EXAMPLE 3 Exploiting the Condorcet Voting Paradox

We had to be careful in stating the theorem that asserts Concorcet's method is non-manipulable because, as we've seen, elections occur in which there is no winner using Condorcet's method. With three voters and three candidates, it is possible for a voter (the one on the left in this example) to unilaterally change an election from one that yields his or her second choice as the sole winner (Candidate in the example), to one in which there is no winner at all, as this example shows:

Election 1
Rank Number of Voters (3)
First choice
Second choice
Third choice
Election 2
Rank Number of Voters (3)
First choice
Second choice
Third choice
image
Paper ballots are still used in elections in many states. A lingering controversy from the 2004 presidential election is the use of electronic ballots, which do not leave physical evidence, thus making it extremely difficult to do a recount in potential disputes about the plurality or majority.

A voter's ability to bring about this kind of change in an election unilaterally, however, is not something that falls within the scope of our formal definition of manipulation. nevertheless, one could argue that there are situations in which you might well prefer having an election with no outcome at all to having an election in which a candidate other I than your top choice emerges as the sole winner.