I've got these handy arguments against AV from the Electoral Reform Society:
• It can be less proportional than First-Past-the-Post.
• It does very little to improve the voice of traditionally under-represented groups in parliament, strengthening the dominance of the 'central' viewpoint.
• There is no transfer of power from party authority to the voters.
• It is prone to a certain amount of 'Donkey voting', where voters rank candidates randomly, not knowing enough about all of them to make an informed decision.
• Under certain circumstances, a shrewd voter can get a better result by lying. If, for example, it is known that the contest will be fought between two strong candidates, supporters of one might rank third parties above the other, even if the other is technically their second choice.
• In a broadly three-way race, where there are two strong parties who actively dislike each other and a third 'compromise' candidate sitting in between, the compromise candidate is likely to be defeated in the first round, despite the fact that they could well be the most universally acceptable option.