Whether AV is complicated depends on your point of view. Under FPTP you can easily find yourself getting into tactical thinking: "I want to vote Labour, but in this area the Tories are stronger. If I was really confident the Tories would win, I'd vote Labour with a clear conscience. But their might not really be quite so strong, and if we don't give them enough votes, the BNP could get one of the concil seats. So I'd better vote tactically for a party I don't want to win to keep out the party I *really* don't want to get anywhere. But I'm doing all this based on reports, and what if the Labour vote is stronger than it seems. Then I'd be voting against the party I really want, and helping keep them out. So maybe I'd better vote Labour after all."

The AV alternative: put everyone in the order you like them.

And they claim the second is more complicated!