Gunpowder and Game Theory: Gilbert's Utopian Government
In Gilbert and Sullivan's penultimate opera Utopia (Limited) W.S. Gilbert proposes a system of government designated “Despotism tempered by Dynamite.” According to this system, the land of Utopia is governed by a King who wields absolute autocratic power, but is supervised by two Wise Men. If the two Wise Men feel the King is abusing his power, they denounce him to the Public Exploder. The Public Exploder then blows the King up with dynamite, at which point the Public Exploder becomes the new King. The result, according to the opera, is “an autocrat who dares not abuse his autocratic powers.”
An absurd system of government to be sure, but on closer analysis, it presents an interesting example of the concept of Separation of Powers. Separation of Powers is a model utilized by many modern major governments with the aim of preventing any one individual from acquiring too much power. The idea, as stated by James Madison in Federalist No. 51, is that in giving each branch of government the “constitutional means, and personal motives, to resist encroachments of the others,” no one branch will be able to take complete control. Madison said that “power is an encroaching nature” (Federalist No. 48) and that, given time, government positions would surely be held by people driven primarily by ambition -- the desire to wield as much power as possible. The separation of powers ensures that in order to acquire said power, each branch of government must keep the others in check.
The most common number of branches is three. The French philosopher Montesquieu observed that the Roman Republic had such a system, and articulated it in 1748 in The Spirit Of The Laws. Montesquieu describes three branches of government. The legislature, the executive, and the judiciary. Some governments have four, five, or more branches, but three is the most common, and where three branches are present, they are usually basically these three, although the exact distribution of powers may differ from government to government.
In Utopia (Limited), Gilbert has (perhaps unwittingly) supplied us with an example of a three-branch system of government, albeit, not one that is exactly analogous to Montesquieu’s proposal. All the same, given Madison’s assumptions that, given time, ambition will be the primary driver of the people in office, “Despotism tempered by Dynamite” does provide a system of checks and balances.
It’s easy to suppose that the Wise Men have all the power -- and, indeed, the plot of Utopia (Limited) more or less begins this way. The King is the one who has the most power theoretically, but if he does anything the Wise Men don’t like, they can order the Public Exploder to blow him up. The corollary to this is that, in addition to preventing the King from doing anything they don’t like, the Wise Men have the ability to force the King to do whaever they do like, or threaten him with explosion. Under this system, Utopia is still an autocracy, just one where the true seat of power is one level up from where it’s presented to be.
But there is one key element that forces everything into place and makes Utopia’s government a true system of checks and balances. And that is the small detail, practically glossed over in Gilbert’s libretto, that upon the explosion of the King, the Public Exploder becomes the new King. This introduces an ambitious motive for the Public Exploder -- he wants to become King -- but it also introduces an element of risk -- he is then at the mercy of the Wise Men and the new Public Exploder.
(Note: There are two unclear elements that could have serious ramifications in how this model of government functions. Gilbert does not explain how either the Wise Men or the Public Exploder are appointed, and he does not explain how power is transferred if the King resigns or dies by non-explosion-related means. It is, however, somewhat suggested that in such an instance, the Kingship would not pass to the Public Exploder, and therefore the only way for the Public Exploder to become King is by blowing him up.)
From here on out we assume perfect gameplay. That all parties want as much power as possible, that all parties can think as many steps ahead as needed, and that all parties behave with perfect logic. And further, that all parties know that all other parties will also have perfect gameplay.
In the way the system is supposed to work, the King will run Utopia as he sees fit, but the moment he oversteps his boundaries, the Wise Men will denounce him to the Public Exploder, who will then carry out his duty, assured that he won’t meet the same fate so long as he’s a good King.
If the Wise Men begin to abuse their power, by forcing the King to do their bidding, they lose their power in the same motion. The Public Exploder can simply refuse to explode the King. And if the Wise Men are abusing their power, the Public Exploder has every motive not to explode the King, because then he would be at the mercy of the very same Wise Men, who could just as easily order him blown up. Therefore, it is in the Wise Men’s best interest for the Public Exploder to trust them, and trust that they will be fair and just Wise Men. And so they cannot abuse their power.
Conversely, if the Wise Men neglect their authority, then the Public Exploder can blow up the King with impunity, secure in the knowledge that the Wise Men are lax in their duty, and will most likely not order him blown up. It is therefore also in the Wise Men’s interest that they do perform their duty as intended.
The King, meanwhile, can do as he pleases, up to the point where the Wise Men threaten him with explosion. If the Wise Men abuse their power by trying to force the King to do something immoral or unjust, the King can freely refuse them, knowing that, under these circumstances, the Public Exploder will not follow through. Conversely, if the Wise Men are in fact being reasonable in their requests, the Public Exploder is more likely to comply, and so the King had better listen. The King must therefore obey any demands that are in the best interest of the Public Exploder, and the Wise Men should only make demands that are fair and reasonable. If the Wise Men conspire with the Public Exploder against the King, the Public Exploder has no guarantee that they won’t do the same to him.
Finally, the Public Exploder is prevented from abusing his power by virtue of the fact that if he explodes the King against the wishes of the Wise Men (or threatens the King with explosion without the consent of the Wise Men) then the moment he becomes King, the Wise Men will surely order the new Public Exploder to explode him on the spot. Conversely, the Public Exploder will explode the King if he thinks the Wise Men are being reasonable, because, remember, everyone wants as much power as possible. The Public Exploder wants to be King, but only if he has reasonable pretext to suppose the Wise Men will not abuse their power on him as well.
There is one more key point, and that is the fact that there are two Wise Men. Each Wise Man wants as much power as possible, but their only power is derived from being able to threaten the King with explosion, and independently lack the ability to do anything else. The two Wise Men are therefore dependent on each other. Without one, the other is helpless.
In short, there is a perpetual stalemate between these three branches. If the King abuses his power, the Wise Men will order the Public Exploder to blow him up. If the Wise Men abuse their power, the Public Exploder will refuse to blow up the King, rendering them powerless. If the Public Exploder abuses his power, the Wise Men will order him blown up the moment he becomes King. And everyone will always exercise exactly as much power as they are given because of rule number one, everyone wants the most power possible.
Of course this is not how it works in the libretto. By the time we join the action of the opera, the Wise Men are absolutely abusing their power, forcing the King to humiliate himself for their enjoyment. They make him write incriminating articles about himself in the newspaper, and compose original comic operas making fun of himself. All this he does under pseudonyms, which has led Tarara, the Public Exploder, to believe that the King is incredibly immoral. He is baffled by the fact that the Wise Men have not yet denounced him. As far as Tarara is aware, he should be free to blow up the King with impunity, but he does not. Conversely, in Act II, Tarara willingly assists the Wise Men in a plot to depose the King, despite the fact that it puts him in the dangerous position being King at the mercy of the same two Wise Men. Why doesn’t Tarara behave according to our model? Why do the Wise Men feel safe in abusing their power? Why hasn’t the King worked out that he’s free to disobey them, so long as Tarara is playing with perfect logic?
Well, that’s kind of the thing. For this perpetual stalemate to work, it requires that everyone play with perfect logic, which they don’t, and rests of the assumption that each player knows that they others will also play with perfect logic, which they don’t. It also counts on the Public Exploder having a consistent assessment as to how fair he thinks the Wise Men are being -- that is to say, how much risk he would incur by exploding the King. If the Public Exploder is incredibly meek, and does not want to put himself in any danger under any circumstances, he will never blow up the King even if the Wise Men have the best reasons for ordering it. Utopia’s government is, in short, a curious logic puzzle, but a failed government.
Now I don’t suppose that Gilbert did a comprehensive game theory analysis on this system of government while he was creating it. Gilbert is not a stickler for logical consistencies, and his 1890s libretti are notoriously messy and inconsistent. But there is certainly an overall satirical point to this power structure. Utopia (Limited) wears its satire much more openly than many of Gilbert’s other works, and it all builds up to a sardonic punchline with all the subtlety of a chorus of Pirates sneaking up on a Major-General.
Real-world governments that utilize separation of powers are usually much more successful in it than Utopia, and for obvious reasons. Real-world governments tend not to be set up in such blatantly stupid ways. But that doesn’t mean it always works out. On the contrary, power frequently ends up accumulating among particular groups of people. But it is not groups dictated by the setup of the government. It is rather, political parties, which exist independently of any state constitution, and thereby provide an independent power structure that can diminish the intended separation of powers by transferring said powers from a structure that was designed to keep them separate into a different structure designed to bring them together.
In the real world, separation of powers is eroded by the encroachment of political parties. In Gilbert’s Topsy-Turvy Utopia, a failed attempt at separation of powers is fixed by their introduction. Zara’s climactic speech in the final scene offers up a two-party system as the ultimate system of checks and balances.
“Government by party!” Zara says before the finale, “Introduce that great and glorious element… and all will be well! No political measures will endure, because one Party will assuredly undo all that the other Party has done… Then there will be sickness in plenty, endless lawsuits, crowded jails, interminable confusion in the Army and Navy, and, in short, general and unexampled prosperity!”
An absurd system of government to be sure, but on closer analysis, it presents an interesting example of the concept of Separation of Powers. Separation of Powers is a model utilized by many modern major governments with the aim of preventing any one individual from acquiring too much power. The idea, as stated by James Madison in Federalist No. 51, is that in giving each branch of government the “constitutional means, and personal motives, to resist encroachments of the others,” no one branch will be able to take complete control. Madison said that “power is an encroaching nature” (Federalist No. 48) and that, given time, government positions would surely be held by people driven primarily by ambition -- the desire to wield as much power as possible. The separation of powers ensures that in order to acquire said power, each branch of government must keep the others in check.
The most common number of branches is three. The French philosopher Montesquieu observed that the Roman Republic had such a system, and articulated it in 1748 in The Spirit Of The Laws. Montesquieu describes three branches of government. The legislature, the executive, and the judiciary. Some governments have four, five, or more branches, but three is the most common, and where three branches are present, they are usually basically these three, although the exact distribution of powers may differ from government to government.
***
In Utopia (Limited), Gilbert has (perhaps unwittingly) supplied us with an example of a three-branch system of government, albeit, not one that is exactly analogous to Montesquieu’s proposal. All the same, given Madison’s assumptions that, given time, ambition will be the primary driver of the people in office, “Despotism tempered by Dynamite” does provide a system of checks and balances.
It’s easy to suppose that the Wise Men have all the power -- and, indeed, the plot of Utopia (Limited) more or less begins this way. The King is the one who has the most power theoretically, but if he does anything the Wise Men don’t like, they can order the Public Exploder to blow him up. The corollary to this is that, in addition to preventing the King from doing anything they don’t like, the Wise Men have the ability to force the King to do whaever they do like, or threaten him with explosion. Under this system, Utopia is still an autocracy, just one where the true seat of power is one level up from where it’s presented to be.
But there is one key element that forces everything into place and makes Utopia’s government a true system of checks and balances. And that is the small detail, practically glossed over in Gilbert’s libretto, that upon the explosion of the King, the Public Exploder becomes the new King. This introduces an ambitious motive for the Public Exploder -- he wants to become King -- but it also introduces an element of risk -- he is then at the mercy of the Wise Men and the new Public Exploder.
(Note: There are two unclear elements that could have serious ramifications in how this model of government functions. Gilbert does not explain how either the Wise Men or the Public Exploder are appointed, and he does not explain how power is transferred if the King resigns or dies by non-explosion-related means. It is, however, somewhat suggested that in such an instance, the Kingship would not pass to the Public Exploder, and therefore the only way for the Public Exploder to become King is by blowing him up.)
From here on out we assume perfect gameplay. That all parties want as much power as possible, that all parties can think as many steps ahead as needed, and that all parties behave with perfect logic. And further, that all parties know that all other parties will also have perfect gameplay.
In the way the system is supposed to work, the King will run Utopia as he sees fit, but the moment he oversteps his boundaries, the Wise Men will denounce him to the Public Exploder, who will then carry out his duty, assured that he won’t meet the same fate so long as he’s a good King.
If the Wise Men begin to abuse their power, by forcing the King to do their bidding, they lose their power in the same motion. The Public Exploder can simply refuse to explode the King. And if the Wise Men are abusing their power, the Public Exploder has every motive not to explode the King, because then he would be at the mercy of the very same Wise Men, who could just as easily order him blown up. Therefore, it is in the Wise Men’s best interest for the Public Exploder to trust them, and trust that they will be fair and just Wise Men. And so they cannot abuse their power.
Conversely, if the Wise Men neglect their authority, then the Public Exploder can blow up the King with impunity, secure in the knowledge that the Wise Men are lax in their duty, and will most likely not order him blown up. It is therefore also in the Wise Men’s interest that they do perform their duty as intended.
The King, meanwhile, can do as he pleases, up to the point where the Wise Men threaten him with explosion. If the Wise Men abuse their power by trying to force the King to do something immoral or unjust, the King can freely refuse them, knowing that, under these circumstances, the Public Exploder will not follow through. Conversely, if the Wise Men are in fact being reasonable in their requests, the Public Exploder is more likely to comply, and so the King had better listen. The King must therefore obey any demands that are in the best interest of the Public Exploder, and the Wise Men should only make demands that are fair and reasonable. If the Wise Men conspire with the Public Exploder against the King, the Public Exploder has no guarantee that they won’t do the same to him.
Finally, the Public Exploder is prevented from abusing his power by virtue of the fact that if he explodes the King against the wishes of the Wise Men (or threatens the King with explosion without the consent of the Wise Men) then the moment he becomes King, the Wise Men will surely order the new Public Exploder to explode him on the spot. Conversely, the Public Exploder will explode the King if he thinks the Wise Men are being reasonable, because, remember, everyone wants as much power as possible. The Public Exploder wants to be King, but only if he has reasonable pretext to suppose the Wise Men will not abuse their power on him as well.
There is one more key point, and that is the fact that there are two Wise Men. Each Wise Man wants as much power as possible, but their only power is derived from being able to threaten the King with explosion, and independently lack the ability to do anything else. The two Wise Men are therefore dependent on each other. Without one, the other is helpless.
In short, there is a perpetual stalemate between these three branches. If the King abuses his power, the Wise Men will order the Public Exploder to blow him up. If the Wise Men abuse their power, the Public Exploder will refuse to blow up the King, rendering them powerless. If the Public Exploder abuses his power, the Wise Men will order him blown up the moment he becomes King. And everyone will always exercise exactly as much power as they are given because of rule number one, everyone wants the most power possible.
***
Of course this is not how it works in the libretto. By the time we join the action of the opera, the Wise Men are absolutely abusing their power, forcing the King to humiliate himself for their enjoyment. They make him write incriminating articles about himself in the newspaper, and compose original comic operas making fun of himself. All this he does under pseudonyms, which has led Tarara, the Public Exploder, to believe that the King is incredibly immoral. He is baffled by the fact that the Wise Men have not yet denounced him. As far as Tarara is aware, he should be free to blow up the King with impunity, but he does not. Conversely, in Act II, Tarara willingly assists the Wise Men in a plot to depose the King, despite the fact that it puts him in the dangerous position being King at the mercy of the same two Wise Men. Why doesn’t Tarara behave according to our model? Why do the Wise Men feel safe in abusing their power? Why hasn’t the King worked out that he’s free to disobey them, so long as Tarara is playing with perfect logic?
Well, that’s kind of the thing. For this perpetual stalemate to work, it requires that everyone play with perfect logic, which they don’t, and rests of the assumption that each player knows that they others will also play with perfect logic, which they don’t. It also counts on the Public Exploder having a consistent assessment as to how fair he thinks the Wise Men are being -- that is to say, how much risk he would incur by exploding the King. If the Public Exploder is incredibly meek, and does not want to put himself in any danger under any circumstances, he will never blow up the King even if the Wise Men have the best reasons for ordering it. Utopia’s government is, in short, a curious logic puzzle, but a failed government.
***
Now I don’t suppose that Gilbert did a comprehensive game theory analysis on this system of government while he was creating it. Gilbert is not a stickler for logical consistencies, and his 1890s libretti are notoriously messy and inconsistent. But there is certainly an overall satirical point to this power structure. Utopia (Limited) wears its satire much more openly than many of Gilbert’s other works, and it all builds up to a sardonic punchline with all the subtlety of a chorus of Pirates sneaking up on a Major-General.
Real-world governments that utilize separation of powers are usually much more successful in it than Utopia, and for obvious reasons. Real-world governments tend not to be set up in such blatantly stupid ways. But that doesn’t mean it always works out. On the contrary, power frequently ends up accumulating among particular groups of people. But it is not groups dictated by the setup of the government. It is rather, political parties, which exist independently of any state constitution, and thereby provide an independent power structure that can diminish the intended separation of powers by transferring said powers from a structure that was designed to keep them separate into a different structure designed to bring them together.
In the real world, separation of powers is eroded by the encroachment of political parties. In Gilbert’s Topsy-Turvy Utopia, a failed attempt at separation of powers is fixed by their introduction. Zara’s climactic speech in the final scene offers up a two-party system as the ultimate system of checks and balances.
“Government by party!” Zara says before the finale, “Introduce that great and glorious element… and all will be well! No political measures will endure, because one Party will assuredly undo all that the other Party has done… Then there will be sickness in plenty, endless lawsuits, crowded jails, interminable confusion in the Army and Navy, and, in short, general and unexampled prosperity!”
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