This is the heyday of female leadership in Israeli politics. The election of Shelly Yacimovich to head the Labor Party, Zahava Gal-On to head Meretz and Tzipi Livni's declaration to run on January 22 as head of her new party Hatnuah have created a new and fresh situation. Without referring to these leaders' political positions, we have to admit they represent clean, high-quality management. For the first time, there is a chance that a female discourse less violent and more intelligent than the macho male version will take center stage.

Livni's declaration has created shock waves; the biggest loser is Yesh Atid's Yair Lapid, but other parties have been weakened, too. Yacimovich recently called on Livni to join forces with her and described her running independently as a bitter mistake. Livni's refusal to be number two gave the impression of an ugly ego struggle.

But that's a mistake. Analysts say Livni, Yacimovich and Gal-On belong to the same center-left bloc and that Livni's decision will split this bloc, but this argument doesn't hold water. Meretz, Labor and Hatnuah represent different positions, so they don't need to unite or compete for the same votes.

Among the three, Meretz is the only left-wing party, so all those who believe in a diplomacy-friendly and social left should vote for Gal-On, or at least not waste their votes on parties to the right of Meretz, even if these parties sometimes pretend they're left-wing. If that's what happens, Meretz is likely to be much stronger than what the polls are predicting.

To Yacimovich's credit, she has admitted that the Labor Party under her leadership, like its predecessor Mapai, isn't left-wing but rather centrist. Yacimovich's support for the "settlement enterprise" and Operation Pillar of Defense has embarrassed many people on the left, but that embarrassment merely reflects shortsightedness.

It would be fitting for Livni also to show her cards so as not to mislead the public. She supported bringing down Hamas, and still does so. She backed a ground operation in Gaza during Operation Cast Lead and the prolonging of the operation, contrary to the opinion of Defense Minister Ehud Barak.

Nowadays, Livni is talking about strengthening Palestinian President Mahmoud Abbas and is trying to wear the mask of the left in diplomatic affairs. But we must remember that, in the Kadima government's talks with Abbas, Livni held positions that were more right-wing than those of the prime minister at the time, Ehud Olmert. And there is no evidence she has changed these positions. Her declaration earlier this week that she was running opened with comments about our right to this land.

Livni was born in Likud, and in the 2009 election she played the role of the Trojan horse and destroyed Israel's left. Even people who traditionally supported Meretz bought the slogan "Either Tzipi or Bibi" and with amazing naivety supported the right-wing Kadima party, destroying their home with their own hands.

This manipulation - whether in its original version or the version "Either Shelly or Bibi" - must not be allowed to return in the 2013 election. Livni must make clear that Hatnuah is a sane right-wing party and must erode the strength of Likud, which has become an extremist right-wing party in the wake of its primary. It must not erode the strength of Yacimovich and Gal-On.

Gal-On, Yacimovich and Livni are high-quality leaders who offer a discourse of hope in various shades. Together they cover most of the political spectrum - left, center and right. If the voters in this broad spectrum choose them, we may have a chance for a different kind of Israel - with a woman at its helm.