JERUSALEM — Speaking to a group of ultra-Orthodox men shortly before he officially entered politics, Yair Lapid, a proudly secular talk-show host, declared that in a century-long competition to define Israel’s character, “we lost and you won.”

“Not only in terms of numbers,” Mr. Lapid said in late 2011 at a college for religious students, but also in politics “and as a consumer force and in the streets and in the culture and in the educational system — you won in all these places.”

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