Hello, Xiong. The writers are referring to some mathematical description of voting behavior called a "Condorcet cycle". Here's a link to a page describing what one of these Condorcet cycles is: http://rangevoting.org/CondorcetCycles.html
The point seems to be that bad choices can come out of majority decisions. Here's a quote I found pertinent: If your value judgment is "X must be better than Y if preferred to Y by a majority", then you can ultimately contradict yourself.