I can't be bothered to explain it all fully but the smaller parties would still need an overall 50% of the vote, either by 1st choice of choices after that, the big 3 will (nearly) always get far more 1st choice votes and if they don't they will easily make up the difference to 50% from 2nd/3rd/4th choice. With AV there is more chance of people voting for a smaller party as 1st choice because they know their backup can be a big party.
I've probably explained this very poorly, but thankfully someone else will step in and explain it better.