In my experience the bulk of "irrational" alliance selection decisions occur when teams don't really talk to their potential picks before alliance selections. I think one of the clearest examples I've seen of this was this year's New York City regional.
First of all, I believe that my team (694) was the strongest robot at the New York City regional, but we only managed to seed 8th given the fact that we spend almost two entire matches not moving. It's not irrational to not want to pick a team that had these kinds of issues, however, I was surprised by how few teams asked us what actually happened.
The second strongest robot at the regional almost definitely team 3419, who seeded third. Going into alliance selections, I personally think that the most rational picks for the first seed (team 375) would be first team 3419, knowing they would most likely reject, then to pick us, who would almost be forced to accept given our low seed.
The reason I think that this would be optimal is that that I predicted that team 375 would be either eliminated by us, or by team 3419 (I admit that some of this prediction was due to my own conceit).
The key is that all of this is only optimal given the fact that our dead matches were not for repeatable reasons, and even then, it's still very much arguable that this wouldn't be optimal, as we could have more issues in eliminations.
As it turns out, our two consecutive matches of non-action were due to
- Forgetting to revert to competition code after pit testing
- leaving our breaker switch loose
Both issues were fixed completely, and I think if team 375 had known this, they might have picked us. Instead, however, we were picked by the fourth alliance and went on to win the regional without a single loss in eliminations.
Disclaimer: I don't know that 375 didn't have this information, only that they didn't ask me for it, or ask anyone in the pit while I was there. In fact, we may have talked to members of their team about it, but it is sometimes difficult to find the right person to talk to when negotiating about alliance selections.
Basically, I think that a lot of teams fail to make "rational" decisions are acting perfectly rational based off of the information they had at the time.