Analysis has previously been carried out on the 2005 election, as to what would have happened under AV. In this case it's suggested that Labour would have increased their majority under AV, despite the controversy over the war.
These analysis' are always risky. For a start they assume that every person would vote exactly the same first preference under AV, something we know isn't the case, even on the most conservative estimates of tactical voting. Secondly they assume preferences based on a leading question.
"If the voting paper had required you to give two votes, in order of preference, which party would you have put as your second preference?"
Thirdly this study is a national study that, despite likely being broken down in to key political areas (North West, South West, London, etc), can't give an accurate appraisal of local views and deviation from the national average.
So on several levels we should be cautious about the study. Realise I'm saying this in relation to the broadness of what information is used, and as such not only could it be over-estimating the benefit Labour would have gained...it could also be under-estimating it. My only suggestion here is that it's not a good practice to rely on this data too heavily.
But let's assume this study is bang on.
Is it proof that AV would be less fair?
Arguments can easily go that as it would make parliament less proportional, this is less fair. It's a fine argument, legitimate...but unfortunately not one that has any place in a debate between two systems that simply do not care about proportionality. One year's system that provides a less proportional result could provide a more proportional the next...it's based solely on spread of opinion, not the system.
For example, in 2005 AV would have made (if we believe the study 100%) things less proportional. In 1992 it would have made things more proportional. It's swings and round abouts, based on the *real* popularity of the parties.
The thing with 2005 is that if Labour really would have won a greater majority under AV, it'd be because that's what people wanted.
It would have come down to the fact that there were more constituencies where Lib Dems were placed third than where other parties were placed third, and that Lib Dem voters would tend to feel that (despite the centralised campaign being so vocal about the war) voting for Labour is a better evil than letting the Tories in with their (at the time) heavy anti-immigration and anti-poor agenda.
This comes back to my previous post about what is "fair". Crying about the potential for someone you (as an individual) really dislike getting a better share of the House of Commons under AV...and claiming this is proof of AV's failing, completely ignores the greater will of the nation, and ignores the narrow relevance of your own individual view on what is a "correct" result.
In 2005 less people will have got their first preference under AV, assuming that under FPTP everyone has voted entirely the way they truly wanted the result to go, but they would have got a parliament that really represents the balance of their views from a local context, not allowing (in this case) Tories to pick up seats where local constituents would rather have backed Labour than the Tories.
In short, if 2005 would have caused a larger majority for Blair, it's because people still really didn't get along with the Tories on a constituency by constituency basis.