### Typical simple example of "add-top failure"

There are many many voting methods out there, and (like this one) all sound like reasonably good ideas, at least at first. We are just considering BTR-IRV here as a typical example. Because BTR-IRV is a Condorcet method, a general-purpose theorem tells us it must exhibit "add-top failure." Our goal on this page is to make that completely concrete by actually exhibiting a BTR-IRV election in which that happens. Here it is:

#voters Their Vote
3 A > D > B > C
3 A > D > C > B
4 B > C > A > D
5 D > B > C > A
4 C > A > B > D
In this 19-voter example, A wins (C, B, and D are eliminated in that order). But if we add 6 new voters each of whom votes A>C>B>D, i.e. all ranking the current winner A top... then C wins! One of the new votes ranking the current-winner top actually causes him to lose! (End of example.)

The proof of the "general-purpose theorem" is not at all mysterious. It simply exhibits about 7 different fully-concrete election scenarios just like the table above (in fact this is one of them) and argues via a case analysis that no matter what election method you use, if it is a "Condorcet method," then it must exhibit add-top failure (that is: adding some new votes all ranking the current winner top, causes him to lose) in at least one of those 7 scenarios.

### Another example

Here is another example of add-top failure, this time for "Rouse's voting method," another (fairly complicated to describe) elimination method that elects Condorcet winners whenever they exist.

#voters Their Vote
5 C > A > B
4 A > B > C
2 B > C > A

In this 11-voter example, A wins (C then B are eliminated). But if we add 2 new voters each of whom votes A>C>B, i.e. all ranking the current winner A top... then C wins! (B then A are eliminated.) One of the new votes ranking the current-winner top actually causes him to lose!