Her main rival was Shaul Mofaz who, as we will see below, made a public fool out of himself after jumping to the Kadima party after publicly announcing that he would never do such a thing.
Shaul Mofaz was the chief of staff of the army and upon retirement went into politics. The most interesting thing about Mofaz is the way that he jumped from the Likud to Kadima. When founder of the party Ariel Sharon formed Kadima, he pulled a large number of ambitious and unscrupulous politicians with him. Mofaz claimed that he was not one of those terrible politicians who would betray the wishes of the voter. As a matter of fact, he sent a letter to that effect to all the members of the Likud.
However, while the letters were still in the mail he decided to join Sharon. It was really fascinating that the Likud members got a letter from Mofaz saying he would never leave the Likud on the same day that the headlines announced that he was leaving the Likud to join Kadima. One would think that after making a fool of himself on the national level, he would hide his face in shame and leave politics forever. But Israeli politicians have no shame, and he stayed on and actually became a serious candidate for leadership of Kadima.
Tzipi Livni comes from a very famous and patriotic family. Her father was Eitan Livni. Eitan Livni, was a member of the Etzel (Irgun) underground during the time of the British mandate. He arranged the breakout from the Akko (Acre) prison. If you saw the movie Exodus with Paul Newman, there was a very vivid portrayal of the prison escape. Eitan Livni was a member of Knesset on the Herut party ticket which was headed by Menachem Begin. Livni's family fought for Israel's independence at the risk of their lives.
Tzipi Livni's prime characteristic is loyalty to her ambition and a creative ability to attach herself to people who can further her personal ambition. With Olmert as prime minister, she was appointed to a series of ministerial positions. She was minister of absorption, minister of justice, and headed several other ministries until being appointed foreign minister. She held five or six ministries in just about the same number of years which simply means that she jumped from one ministry to the next without leaving any impression nor doing anything worth mentioning.
As foreign minister she was as responsible as the prime minister for the fiasco of the war in Lebanon two years ago.