MOC actually submits a competitive slate -- thus, technically, all 10 are tied for the principal nom when in fact no one is ranked higher than the other. However, it makes people feel better to think they were "tied" for the principal nomination vs. 1 of 10 on a competitive slate.

It could mean the MOC person who called you doesn't understand terminology and is not using the term "principal" correctly as a term of art (rather, thinking all nominees are "principals"). It could also mean that the MOC is telling you that there's a tie but could be listing only one person as principal on the slate they submit -- IOW, at the last minute, the MOC breaks the tie.
As Hoops said, USNA almost always selects the principal nominee provided he/she is fully qualified. However, there is a bit of "wiggle room" in the law, so not the certainty that there is for the other SAs.