You make a good point. For example, the rule of law in North Korea or Equatorial Guinea is whatever the HMFIC says it is. And that's written in law, the police and courts enforce it, all proper and aboveboard in a legalistic sense. Just not in common sense.
As far as the poorest 10%, though: There is always a poorest 10%. And a poorest 50%. If you're in the middle class or higher, you have every reason to prevent the poor from revolting and taking what you have. This can be accomplished by a vast array of carrots and sticks. Some countries lean more toward the carrot - we call them liberal democracies. Autocratic states use the stick.
But although greater wealth inequality may be a good indicator of the tendency of the lowest 10% to become lawless, it is not a good indicator of which method is used to keep them in check. Cuba has pretty amazingly low levels of wealth inequality - essentially everyone's poor. Keeping them from rebelling, however, is all stick, precisely because any kind of economic carrot would undermine the philosophy that it's better for everyone to be poor than to have wealth inequality.
As far as the poorest 10%, though: There is always a poorest 10%. And a poorest 50%. If you're in the middle class or higher, you have every reason to prevent the poor from revolting and taking what you have. This can be accomplished by a vast array of carrots and sticks. Some countries lean more toward the carrot - we call them liberal democracies. Autocratic states use the stick.
But although greater wealth inequality may be a good indicator of the tendency of the lowest 10% to become lawless, it is not a good indicator of which method is used to keep them in check. Cuba has pretty amazingly low levels of wealth inequality - essentially everyone's poor. Keeping them from rebelling, however, is all stick, precisely because any kind of economic carrot would undermine the philosophy that it's better for everyone to be poor than to have wealth inequality.