Another Counter-example to Act-Utilitarianism from Punishment?

I recently thought about another counterexample to Utilitarianism. I don't know if it is already in existence, but I thought I'd share it with you here.

First we must establish what Act-Utilitarianism (AU) is. I take AC to be the following:

(AU) An action is right just in case it maximizes overall well-being.

AU presupposes that the only intrinsic good is well-being. Hedonistic Act-Utilitarianism (HAU) holds that well-being = pleasure/happiness in the absence of pain. So that HAU is:

(HAU) An action is right just in case it maximizes overall pleasure in the absence of pain.

So, what you morally ought to do, given AU, is that which produces the greatest amount of well-being, from among the available options, for the greatest number. HAU just equates this well-being with pleasure for the greatest number.

The counterexample is as follows.

Suppose Joe decides that he wants to brutally murder once and only once. So, we can suppose, that, if Joe murders, then Joe will not murder again. Further suppose that, after Joe murders, he will not commit any other crime. So Joe brutally murders Sally. But let's flesh out "brutally" so that it is vivid to us. Joe causes Sally to experience excruciating pain in the process of murdering her. Did Joe do something very wrong on AU and HAU? Well, certainly he did. Joe didn't maximize well-being. In fact, Joe produced less well being. But, given AU and HAU, ought Joe be punished?

In order to answer this question, let's inject more data into our scenario. Suppose a police officer, Jack,  and only Jack (other than Joe himself), knows that Joe brutally murdered Sally. Jack has to make a decision here, in virtue of his being a police officer. He has to decide whether or not to punish Joe by putting him in prison for his acting immorally. So Jack will either arrest Joe and put him in prison, or he will allow Joe to continue living an otherwise normal, happy life. What ought Jack do?

Here I think we need to point something else out about AU and HAU. AU and HAU aren't to do with expected consequences. AU and HAU are to do with actual consequences. So if I do A, and I expect A to cause good consequences, then, if A results in bad consequences, then A is wrong. So my expectations are irrelevant.

Now we can answer our question. One might be tempted to say that Jack ought to throw Joe in prison because Jack has the rational belief that Joe is likely to murder again in virtue of the fact that he has already murdered. But this would be mistaken. Remember, what actually is is that Joe will not murder again. So Jack's expectations, though reasonable, do not constitute a reason for the view that Joe ought to be punished. What is the answer then? Given AU and HAU, ought Jack punish Joe? No! It would be very wrong for Jack to throw Joe in prison. Why? This will minimize well-being and pleasure. If Jack punishes Joe then you have Sally's well-being minimized + Joe's well-being minimized. If Joe is allowed to live a normal life you have only Sally's well-being that has been minimized and Joe's well-being is maximized when compared to the alternative of punishing him. The same thing with pleasure. You have a net reduction of pleasure if you punish Joe because that would be a reduction in pleasure for both Sally and Joe whereas allowing Joe to live a normal, happy life produces more happiness; only Sally's pleasure is reduced. So Jack ought to allow Joe live a normal, relatively happy life. It would be wrong of Jack to throw him in prison.

This, I think, is another compelling reason to reject both AU and HAU. Consider the following argument:

(1) If AU (or HAU) is true, then it would be wrong for Jack to punish Joe.
(2) It is not wrong for Jack to punish Joe.
(3) Therefore, it is false that AU is true.

As I have argued, (1) is true. (2) seems utterly obvious. In fact, it is not only not wrong to punish Joe, it seems that punishing Joe is what Jack morally ought to do. So I think we have a good reason to reject AC and HAU on the basis of this argument.

One might be tempted to argue that the outrage of the community at Sally's death is enough to warrant punishing Joe, to give the community a sense of security and closure. But this can be done away with as follows. First, we have assumed that Jack is the only other person that knows Joe committed the crime. We can further stipulate that Jack and only Jack (in addition to Joe) knows that Sally has been murdered, so that nobody would be outraged if Joe went free. Second, to make AU and HAU more implausible, we can suppose that Sally is a Latina in a community of white racists. We can suppose that the community wants Joe to go free, likes that Sally is dead, and would be very upset if Joe were put in jail. This, yet again, tips the utility scale in favor of Joe's going free, for putting him in jail would reduce his and the community's happiness. This makes AU and HAU even more implausible.

So now the Utilitarian must bite another bullet. For the rest of us, Utilitarian has suffered the same fate as views like verificationism: it is part of the ash heap of philosophical history.