If we had no 'authority', what would be the difference between them and us?
For many God is the authority, and for others it is the law, and the police.
I understood you to mean that people would behave properly, and with ethics, if left on their own.
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Right now we have boh religions and governments either protecting people from heir mistakes or giving them an excuse for their abuses of their fellow humans. Without POWER inherent in governments, all you have are individuals dealing with each other.
Social mores and standards regain importance. How are you going to buy groceries if no one in town will sell them to you because you are an a$$hole? Or a known pervert? Or a Satanist in a town of Christians? Or known for renegging on contracts or debit?
Anarcho-capitalism begins by assuming everyone is their own Master and no one other person has soverign Rights over another or their property. Dealing with each other as equals just follows from that. As does keep a close on on each other with a certain amount of distrust. This works a lot better than just excusing peoples behavior, setting up power structures rife with abuse to try and get segements of the population to "behave", and makes the consequences of your actions that muh more immediate and important to every individual.