The ultimate goal of legal research is to find the relevant primary law (statutes, regulations, cases, etc.) that governs your legal issue. Ideally, you are looking for mandatory authority - that is, primary law that is binding on the court that you are appearing before. Sometimes, though, it can be tricky to determine whether a bit of primary law is mandatory, and sometimes you may have to resort to persuasive authority - that is, primary law that is not binding, but that may be instructive for the court. This page provides an overview of the mandatory vs. persuasive authority distinction.
Higher courts bind lower courts within their particular state or circuit.
Remember the State/Federal distinction - state courts usually bind only courts within that state, and federal courts usually bind only courts within that circuit.
But things get weird when Federal courts apply State law...
For many legal issues, there may be federal and state constitutional provisions, statutes, or regulations on point. While federal law generally trumps state law, this is not always the case. It is possible that both laws may apply, or even that only the state law will apply.
The U.S. Constitution provides a floor of protections, not a ceiling. That is, state constitutions may provide additional protections. Where such a conflict exists, the state constitution will govern in that state's courts.
The same may hold true when federal and state statutes or regulations conflict as well. For example, California law explicitly provides for protection against employment discrimination on the basis of sexual orientation, while federal law does not. In California, this state law will apply. However, if the conflict occurred in the opposite way (i.e., federal law provides a protection that state law does not), the federal law would apply.
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