Paris trip with free breakfast and a Rome trip with free breakfast. We cannot decide between the two because we love Paris and Rome equally.
Simply adding a third option - an "A minus" version of one of the options, will cause us to pick the A version, over the equally atractive B version.
Thus, the simple addition of a third "A-" option, "Paris without a free breakfast", will cause us to choose "Paris with a free breakfast", the "A" option, over "Rome with a free breakfast", the equally attractive "B" option.
Similarly, had the third option added been "B minus" - "Rome without a free breakfast", we would have selected that "B" option - "Rome with a free breakfast".
This is irrational behavior because in the presence of two equal options, we couldn't decide between the two, and the presence of a third, inferior option, shouldn't cause us to suddenly prefer one of the two.