It seems to me that you run into the mathematical problem again when trying to calculate the expected utility of its decision process. Some of the outcomes of the decision process are associated with utilities of 3^^^3.

Perhaps. I don't have the math to see how the whole calculation would go.

But it seems to me that the utility of 3^^^3 is associated with a particular execution instance. However when evaluating the decision process as a whole (not the individual decision) the 3^^^3 utility mentioned by the mugger doesn't have a privileged position over the the hypothetical malicious/lying individuals that can just even more easily talk about utilities or disutilities of 3^^^^3 or 3^^^^^3, or even have their signs reversed (so that they torture people if you submit to their demands despite their claims to the opposite).

So the result should ideally be a different decision process that is able to reject unsubstantiated claims by potentially-lying individuals completely, instead of just trying to fudge the "Probability" of the truth-value of the claim, or the calculated utility if the claim is true.