Something definitely feels off, but the people don't directly elect the PM. They did for a while (1996-2001) but the governments always failed because they could never hold a coalition. They went back to the old system after that.
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[/SUP]So you are being way too simplistic in your criticism. The people vote for the Knesset and the ruling party has to get a PM elected. The previous coalition to stop Bibi (Far Right and Far Left united to take him down) ended up failing and somehow Bibi was able to put together a viable government. I dont pay attention but my guess is Likud holds a lot of seats and no one else has the power to stop him in the party. They don't have a two party system so it wasn't a black or white choice anyways. Blaming the voters for what Bibi is doing is like blaming people in Chicago for the election of Trump.
If I read right the President suggested Bibi not do this but since the President has no real power (PM is Head of Government) it didn't matter. Likud is risking another split because of this. They are paralleling the GQP way too much. Many of the moderates left years ago much like the Lincoln Project style Republicans here and actually had a viable Party and leadership.
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Unlike here when Trump got elected these people are actually taking action. There were fires in the streets. Highways in major cities were shut down. Full on strikes in the public sector and government jobs and universities shutting down. Airports no longer functional. We handed out cool hats and sang songs...we wait until cops kill Black Men on camera before we do anything of value.