By Meditations of a Madman
A quick thought experiment:
Imagine a society wherein a murderer, lets call him X, is sentenced to death. Because specificity here helps with the experiment, let say he will be executed by hanging.
And let's assume that, by whatever mechanism, the whole of that society has determined that such a punishment is 100% just.
However, imagine that in addition, the victim's spouse is overwhelmed by a desire for revenge.
Upon X's execution, everyone will get the positive emotions associated with recognizing that justice has been served, including the spouse, however the spouse will still be left with a negative emotion, the desire for revenge, and potentially a new, additional negative emotion, the regret of now never having the opportunity to exact that revenge.
If we allow the spouse to actively contribute, in this case, put the noose on, pull the lever so-to-speak, or at least give out the order to do so, then to whatever degree the victim feels their revenge satisfied, the whole of society is made better off. It would be Pareto efficient.
All of society would feel the same positive sense, and the spouse would feel net-net more positive emotions.