You almost got what the shari3ah actually says in these matters without having studied it. Nice job pilot!
However, there's several misunderstandings (that everyone who has posted has) I'd like to try clarify:
Here's the deal with "Sharia" law in non-Muslim States like the USA, Britain, many others...
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"The Law of the sharii3ah" would be a better term. sharii3ah is not law itself. The word itself derives from shar3 i,e, a path you take. The feminine form sharii3ah gives it constancy and longevity i.e. it is your usual commuter route. There's laws of the road that apply to the traffic, but the road isn't itself law! The sharia (dropping the convoluted spelling convention) includes therefore the creed, the acts of worship, a worldview etc etc, and yes, laws.
I'd even improve the term to "The Law of the CURRENT shariah". The sharia has reached its culminative version, butprevious ones not only existed by continure to exist, concurrently as well as part of the current version. For example, some parts of the previous sharia, which you'd have heard called as the Mosaïc Law or the Halakha, were not updated and remain unchanged, e.g. no new revelation came, wAllahu a3lam, about the adulterer and the Jewish punishment of stoning continues.
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So long as there is no actual crime, parties are free to pursue judgement by whatever means they desire. Let's say two Muslims agree to abide by a ruling given by a cleric. They can go before him, state their case, and allow the cleric or mullah to decide. This is simply a different form of arbitration.
The thing is, the ruling is not legally enforceable. The cleric cannot FORCE one man to pay $$ to another, for example. And of course, he cannot send someone to jail.
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You're talking about the law part of the sharia, and specifically in case of a parallel law of the land prevalent, arbitration. Arbitration is voluntary but binding once arrived at at least in the U.S, so in that country there's that element of obligation ("...legally enforceable...") that you refer to. Same here in Pakistan.
One thing you got wrong if the "cleric". Since there's no clergy and no church, the person who you actually want to refer to is the judge, and in this specific case, the arbiter. Otherwise, the judiciary tries to ensure correct judgement and the executive its enforcement.
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So the reality is that there are little snips of Sharia all over the world. It happens every time two parties seek counsel on a dispute and agree to abide by the decision of the judge.
Exactly.
As a case in point, your country's legal system is quite compatible with the sharia, except in some areas where it isn't. Of the top of my head I can think of e.g. waiver in punishment in exchange for making testimony etc. I'm not a law person so can't help you with these.
When you're in court, the process of decision works through similar logical steps. But outside of it, the sharia is a very vast concept, and the Americal Muslims polled apparently do not know about the creed they profess to represent, a malaise fairly universal today, along with the second: deciding without knowledge "no the sharia doesn't apply", "yes organ transplant is permissible", "yes suicide bombings are ok", instead of "I. DON'T. KNOW".