As I see it there are a number of ways of looking at this.
(In any case I'm unsure a second choice vote should carry the same weight as a first choice. Value should half each move surely ?)
Anyway, either a change will make no difference to the result, or it will make a difference.
If in practical situations changing the system turns out that the middle-of-the-road candidates always go out first, leaving the field as a straight choice between left and right, then we are just wasting millions of £s to make a few folk feel better.
However if changing the system tends to result in either the left or right candidate going out first, then few votes are going to switch for the candidate with the opposing view, so middle-of-the-road candidates pick up any movement, and have been given an advantage.
Would this be a good thing ? You'll reduce the chance of enacting any extreme measures that could need to be done in order to sort something. You'd have compromise in all legislation. And as a consequence many more coalition compromise governments than before with the usual problems that entails..
In fairness the AV is the best of the alternative systems, since at least it doesn't make it even harder to separate parties from parliament, and it is obvious that a candidate that has to toe a party line can't at the same time guarantee to be voting according to their electorates wishes, so parties are the antithesis of democracy. But whether it is better than the current system is very debatable.
IMO the claim that present day MPs are elected with more folk voting against them than for them is patent nonsense. When you vote for a candidate it is a vote for someone, not against someone else. I think this is just trying to make folk feel better when the candidate they didn't really want but could suffer if need be, gets in. Something to keep the proletariat content and quieten them