"Minister, Britain has had the same foreign policy objective for at least the last five hundred years: to create a disunited Europe. In that cause we have fought with the Dutch against the Spanish, with the Germans against the French, with the French and Italians against the Germans, and with the French against the Germans and Italians. Divide and rule, you see. Why should we change now, when it's worked so well?"
A concept in international relations, but one with a lot of relevance in fiction.
To give a hypothetical example, you have five countries:
A- a Great Power
B- another Great Power, roughly equal and hostile to A
C- a lesser power associated with A
D- Another lesser power roughly equal to C, associated with B
E- Another lesser power that is neutral
A+C equals more or less B+D, so any kind of war between them would be indecisive or have an outcome that is hard to predict. A protracted war would be incredibly expensive, and bloody, to boot. It's in everyone's interests to prevent or limit A-B conflict.
However, if E decided to align itself with A or B, that trio could have a decisive advantage in a limited conflict (before the duo brings their full resources to bear). A protracted conflict between the five would be even more incredibly bloody and expensive than one between the four, however, and its outcome would still be in doubt despite the slight advantage held by one side. Furthermore, it might be in E's best interests to keep A and B balanced against each other, leaving itself free to steer an independent course as neither of the two would wish to drive it into the other's camp by behaving too aggressively against E.
The problem with these arrangements is that not all the powers involved will always have an accurate idea of the other powers' intentions or the relative strengths of all the powers. This can prove disastrous when a power decides to start a war because its leadership isn't in touch with reality.
This trope is a major reason for both Realpolitik and Enemy Mine - A may not necessarily like C, but if both feel B is the bigger threat they will have a good reason to cooperate.
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The One Piece 'verse has a Balance of Power crucial to the overall plot of the story. Types A and B consist of Marine Headquarters versus the Four Emperors (The World Government's military and the four most powerful pirate crews in the world, respectively). In the middle are the Seven Warlords of the Sea, who (on paper at least) are a Type-C, aiding the World Government against the Emperors. However, almost all of them are carrying out their own agendas on the side and some of them have casual and even friendly contact with Emperors and up-and-coming pirates, making them more of an Type-E in practice. Threats to this balance include single-minded pirates like Monkey D. Luffy and the deliberate actions of Dragon the Revolutionary.
Late in the story, Naruto has revealed that the Tailed Beasts, the Bijuu, and their hosts, the Jinchuuriki acted as a balance among the various nations. Konaha and Suna, each having only one bijuu, allied with one another after the last war to deter Kumo and Iwa which both hosted two; Kiri's natural defenses and two bijuu allow it freedom in operation but it lacks the unity needed to take advantage of that. Taki's single bijuu and lesser standing make it an ideal buffer between Kumo and Konoha. Most of the lesser villages align with other villages, have treaties via their daimyo lords, or are located in places where attacks will spark retribution from neighbors. The existence of a free Bijuu would spur other villages to attempt to claim it and gain an advantage, thus necessitating its capture.
Despite the long time it took to be introduced, this balance was eventually revealed to be crucial to Naruto's backstory. Because maintaining it was one of the biggest reasons that the Fourth Hokage sealed the Nine Tailed Fox inside of him.
The Vatican Treaty in Rebuild of Evangelion dictates that no single country can have more than three active Evas at any given time.
In Aeon Natum Engel, the defences of Esoteric Order of Dagon-controlled Iceland are partly based on this principle; neither the New Earth Government nor the Migou can attack without weakening their position against the other, thus stopping them from taking the territory. Of course, the assumption that the NEG is after the Dagonite-controlled territory turns out to be painfully flawed.
In Aeon Entelechy Evangelion the NEG and the Migou had a status quo for six years since the Fall of China, with no major morale-breaking loses for the NEG since then. Then Mot shows up and destabilizes the Eastern Front.
Some of the intrigue in The Godfather comes from the families negotiating about this.
The United States and the Soviet Union in Thirteen Days are the A and B. The biggest C's and D's in the movie are Cuba (whose hosting of Soviet missiles was the central issue of the movie) and Turkey (whose hosting of American missiles plays into the negotiations); other players include Chile and Romania (the UN Security Council meeting) and the rest of Latin America via the Organization of American States (unanimous vote in favor of the US "quarrantine").
China and India are also mentioned when the former invaded the latter - though they don't play a role in the plot itself, their mention even when the Kennedy administration's primary focus was already on Cuba and the Soviet missiles there illustrates the breadth of scope the US had in its foreign policy during the Cold War.
In The Third World War, the war starts because the USSR is worried about losing D (the Warsaw Pact) and is won by the West partly because of the role of two Es, namely Ireland and Sweden.
Oceania, Eurasia, and Eastasia of 1984; at any point, two are allied with each other, but the alliance always crumbles before the third is defeated because one of the two grows too powerful, and the alliances are reshuffled.
Isaac Asimov'sFoundation Trilogy starts out this way. As the Galactic Empire starts to decline, the planet of Terminus is surrounded by the 'Four Kingdoms', who are looking to expand their own influence. They've also reverted to primitive forms of technology though, so when Salvor Hardin, the Mayor of Terminus, lets slip to one of the Four Kingdoms' ambassadors that Terminus still has nuclear power, it looks like Terminus is going to get invaded for its technology. Hardin, the Magnificent Bastard that he is, also let slip Terminus has nuclear power to the other three Kingdoms. None of the four kingdoms are willing to invade Terminus now, under threat of joint retaliation from the other three kingdoms.
One of the central themes of Babylon5 is the galactic balance of power between Humans, Narns, Centari, Vorlons, Mimbari, and the League of Non-Aligned Worlds. It starts off being about as equitable as might be reasonably expected, but naturally it all turns to custard by season 2.
Twilight Struggle has the US and Soviet Union as the A and B, with pretty much every other country on the board as potential C's and D's depending on who controls them. The only real E on the board is Communist China, who is represented as a card rather than a space that can be played by one of the powers for influencing other countries on the board (bonus if it's in Asia) and gets passed between each superpower once played.
Sort of subverted: All the powerful treaty signatories (Turian, Asari, Salarian and later Human) are closely allied and the only races that could possibly compete with them (e.g. the Geth and maybe the Quarians and Batarians) are outside the treaty, the purpose of the treaty is more about enforcing the unipolar power of the citadel council races than making any sort of balance of power.
Final Fantasy XII has this as a major driving factor behind its plot. What triggers the game's main story is that the balance between two empires, the Archadian and the Rozarrian empires, has been overturned when the Archadian Empire annexes the E power Dalmasca and destroys another one, Nabradia, both of which also served as buffer states between the two empires.
It has been argued that much of England's and then Great Britain's foreign policy from the 1500s until the 20th century was keeping a balance between France and Spain (and later Germany), to ensure that neither got big enough to take on England/Britain itself. This was explicitly spelled out as foreign office policy in Yes Minister, in both past and present. It was claimed the only reason Britain went into the EU was to ensure they could keep the other major powers acting without them.
This isn't argued, it's accepted that this was England's policy for centuries. In essence, if anyone dominates the continent, they become a threat to England, so the soundest foreign policy is to make sure no one nation becomes overly strong. It's why England was against France in the time of Napoleon and with France in the run-up to and during World War I. The major concern was Belgium and the Netherlands, which would have been excellent staging areas for an invasion of Britain. This is one of the reasons that when Britain entered World War One, it did so explicitly to defend Belgian neutrality.
Some newly found soviet conversation logs from around 1990 proof that Margaret Thatcher was actively opposing the reunification of Germany even when the whole east of Europe was already revolting against the Soviets. Only to keep the Balance of Power intact.
Confirmed by the diaries of her junior minister Alan Clarke, who was disappointed that she didn't back the reunification he realized was inevitable.
Even at that time she was quite obviously not in favour of the reunification, so probably no one is surprised about the discovery.
Pre-World War One Europe was much like this, except that there were three to six top-tier powers (Britain, Germany, and France at minimum, then Austria-Hungary, Russia, and Italy), with alliances shifting more frequently than you can shake a stick at. On top of that, there were the smaller powers, such as the neutral Low Countries, and the newly-minted and aggressively nationalistic countries of the Balkans (Serbia, Greece, and Romania topping the list in bellgerency and grandiose designs).
The Cold War was very much about this, although the Superior Firepower and Mnogo Nukes meant that outright war was relatively unlikely. Instead, the US and USSR decided to fight by proxy. There is some variation as both the United States and Soviet Union were so powerful that even if one of them lost a useful ally like China - as per the Sino-Soviet split and Sino-American rapprochement - the balance never shifted firmly in favor of the other side.
The Peloponnesian War represents how the equation can go awry. It was very bad to be an E. Both A & B (Sparta and Athens) decided that the situation was a lot more stable if there weren't any Es around, and generally went about destroying them. Also, it was the Cs & Ds (like Corinth) who started and restarted the war between A & B, figuring that the worse off the superpowers were, the better off the medium powers were.
Ancient Mayan city-states decllined in a similar way, as well as literal Poisoning The Well
Ancient Rhodes, a noted Merchant City in the Hellenistic era survived by it's expertise in maintaining the balance between the Successor States, and ensuring that it's small but extremely skilled navy was capable of tilting the balance back whenever one warlord became more powerful then the Rhodians liked.
Renaissance Venice did this as well between Spain and the Ottomans.
Wolfers was a political scientist who wrote about how a balance of power is impossible to achieve because, even if it is attained (or roughly attained), it's never in A or B's interest to maintain a situation where they are as powerful as their foe, which means that they fight client wars in spheres of influence and get into arms races.
Arguably Balance of Power is best thought of as a classic strategy to ensure the survival of one faction (as witness Rhodes and Venice above), rather then a way to keep the general peace. In other words the main point is that other people are fighting each other rather then ganging up on you. The exception, of course, is the modern iteration of the strategy, Mutually Assured Destruction: where if A and B fight, everyone loses.