It is not true that 1/120 of the vote gets a seat. It is %1.5 minimum (almost double 1/120). Also, surplus votes are redistributed proportionality according to the size of the various parties, with the exception that parties can make public redistribution agreements with each other prior to the election. 2,500 eligible voter signatures, a platform, and a list of candidates are required for a party to compete.
Elections for the Knesset are held when any of the following happens: Knesset rejects the list of ministers proposed by the prime minister, 61 Knesset members vote no-confidence in the prime minister, no budget is agreed upon within 3 months of start of fiscal year, the Knesset votes to dissolve itself, with the president's consent the prime minister resigns and dissolves the parliament.
An election for prime minister is called if 80 (2/3) or more Knesset members vote for election, if majority of Knesset votes against prime minister following conviction for offense categorized as moral turpitude, if prime minister fails to appoint minimum eight ministers, if prime minister is permanently unable to function as such (death or disability), if prime minister resigns.


James wrote:
Israel uses closed party list in one national district. This is the
worst possible combination of all PR systems. Any group that can secure 1/120th of the national vote will get a seat in the Knesset. This give representation to very small groups which makes it possible for the extremes of the political spectrum to gain representation. The system does not encourage them to seek any accommodation with those of less extreme views. Allied to this is the effect WITHIN parties of the closed list. The candidates of a minority faction within a party may be included on the party's list to ensure that the faction's supporters vote for the party, but those candidates will be placed well down the closed list so that they have no chance of election. To overcome this, the faction splits off to form its own party, when its candidates will, of course, be at the top of its own list. If it can secure at least 1/120th of the national vote, it will get at least one of its candidates elected. This is what has happened over many years in Israel.


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