BPV works well for elections with one, two or three candidates, but it becomes increasingly inadequate when there more than three candidates. With BPV, a vote against a candidate is effectively a vote of support for all the other candidates. With candidates A, B and C, a BPV ballot that shows support for A could, just as easily be interpreted as showing opposition to both B and C. This allows a voter to express any combination of support and opposition when there are at most three candidates.
In a four-candidate election, voting against a candidate is a way of supporting the other three candidates; some voters (but not all) might find this is what they need but many would find this option of no use. But if there were eight candidates, a vote against one of them would have the same effect as a vote of support for all the other seven candidates. While this may describe the opinions of a very small minority of voters, most voters would not find that useful. Instead, most voters would find BPV to offer nothing compared with plurality voting.
An example might help clarify this situation. The BAV voter who supports candidates A and B while opposing C and wanting to abstain with respect to D. There is no way for a BPV ballot to express this combination of opinions. Casting a vote against C comes close, but that would express support for D rather than indifference. Matters would be even troubling if the BPV voter opposed D as well as C.
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