Nothing. Israel is nothing more than Little Amerika-- and Amerika would never countenance being tried internationally.
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International institutions work for the status quo, nothing will fundamentally change with a verdict.
I'd say what happens when the UN passes a resolution on a ceasefire? Someone has to enforce it and the US is the only one isntreal will listen to.
Short of another country literally invading to enforce it, it's very likely nothing will happen.
The point of comparison is the pressure campaign against apartheid in South Africa, which took decades to succeed.
A ruling that Israel is committing genocide could provide a lot of cover to expanding boycott/divest/sanction activities (this happened to South Africa over less, including high-profile actions like banning them from the Olympics for 30 years), and those combined with the ruling itself could solidify public consensus against Israel. Imperial governments don't run on consensus, of course, but public discussion could go from "you must support Israel to run for even local office and you're an antisemite if you don't" to a contested issue, to being a liability.
This would work more quickly outside the imperial core, and as the U.S. declines that will matter more as every year passes.
EDIT: It would also have secondary impacts on all the other accusations of genocide that are tossed around more and more casually.
While I doubt much tangible would come from such a ruling (if they will rule properly to begin with)- it will be yet another nail in the coffin for US and Israeli narratives and legitimacy worldwide- and another nail in the coffin of the ICJ and the "rules-based international order" as well, if they (predictably) rule otherwise. Whatever way it goes, I expect it will simply be another reminder to the vast majority of humanity of the true nature of the western states and elites- that the western imperialists are not existing in the same reality as the poor and colored masses they see as nothing more than vermin to be exploited or exterminated, and that all they offer the world is empty platitudes, hypocrisy, and treachery.
Maybe I'm being overly pessimistic- but I don't see Israel likely being banned from the Olympics and various other international events, and I don't see much cover being granted to BDS activities in the west- particularly not AmeriKKKa, which has a history of if anything, trying to force the opposite on its citizens. I don't think it would even matter if the majority of the population in the west were anti-Israel in this regard; the veneer of democracy is already rapidly fading away, and Israel has played its cards right in lobbying and ingratiating itself into western politics to an extent that apartheid South Africa never managed.
I don't think change will come from the imperial cores. Red Nazi, blue Nazi, or orange Nazi, all the same, all the various different Nazis love Israel and recognize its necessity as the genocidal chokehold of western influence in the region- their unsinkable aircraft carrier to permanently destabilize the Muslim world. If change will come it will come from the Arab client-states of the west breaking fully away from the devil west- from Arab, Iranian, Russian, Chinese, South African and other pan-African, BRICS, anti-imperialist actions, IMO.
nothing. it will be in the news cycle for a few days at most and everybody in the west will forget about it.
From what I can tell a likely scenario is:-
- ICJ correctly rules on genocide, provisional measures are supposed to then come into effect
- Israel flouts the rules, withdraws from ICJ
- Issue is forwarded to the UN security council
- America uses its veto against any security council measure against Israel.