There is no Condorcet winner if A beats B , B beats C , and C beats A . This is called a voting cycle . But on a smallcouncil with 3 factions, inadvertent ties are fairly common. And manipulators of Condorcet's rule try to create voting cycles.
Voters can often forge a cycle by ranking the central item below an opposition item.
In our first example C was a Condorcet winner. But if voter 1 changes his ballot to rank C below D , we find a voting cycle in which D beats C , C beats B , and B beats D . Each wins by 4 ballots to 3. But the examples above and below show it can be easy in a council with a handful of factions. If, for example, supporters of C miscalculate and try to fcreate a cycle by adding their support to A , she wins.