This was a difficult vote for me, I voted for Edin Džeko in the end and I'll explain my rational as to why.
Hart and Kompany ended the season very strongly but it can't be denied that at the start of the season, they had difficulty adapting to the high defensive line.
Zabaleta has been outstanding all season and I would have voted for him.
However, the most improved 4 players over the course of this season have been Kolarov, Demichelis, Garcia and Džeko. They are also the 4 who we as fans seem to abuse above all others. I've lost track over the last 3 years if the amount of times they have been called wank, shit, cunts etc. I won't lie, I've done it myself (only when at the end of my tether though, usually reactionary after a bad loss). It's perfect how these 4 were the ones who were mainstays in the team for the last few matches. Demichelis commanding the defence. Kolarov attacking like a winger and doing his duties defensively, winning every header against Villa and West Ham's long ball tactics. Garcia anchoring the midfield and letting Yaya go forward and put teams to the sword. And Edin Džeko leading the line when all of our other strikers were injured and out of form. First goal against Palace, 2 against Everton, 2 against the swamp dwellers, 2 against Villa.
So yeah, for me it's Edin purely because he started the season playing as he has done for the last few seasons, but has ended it as one of the league's best strikers.