Nothing, says rabbi historian Dr. Marc Shapiro.
In his first lecture on Rav Zvi Yehuda Kook for Torah in Motion, Dr. Shapiro says: "What were R. Meir Kahane‘s accomplishments? How did he influence the state of Israel? He got his party banned. Had he remained in the knesset and achieved numbers? He had no lasting contributions. Gush Emunim had enormous contributions. Right before Kahane was killed, polls showed he was going to get ten seats in the Knesset, which is why they had to ban him.
"Kahane was the first one to call attention to the demographic threat.
"I went with my father to interview Kahane in Israel in the 1982.
"Kahane had no real Israeli following. He had more influence in America. He was the one who brought Soviet Jewry to wide attention. He started the shomrei patrols. Even that was an influence for 10 or 20 years, but it doesn’t live on.
"He lives on in Igrot Moshe. One of the responsas about bat mitzvas is addressed to Meir Kahane when he was a rabbi in Bensonhurst."
In a recent listing of the top ten people who have influenced the modern state of Israel, only one rabbi made the list — Rav Zvi Yehuda Kook.
Dr. Shapiro says that the religious Zionists account for twice the number of Israelis of voting age as the charedim yet it seems that the charedim hold all the cards.