The trouble with the word 'coalition' is that we naturally think about it in terms of the current system, but it ain't necessarily so.

Take an issue like Europe. It is perfectly feasible for a pro-Europe Conservative and an anti-Europe Conservative to stand in the same election. One imaginary set of results is shown here:-

Pro - 20%
Anti - 25%
Labour - 30%

Here there is a clear overall Conservative lead, but under FPTP the Labour would win because of the Tory split. But under AV, the 'Anti' would win - with exactly the same overall margin as if a single Conservative candidate had stood in the first place. However, the voters have also given him or her a 'mandate' to take an 'Anti' stance.

In government, there is still (probably) a coalition, but it would be between the two wings of the Tory party, not two parties. So that's my message: want a vote on Europe [or other issue of your choice]? Vote yes to AV!