It happens today in business contracts. When signing a contract with another business, both agree on a single court will uphold your agreement or be arbitrators.
Arbitration is also actually way more cost effective than court of law. Used all the time and in a private manner. Trying to reach settlement, with an independent 3rd party, before the case sees the light of public scrutiny.
With the business contracts they agree on using a particular public court of law, or a private one?
I was more curious about the example above regarding externalities. Like a toxic chemical dump due to gross negligence or willful planning.
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About half of the legal systems in the world are called "Civil courts." They are wholly separate from the criminal courts run by the state's judicial branch.
Private law is just as common as state law in most countries. You may have used civil courts already without knowing you did so, such as if you bought real estate.
Cases with externalities like toxic dumping usually wind up in the criminal courts, but that really depends on if there was a pre-existing contract between the plaintiff & defendant.
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