TEL AVIV—The man predicted to win Israeli elections if they were held today picks a seemingly contradictory way of describing himself: “an extreme moderate.”

Once dismissed as a passing fad, Yair Lapid, a 53-year-old former TV anchor, has emerged as the most serious political rival to Prime Minister Benjamin Netanyahu. And he has done so by trying to dispense with the traditional left-right divide of Israeli politics, adopting instead the vague but resonating language of ”sanity” and “responsibility.”

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