Imagine you are in a party of 21 and there are four restaurants within reach for a work-time lunch; in alphabetical order: Lentil Heaven, Liver Lounge, Pizza Palace and Thai Temptation.
One strange individual plumps for Liver Lounge and puts down Thai Temptation as his second preference. Nine people vote for Thai Temptation as their first choice; it subsequently turns out their second choice isn’t relevant - likewise for the seven people who choose Pizza Palace. The four people who remain are vegetarians, they’re cool; they don’t really care where they eat so long as they can avoid the liver.
That’s fair enough, and the best way to achieve 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 option – by voting for all the others. In our example the vegetarians do exactly this, and since they don’t have a preference with the other options 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.
With the vote in, the count begins, and after the first round Liver Lounge, having the fewest votes, is eliminated. The next preference of that singular person is now added to the vote to give us the following: just over 47% of you would like a Thai, with around 33% opting for Pizza. It’s still not quite a majority so Lentil Heaven is eliminated… and something interesting happens. The ‘second preferences’ of the vegetarians are added to the count; those would be the people whose only real preference was to avoid the liver and who consequently voted for the other options in the order that they appeared - despite having significantly less of the ‘positive’ vote, Pizza Palace wins through having a superior position in the alphabet.
What this illustration and others show is how AV can work; the result - fair or otherwise - depends on how the example is framed. What this particular example shows is that under AV it's possible to have a result that many people would consider unfair; it's a system not quite as simple as some would have us believe.