Some imperial Chinese officials who admitted to the use of substitute criminals justified its effectiveness. After all, the real criminal was punished by paying out the market value of his crime, while the stand-in’s punishment intimidated other criminals, keeping the overall crime rate low. In other words, a “cap-and-trade” policy for crime.That, of course, is nonsense. You could get the result in a simple model where every agent is identical. When everyone is identical it is easy to talk about the right tax level to internalize the externalities of your crime because everyone faces identical constraints with identical preferences. But one of the obviously important facts is that a stand in and the criminal perceive the cost of the punishment differently (or the benefit or the money exchange) hence the "trading" of places.
How much do you think Li Gang's son would have to had to pay for the college girl to accept being murdered? That is the real "market price" of his crime, not the amount the lowest bidder is willing to pay to be executed.
And hasn't the CCP ever heard of public goods? Do you think Li Gang's son has enough money to compensate the hundreds of millions calling for his head, each of whom would gladly pay a few yuan to watch him die? I think in CCP logic he should be executed to ensure the "Pareto efficient" outcome.*
* - Yes, that is sarcastic. Pareto efficient means all parties are better off or at least as well worse after the trade. Surely Li Gang's son would not agree to die even for that enormous "market price" any more than the woman he killed would have agreed to die for the CCP dubbed "market price" of her life.