Commentary on the Parable of the Three Executioners
1.
In the parable of the Three Executioners what are the incentives?
They could all agree to desist from the execution. But in order not to be the third to fire they would have to monitor one another. In order to be the second to fire they would have to monitor one another.
So that they wouldn't have to monitor one another they would have an incentive to murder each other. If one were to murder the others he could comfortably not execute the condemned man and live out his life however he saw fit. He could not claim the reward of the Emperor of Meshica but he would not have to worry about the execution.
If one were to murder only one other there would be an incentive to murder the third but there would also be an incentive to induce the third to execute the condemned. This could be done by feigning a first shot from the murdered executioner and waiting for the third to fire as a matter of course, thinking it the second shot. Or it could be done by tricking the third into thinking he was murdering someone else but substituting instead the condemned man.
At that point, the tricky executioner would not strictly speaking have to fire in order to avoid the condemnation of the Emperor of Meshica. Of the two other executioners one would be dead and murdered and the other would be executed for shooting first. But in order to claim the Emperor's reward they would have to shoot.
So the condemned man's best chances exist if one of the executioners murders the other two.
On the other hand, if the condemned man were to murder at least two of the executioners he would be clear. The remaining executioner could not kill him because of the resulting condemnation of the Emperor of Meshica for firing first. If the condemned man murdered all three executioners he would also be free. If we were to assume there are externalities to the act of murder it would suffice to murder only two of the executioners. Provided, that is, that the remaining executioner know and have good reason to know that the other two were dead. The balance of externalities between three murders and two public murders is a more subtle calculation that is context-dependent.
2.
There is no reason the murder of the other executioners could not occur after the execution. So that one executioner, firing either first or last, would have a strong incentive to murder the others and then to tell the Emperor that he in fact fired second. Or an executioner at a time convenient for the action could execute the condemned and then after arrange to murder the other two.
This would also be a factor in the executioners' plans. It would generally tempt the executioners to keep constant watch on the others or at least on the condemned. Unless they were to murder the others.
3.
By tradition the Three Executioners' names were Beinn, Gracile, and Zidane.
The condemned man's name varies widely with the telling of the tale. The most common variation simply says that his name is completely lost to knowledge because of a damnatio memoriae pronounced by the Emperor of Meshica.
The parable typically omits mention of the thing that would be most important for the mechanism to exist at all—some sort of monitor or arbiter who could confirm the order of shots. Presumably the addition of yet another person takes away from the neat symmetry of the tale. There is an awesome force to the idea of the Emperor of Meshica, and no intermediaries, enforcing the rules of the execution no matter where the condemned man may wander—even over continents and seas—rather than a sober representative of his going around officiously with spectacles and a stopwatch.
Some authors have written about the scenario of the Three Executioners addended by an Emperor's Witness. Naturally there is an incentive to win the Witness over to one's side. An executioner corrupting the Witness could simply execute the condemned man and claim a reward when the Witness falsely reported he was the second shooter. The Witness would have to be prepared to fend off attempts by the others to murder him—which might well be part of the pact struck with the corrupting executioner. The Witness could also try to strike a pact with all three executioners. This could offer protection from pre-emptive murder and also guarantee some share in the reward.
Other variants, as thought experiments rather than parables, have sprung up in the literature over the past 50 y. They are sometimes a sneaky joy to consider—in one's study while drinking tea and smoking yahl. The tale itself without complications is often better yet. Like three lines of a death poem beside the corpse of a disgraced courtier.












