Yes, I've now read John Curtice's number-crunching from BES data on second party preferences that suggests AV would have marginally inflated the 1987 and 2007 majorities, and that the main gains would have been for the Alliance/Lib Dems. (Particularly in 2007, when they would have been within spitting distance of the Tories and therefore have had a much stronger case to present themselves as a creditable opposition.)

So I do understand the LibDem case. But I'm genuinely struggling to see what this system offers over FPTP.