This clip from Auf Wiedersehen Pet has being doing the rounds sparked by a post from Mark Wallace where he claims that it shows how AV is not a good system.
The clip shows the lads trying to decide what colour paint they should use to paint the hut. Because they can't agree on a colour Barry suggests they use a preferential voting system whereby everyone gets 2 choices, their first is weighted with two points and the second is weighted with one point. They then total them up to decide which colour wins. The result is yellow which was apparently nobody's first choice. Cue much hilarity from Mark and others who claim this shows AV is unfair. Mark does concede that the system is not AV but that the same result would have happened under AV too*.
According to Barry in the clip, of the 6 who voted, none of them chose the same first choice colour. Three of them chose yellow for second place so it wins with 3 points vs 2 for all the others that were first placed. We also need to assume that all the other second placed colours were different from those that came first, otherwise at least one of them would have had 3 points and hence it would have been a tie.
I am not so sure that this clip shows AV as being wrong or unfair. Mark implies that AV has chosen the wrong winner as yellow was nobody's first choice but in such an election with such a disparate variety of views amongst the electorate, how else were they supposed to choose the colour? Surely allowing preferences like this is fairer than just one person imposing their first choice view on everyone else despite it only being the first choice of under 17% of the electorate?
In fact, if anything a proper AV system would have been even more fair allowing each voter to express more information about their preferences and hence having an influence on the outcome.
Let's just move this scenario into the voting world for a minute. Let's imagine a constituency with a very diverse range of views amongst its electorate like this. Let's also imagine that like in the example from AWP above that first choice vote is very close, say around 16% to 17% for 6 parties. Something like:
Lib Dem 16.7%
This is about as close to the AWP example as the real world could ever get (it's never going to be an exact 1/6th split amongst all parties) and it is an extreme example but useful to work this through.
In a real world scenario it is statistically highly improbable that 0% of the electorate would opt not to choose a specific party as its first choice but that 50% would choose that party as its second choice as in the AWP example. Far more likely is a party that did not come first in first preferences overtakes the one in first place (but well short of 50%) after the second (and third and so on) preferences are taken into account.
Under First Past the Post the Conservative would take the seat with less than a fifth of the vote. Even if most of the supporters of all the other parties would prefer to have had a Labour MP, no account is taken of that.
So far from "proving" the case for FPTP, this example actually highlights the pernicious effect of First Past the Post.
*Incidentally, Duncan Stott in the comments on Mark's post refutes this claim in that if yellow had received no first preferences it would have been eliminated after the first round.