AV doesn’t give people an extra vote, it just allows people to express 2nd and 3rd choices to be applied if their 1st choice doesn’t get many votes. So for example, a Labour voter in Berwick who wanted to keep the Conservatives out could vote Labour 1st choice and LibDem 2nd choice (this is hypothetical), rather than having to vote LibDem tactically straight off. With first-past-the-post, you have to choose – either vote with your heart or vote tactically, with AV you can do both.
AV isn’t proportional because you only get one MP, and they can’t be part-Tory, part-Labour, part-LibDem or whatever. In proportional systems, you get several people elected in a constituency, so you can have a mix of Tory, Lab, LibDem elected in proportion to the share of the vote. However it is better than FPTP. It has to be better to have an MP who is 2nd or 3rd choice of over 50% of the electors than one who is 1st choice of just 27% and no way of knowing who the other 73% would have settled for.
Yes, the other side of AV (and of proportional systems) is a strong likelihood of a coalition government – and I’d be the first to admit that the current government is not a good advert for coalitions. But, coalition governments have worked well in Germany, France and elsewhere (less well in Israel or Italy where the threshold for getting elected to parliament is too low) – and a significant number of our local authorities are run by coalitions. Northumberland CC would be doing better with a coalition rather than a minority administration.
I've written elsewhere about how campaigning with coalitions in mind would (IMO) lead to less negative campaigning and clearer policy arguments - and will probably do so again.
So, on May 5th don’t vote ‘No’ to punish the LibDems (they aren’t worth it!) and don’t vote ‘No’ because you want a more proportional system than AV (because if the Noes win, we’ll be stuck with FPTP for decades) – only vote ‘No’ if you truly believe that FPTP is the best possible electoral system for the Westminster Parliament – otherwise vote ‘Yes’.