What happens to the precedent (or whatever their interpretation is called) of the judicial branch when a constitution (like in the USA), is amended?
Like, if a constitution said some meats were stupid and bad, and a court case decides that ham is totally chill, and isn't part of the "some meats" group; but the constitution gets amended to say that ham is also stupid. Given this example, what would happen to the court precedent, and the world that's gotten used to having legal ham?
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In an entirely non-technical sense, the courts would decide based on the current law. So when a law is changed (or the Constitution amended), the courts' rulings may change.
In your example, once the anti-ham amendment is passed, it would be expected that the courts would rule according to the current law (which makes ham illegal).
The courts may still use past cases as precedent, but on other specifics of ham-related jurisprudence. For example, does the current law make Canadian bacon illegal? Unless the new amendment specified what "ham" is, the court may use precedent to determine what counts as ham.
As far as the rest of the world - they will have to adjust. Some people might choose not to comply, but they will risk the penalty for consuming ham.
If an appellate court interprets a constitutional clause, that interpretation only has precedential weight as long as the clause (and other clauses it interacts with) go unchanged.
Some aspects of the original interpretation might have some persuasive weight on the way the new clause is interpreted (for example, if the new clause uses language that the court previously used or interpreted). But other than taking potentially persuasive guidance from that kind of interaction, a new constitutional clause is interpreted de novo (anew, without deference to previous interpretations).
An example of this can be found in State Board of Equalization v. Young's Market Co. 299 U.S. 59 (1936). The Supreme Court had to interpret the newly ratified 21st Amendment which ended prohibition.
Prior to the Twenty-First Amendment, it would obviously have been unconstitutional to have imposed any fee for [the privilege of moving beer across a state border].
But, the 21st Amendment changed that (cleaned up):
The amendment which prohibited the transportation or importation of intoxicating liquors into any state in violation of the laws thereof abrogated the right to import free, so far as concerns intoxicating liquors. The words used are apt to confer upon the state the power to forbid all importations which do not comply with the conditions which it prescribes.
The precedent loses power. Here is the US Constitution, Article V:
...amendments to this Constitution shall be valid, to all intents and purposes, as part of this Constitution.
Article VI adds:
This Constitution, and the laws of the United States which shall be made in pursuance thereof, (...) shall be the supreme law of the land; and the Judges, in every State, shall be bound thereby; any thing in the constitution or laws of any State to the contrary notwithstanding.
