I think he was trying to be fair to and build some bridges from last week. But he still couldnt bring himself to pick Kate even after Jade's been playing up all week.

Assume that Alex/Kate are now sworn enemies

Each of Jade and Kate had each spent one week on one side and one week on the other...a difficult choice, but Alex's choice wasn't unfair..

Alex suggested to PJ that he thought kate could handle the poor side better then Jade

and Kate would not have picked Alex if it was her position.