Four days before the Labor Party leadership primary, Ehud Barak and Ami Ayalon are running almost neck-and-neck, with Ayalon slightly in the lead, according to a new Haaretz-Dialog poll.

However, the survey results make a first-round victory for either Barak or Ayalon unlikely, as neither is close to the 40 percent support that this would require. Nonetheless, 9 percent of voters are still floating, and their eventual decisions, combined with a continued drift away from the hindmost candidates, Danny Yatom and Ophir Pines-Paz, could still enable one of the front-runners to eke out a first-round win by handful of votes.

According to the poll, Ayalon has the support of 34 percent of party members, compared to 30 percent for Barak. Peretz garnered 17 percent, while support for Pines-Paz and Yatom stood at 8 percent and 2 percent, respectively.

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The poll also found that 44 percent of Labor members believe the party should remain in the government at least until the Winograd Committee, which investigated the Second Lebanon War, publishes its final report in the summer. Another 25 percent say that Labor should stay in only if Prime Minister Ehud Olmert either steps down or sets a date for new elections, while 21 percent believe the party should quit the government immediately under any circumstances.

Ayalon's position in the lead comes mainly from the fact that he has slowly but steadily been gaining votes from both the Pines-Paz and Yatom camps. However, the efficacy of each candidate's get-out-the-vote machine on election day can often swing the outcome, and both Barak and current party chairman Amir Peretz are thought to have better party machines than does Ayalon. Moreover, it is hard to predict the voting patterns of certain key sectors, like the Arab and Druze communities.

Surprisingly, Barak outpolls Ayalon on many key issues. Some 50 percent of respondents termed him the candidate with executive experience, compared to only 18 percent for Ayalon; 35 percent believe that Barak can defeat Likud Chairman Benjamin Netanyahu, compared to 29 percent for Ayalon; and 45 percent view Barak as a suitable defense minister, which is the position awaiting the new Labor chairman in the current government, compared to 30 percent for Ayalon. On the question of who would be the better prime minister, they tie.

However, Ayalon wins hands-down on integrity, with 34 percent of respondents deeming him honest, compared to only 13 percent for Barak. Some 35 percent also believe that he would bring Labor more seats in a general election, compared to 28 percent who deemed Barak the better vote-getter. Finally, respondents tapped Ayalon as being better able to unite the party behind him.

More importantly, however, many Labor members still hold a grudge against Barak due to his last stint as party leader, whereas Ayalon carries no such baggage. That is why the poll shows Ayalon easily defeating Barak in a runoff should neither win a first-round victory.