AV is fairer because politicians need the support of most voters.
AV is fairer because you dont have to vote tactically - you can vote for who you really want, in order of preference.
So AV is a system that makes most people happier.
Giddy - everyone votes for who they really want with their 1st choice like the tory and labour leadership system
if no-one has the majority (over 50%), the candidate with least votes is eliminated like the tory and labour leadership system
Their votes then count for their 2nd choice. The other voters still count for their 1st choice. like the tory and labour leadership system
The candidate with least votes continues to be eliminated and votes reassigned until one has over 50%. like the tory and labour leadership system
Your example of the way David Cam was selected is a good example. On 1st choices, David Davis would have won (like FPTP). But most people actually didnt want him. After further rounds (like AV) they found most people prefered Dave Cam. This is exactly what AV does.