The other poll is even worse for the Israeli right: It shows the current opposition winning a majority. This would likely spell the end of Netanyahu’s rule and bring the center and left to power. On the political Richter scale, it would be an 8-point tremor.

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The usual qualifications apply: Electoral forecasting is nearly as inexact a science as predicting earthquakes. Israel’s multiparty system makes it tougher. A difference of a few votes can determine whether a small party reaches or falls short of the 3.25 percent threshold for making it into parliament, potentially tilting the entire political balance. Elections have not yet been called, though mounting corruption investigations against Netanyahu have fed speculation that he will call a snap vote in the next year.

With all that said, the polls point to a shifting electoral mood. The surveys will shake up politicians’ calculations, especially Netanyahu’s. And they crack one of the more persistent myths overseas about Israeli politics.

Start here: Netanyahu’s Likud Party now has 30 seats in the 120-member Knesset. The polls show it losing up to a fifth of its voters. Many of them would apparently switch to the religious nationalist Jewish Home party, which is forecast to gain strongly.

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If that were the only change, you could attribute it solely to the corruption allegations. The police have formally named the prime minister as a suspect in two bribery cases. In one, he allegedly received expensive gifts from businessmen in return for government favors. In the other, he’s suspected of negotiating a deal for favorable coverage from one of the country’s two major newspapers, in exchange for a law that would hurt the other’s circulation. A third investigation, of suspected bribery in a billion-dollar submarine purchase, has reached perilously close to the prime minister.

In recent weeks, Netanyahu has responded by attacking the national police chief on Facebook. His closest cronies in the Knesset proposed legislation to bar police from investigating a sitting prime minister. When coalition partners objected, his allies floated a bill that would keep the police from recommending to prosecutors that they indict him.

So perhaps some solidly right-wing voters can’t stomach the transparent attempt to undermine the rule of law and are switching to a party with a cleaner image.

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But that’s not enough to explain the bigger picture. Voters are moving from the right to the center, and from the center to the left. The biggest gain in the polls is for the centrist Yesh Atid (There Is a Future), shown more or less doubling its current 11 seats in parliament. The change could be due to corruption staining the right as a whole. It may be a vaguer fatigue with Netanyahu and with the right’s fortress mentality, devoid of any message of hope for peace or for a better economic future for the middle class.

Another data point: Support for Labor, historically the Likud’s rival for national leadership, is down. Labor’s recently elected leader, Avi Gabbay, is a former businessman and a newcomer to the party. His attempts to move the party toward the center have been clumsy and seem to have succeeded mainly in pushing some Labor voters to support the left-wing Meretz party.

Fact is, the tectonic plates of Israeli politics have been moving for a while. The perception abroad, sometimes repeated in news coverage, is that the Israeli electorate is moving ever rightward. Election results say the opposite.

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In 2009, the Likud and what are called its “natural partners,” the four right-wing and clerical parties that prefer a Likud-led government, won a majority of 65 seats in parliament. This brought Netanyahu to power. In 2013 elections, they won 61. In the early elections, they got only 59. The new surveys suggest that they’d now garner 52 to 54 seats.