argument, AV

From elsewhere, to serve as inspiration for more complete considerations of the two topics:
Never end with your conclusion! This has caught me out many times before: I build up to it as if making an argument, when what people need is an arbitrary opinion first that you might or might not justify afterwards. What comes first sticks in the mind, so if you start with basic points, consider alternatives, dismiss them and finally lead into the undeniable conclusion you'll have lost people at every turn, and you'll be left with people who don't understand and call you illogical or confused.
If you proceed illogically, with conclusion first and then a few of the more solid justifications, ignoring possible holes or complaints, then you're called a precise and admirable thinker.

Anyway, about AV, anything is preferable to FPTP. Every complaint about the representation of AV can be levelled in some form at FPTP.
For example, the idea that back-room deals between parties after elections are somehow less representative than back-room deals within parties before elections is ridiculous. In FPTP we are limited to two or three major parties, providing us with little real choice. Any AV, AV+ or PR system is likely to give us more choice in party, and therefore each party will better represent its voters. That we'll still have to have compromise in order to have one government doesn't change; what changes is that the compromises will take place on the basis of how many people vote for it, rather than within parties on the basis of what they can get away with.