There are four political parties standing in your constituency; in alphabetical order of party (and as it happens, candidate): BNP, Conservative, Labour and Liberal Democrat.
48,226 votes are cast.
The BNP receives 2,296 first preferences, of those votes the second preference where stated is split 978 for Conservative and 620 for Labour. 20,668 people vote Liberal Democrat; it subsequently turns out their second choice isn’t relevant – likewise for the 16,075 who vote Labour. The vast majority of the 9,187 people who vote Conservative don’t really care for the other two main parties, which shouldn’t surprise anyone, however most of them also loathe the BNP.
That’s understandable, and the best way to express this is a feature of AV that isn’t afforded by our current first-past-the-post (FPTP) system; the ability to vote against one party by voting for all the others. In our example, most of those whose first preference was Conservative do exactly this, and since they don’t have a preference with the other parties they rank them according to the order in which they are listed. This is called a donkey vote and whilst it is most common where full preferential voting is required, it applies equally here. As a result the ‘second preferences’ for those who vote Conservative are divided 8,177 for Labour and 991 for the Liberal Democrats.
With the vote in, the count can begin, and after the first round the BNP, having the fewest votes, is eliminated. The next preferences of those votes are added to the remaining candidates to give us the following: just over 42% would like a Liberal Democrat MP with around 35% opting for Labour. It’s still not a majority so the Conservative vote is eliminated… and something interesting happens when the ‘second preferences’ are added to the count. These would be the people whose other preference was mostly ‘anyone but BNP’ and consequently voted for the other candidates in the order that they appeared.
Despite having significantly less of the ‘positive’ vote, Labour’s candidate wins through having a superior position in the alphabet.
As I stated previously, what this illustration and others show is how AV can work; the result – fair or otherwise – depends on how the example is framed. I could as easily have had the Conservative candidate prosper as a result of Labour’s anti-BNP sentiment; not perhaps to the extent of the numbers used above, but certainly enough to affect the outcome. This example doesn't say how likely it is, only that it’s possible; under AV you can have a result that many people would consider unfair; it’s a system not nearly as simple as some would have us believe.