(NOTE: This also shows the same problem is present in the Cary, NC system where only the top two candidates advance to the second round of counting.)

1. 6: abc
2. 5: cab
3. 4: bca
4. 2: bac

Because nobody has a majority of 9 votes on the 1st round, c, the candidate with the fewest first-place votes (5), is eliminated. His 5 votes go to 'a', who wins with 11 (6 + 5) votes.

Now assume the 2 class (4) voters change their preference ranking to the following:  4'. 2: abc

Again, nobody has a majority of 9 votes on the 1st round. Because b gets the fewest first-place votes (4), he is eliminated, and his 4 votes go to c, who wins with 9 (5 + 4) votes.

In summary, candidate 'a' wins when he is ranked second by the class (4) voters, but he loses (to c) when he is ranked first by these voters.

Thus, 'a' wins when FEWER voters favor him, and he loses when more voters favor him!!!

If all except the top two candidates are dropped in the 1st round (in this example, only one candidate since there are a total of three), nonmonotonicity can still occur.

This example can be easily extended by adding voters and candidates, so that when one drops more than one candidate in the 1st round to eliminate all except the top two, nonmonotonicity can still occur.