Final answer:
Condorcet's criterion is sometimes violated when a majority preference is split between similar options, leading to a minority victory, or during a voting cycle where no option is consistently preferred by a majority.
Step-by-step explanation:
Condorcet's criterion in voting systems is sometimes violated by scenarios where the method used does not always elect the candidate who would win in all head-to-head matchups against other candidates. One example is an election with a split majority vote. If 60% of a population is liberal and 40% conservative, and liberals are split between two candidates while conservatives back one, the conservative may win despite being the minority preference. Another example is the voting cycle, where no single option is always preferred by a majority, such as preferring mountain biking over canoeing, canoeing over the beach, but then the beach over mountain biking.