Just think of the damage that Shimon Peres (whom nobody voted for) is now in a position to do.
Prime Minister Sharon had to make up a new position and pass a new law to find a place for Shimon Peres. Ehud Olmert is still the one who would stand in for the Prime Minister when he is unavailable. In other words I doubt Shimon Peres has any real power.
The Prime Minister is, first and foremost, a politician. He did what he had to do to cobble together a new coalition with 13 of his own party's MKs in revolt. Likud has effectively split in two and the Prime Minister only had 27 seats from his own party. He needed Labor's 21 and Shimon Peres is the leader of Labor.
Why do you think the Prime Minister is negotiating with Shas again? On paper his coalition has 66 seats. In reality it has 53. He still needs the 11 from Shas.