Polarity in international relations is any of the various ways in which power is distributed within the international system. It describes the nature of the international system at any given period of time. One generally distinguishes four types of systems: unipolarity, bipolarity, tripolarity, and multipolarity for four or more centers of power. The type of system is completely dependent on the distribution of power and influence of states in a region or globally.
It is widely believed amongst theorists in international relations that the post-Cold War international system is unipolar: The United States’ defense spending is “close to half of global military expenditures; a blue-water navy superior to all others combined; a chance at a powerful nuclear first strike over its erstwhile foe, Russia; a defense research and development budget that is 80 percent of the total defense expenditures of its most obvious future competitor, China; and unmatched global power-projection capabilities.”
Unipolarity in international politics is a distribution of power in which one state exercises most of the cultural, economic, and military influence.
Apart from excelling in indicators of power such as population, resource endowment, economic capacity, and military might, unipoles are associated with certain foreign policy behaviors like actively participating in binding regional institutions; building ad hoc coalitions of the willing to deal with major security or economic challenges; struggling for legitimacy without applying much coercion; and respecting the sovereignty of second-tier states, who are considered crucial partners. 
The post-Cold War international system is unipolar: The United States’ defense spending is “close to half of global military expenditures; a blue-water navy superior to all others combined; a chance at a splendid nuclear first strike over its erstwhile foe, Russia; a defense research and development budget that is 80 percent of the total defense expenditures of its most obvious future competitor, China; and unmatched global power-projection capabilities.” William Wohlforth, the Daniel Webster professor of government at Dartmouth College, says the puzzle to be explained is “why do so many thoughtful people think the current system is incipiently multipolar?”
Wohlforth believes unipolarity is peaceful because it “favors the absence of war among great powers and comparatively low levels of competition for prestige or security for two reasons: the leading state’s power advantage removes the problem of hegemonic rivalry from world politics, and it reduces the salience and stakes of balance of power politics among the major states." “Therefore one pole is best, and security competition among the great powers should be minimal.” Unipolarity generates few incentives for security and prestige competition among great powers. This idea is based on hegemonic stability theory and the rejection of the balance of power theory. Hegemonic stability theory stipulates that “powerful states foster international orders that are stable until differential growth in power produces a dissatisfied state with the capability to challenge the dominant state for leadership. The clearer and larger the concentration of power in the leading state, the more peaceful the international order associated with it will be." The Balance of power theory, by contrast, stipulates that as long as the international system remains in balance (without unipolar power), peace is maintained.
Nuno P. Monteiro argues that international relations theorists have long debated the durability of unipolarity (i.e. when it will end) but less on the relative peacefulness unipolarity brings among nations within an international system. Rather than comparing the relative peacefulness of unipolarity, multipolarity, and bipolarity, he identifies causal pathways to war that are endemic to a unipolar system. He does not question the impossibility of great power war in a unipolar world, which is a central tenet of William C. Wohlforth in his book World Out of Balance: International Relations and the Challenge of American Primacy. Instead he believes “unipolar systems provide incentives for two other types of war: those pitting the sole great power against a relatively weaker state and those exclusively involving weaker states.” Monteiro’s hypothesis is influenced by the first two decades of the post-Cold War environment, one that is defined as unipolar and rife with wars. “The United States has been at war for thirteen of the twenty-two years since the end of the Cold War. Put another way, the first two decades of unipolarity, which make up less than 10 percent of U.S. history, account for more than 25 percent of the nation’s total time at war.”
The earliest prophet of unipolarity seems to be Fichte, although he did not use the term (using instead "Universal Monarchy"). Paradoxically, the Father of the German nationalism and convinced adherent of the balance of power, he appears to be the path-breaker. Back in 1806, Fichte wrote Characteristics of the Present Age. It was the year of the battle at Jena when Napoleon overwhelmed Prussia. The challenge of Napoleon revealed to him the precarious nature of the balance of power and a much deeper and dominant historical trend:
There is necessary tendency in every cultivated State to extend itself generally... Such is the case in Ancient History … As the States become stronger in themselves and cast off that [Papal] foreign power, the tendency towards a Universal Monarchy over the whole Christian World necessarily comes to light… This tendency ... has shown itself successively in several States which could make pretensions to such a dominion, and since the fall of the Papacy, it has become the sole animating principle of our History... Whether clearly or not—it may be obscurely—yet has this tendency lain at the root of the undertakings of many States in Modern Times... Although no individual Epoch may have contemplated this purpose, yet is this the spirit which runs through all these individual Epochs, and invisibly urges them onward.”
The first thinker to anticipate both the unipolar world and the American Primacy seems to be British politician William Gladstone (Alexis de Tocqueville in the mid-nineteenth century had expected the bipolar world centered on America and Russia but had not advanced beyond bipolarity). In 1878, Gladstone wrote:
While we have been advancing with portentous rapidity, America is passing us by as if a canter. There can hardly be a doubt, as between America and England, of the belief that the daughter at no very distant time will … be unquestionably yet stronger than the mother … She [America] will probably become what we are now—head servant in the great household of the world…
French Economist Michel Chevalier, writing in 1866, did not address the possibility of a unipolar world, but envisaged that the “political colossus who is being created at the other side of the Atlantic” would overshadow Europe by the end of the nineteenth century. Unless Europe united, he wrote, it would be “weak and exposed to disastrous defeats” in the confrontation with the New World.
In 1885, the Chinese Philosopher, K'ang Yu-wei published his One World Philosophy, where he based his vision on the evidence of political expansion which began in the immemorial past and went in his days on. He concludes:
Finally, the present Powers of the world were formed. This process [of coalescing and forming fewer, larger units] has all taken place among the 10,000 countries over several thousand years. The progression from dispersion to union among men, and the principle [whereby] the world is [gradually] proceeding from being partitioned off to being opened up, is a spontaneous [working] of the Way of Heaven (or Nature) and human affairs.
No factor, he believed, in the long run could resist the "laws of empires." K'ang Yu-wei projects the culmination of the ongoing world unification with the final confrontation between the United States and Germany: "Some day America will take in [all the states of] the American continent and Germany will take in all the [states of] Europe. This will hasten the world along the road to One World."
K'ang Yu-wei belonged to a civilization, which experienced the millennia-long unipolar order. He knew how in his civilization it emerged and several times reemerged. Naturally, his theory is very realist, deep, and developed relatively to his Western contemporaries convinced in the universality of the balance of power or, at most, having abstract ideas of the "Parliament of men, the Federation of the world."
Another early scientist who drew a hypothesis of the forthcoming unipolar world order and the American primacy was the French Demographer, Georges Vacher de Lapouge, with his L`Aryen: Son Role Social published in 1899. Similarly to K'ang Yu-wei, he outlined the logistic growth of empires from the Bronze Age till his days, when "six states govern... three quarters of the globe," and concluded: "The moment is close when the struggle for the domination of the world is going to take place."
Vacher de Lapouge did not bet on Washington and Berlin in the final contest for world domination like K'ang Yu-wei. Similarly to de Tocqueville, he guessed the Cold War contenders correctly but he went one step further. He estimated the chances of the United States as favorite in the final confrontation:
"The reign of Europe is over, well over… The future of France seems less certain but it is unnecessary to become illusioned… I do not believe by the way that Germany might count for a much longer future… We could… envisage… the possibility that England and her immense Empire comes to surrender to the United States. The latter… is the true adversary of Russia in the great struggle to come… I also believe that the United States is appealed to triumph. Otherwise, the universe would be Russian.".
The year after Vacher de Lapouge published his vision, H. G. Wells in Anticipations (1900) envisaged that "the great urban region between Chicago and the Atlantic” will unify the English-speaking states, and this larger English-speaking unit, “a New Republic dominating the world,” will by the year 2000 become the means “by which the final peace of the world may be assured forever." It will be “a new social Hercules that will strangle the serpents of war and national animosity in his cradle.” Such a synthesis "of the peoples now using the English tongue, I regard not only as possible, but as a probable, thing.” The New Republic “will already be consciously and pretty freely controlling the general affairs of humanity before this century closes…” Its principles and opinions “must necessarily shape and determine that still ampler future of which the coming hundred years is but the opening phase.” The New Republic must ultimately become a "World-State." Wells' compatriot, Journalist William Thomas Stead, titled his 1901 book The Americanization of the World or the Trend of the Twentieth Century.
The visions of William Gladstone, Vacher de Lapouge, H. G. Wells and William Thomas Stead were borne out. The United States is the only country in the early 21st century that possesses the ability to project military power on a global scale, providing its full command of the global commons. With no viable challenger on the horizon in the short term, the current distribution of power overwhelmingly favors the United States, making the world order it set out to construct in 1945 more robust. The question that remains for international relations theorists is how long this “unipolar moment” will last. Sean M. Lynn-Jones, editor of International Security, provides a summary of arguments put forth by Kenneth Waltz, John Ikenberry, and Barry Posen.
Kenneth Waltz, the founder of Neorealism, in his epochal Theory of International Politics (1979) precluded the possibility of unipolarity. Two, he stated (1979: 136), is the smallest possible number of poles in a system. Within twelve years, unipolarity emerged. In two papers of 1993--“Structural Realism after the Cold War” and "The Emerging Structure of International Politics"—Waltz defends the neorealist theory against a cascade of criticism that emerged after the Cold War. First of all, he stresses that unipolarity is “the least durable of international configurations.” He provides a realist analysis of the currently unipolar structure of world politics, arguing that realism is the best theoretical lens to understanding international politics and the short future of U.S. primacy.
Waltz also takes on the democratic peace theory, which holds that no two democracies will go to war with each other, as one that doesn’t present a proper challenge to realism. War is rooted in the anarchic structure, or a self-help environment, of the international system, Waltz argues. Simply changing the domestic political structure of countries will not eliminate war, Waltz notes. However, “democracies seldom fight democracies”, although democracies are more likely to initiate wars against non-democracies because the former believes the latter must become democratized so as to make the democratic peace more robust. Thus, the spread of democracy can decrease the amount of war in the world in Waltz’s view. The second challenge to realist theory argues that economic interdependence promotes peace. Waltz believes this causal logic is backward: Peace can promote economic interdependence. Peace abounds when a political monopoly on force, or a favorable balance of power, prevents revisionist powers from altering the status quo. After all, Waltz argues, strong economic interdependence did not prevent war in 1914.
The third challenge that Waltz confronts is the rise of international institutions as primary actors in international politics. Waltz argues that the structure of power in the international system determines the role of institutions. NATO, for example, is often cited as an institution that has outlived its original mandate—preventing a Soviet onslaught of Western Europe. In Waltz’s view, NATO’s continued existence conveniently “illustrates how international institutions are created and maintained by stronger states (e.g., the United States) to serve their perceived and misperceived interests.” Finally, Waltz turns to the question of international politics and provides a realist interpretation to the U.S. unipolar moment, which he believes is fleeting for two reasons. With no great power to check its adventurism, the United States will weaken itself by misusing its power internationally. “Wide latitude” of “policy choices” will allow the U.S. to act capriciously on the basis of “internal political pressure and national ambition.” Secondly, even if the United States acts benevolently, states will still attempt to balance against it because the power asymmetry demands it: In a self-help system, states do not worry about other states’ intentions as they do other states' capabilities. “Unbalanced power leaves weaker states feeling uneasy and gives them reason to strengthen their positions,” Waltz says. He sees China as already beginning to counter U.S. power. In conclusion, the U.S. unipolar moment is fleeting and multipolarity is already materializing.
As the unipolarity persisted longer than Waltz expected, Thomas Mowle and David Sacko published a book titled, The Unipolar World: An Unbalanced Future (2007). “This book, they introduce, develops a theory of unipolar politics to complete Waltz’s theory.” They explain the necessity of the subject:
“Shortly after Waltz deduced his theory of international politics, the world shifted … not back to the world of prior theory but to something previously unseen. Our discipline has tarried too long in the wreckage of history, spent too long trying to recover something familiar from the ruins ... We must complete the realist theory, integrating an understanding of unipolarity into our knowledge of multipolarity and bipolarity.”
The “something previously unseen” is the fact that the power of the United States remains unbalanced. “To date, political science has not explained this puzzle.” Realism “has little to say about this situation.” The “leading theory of international politics is lost because it expects a world of multiple major powers. Realists expect states to balance against rising powers, which would prevent a unipolar distribution of power from developing.” Mowle and Sacko offer an explanation to the failure of research on unipolarity:
“To a Western society steeped in a history of balancing and individualism, unipolarity seems autocratic. To states with a proud past as an international actor, unipolarity seems intolerable… To those who wish to teach history and international relations, unipolarity seems Fukuyamish.”
Although unipolarity is generally undesirable, it prevails: “While many people wish that power were distributed in a different manner, unipolarity is real.” It seems natural, therefore, that structural realism should develop a set of hypotheses for a unipolar world. Instead, however, realists have “resisted the conclusion that the world is unipolar and sought evidence of balancing by other states. In particular, some have advanced the concept of soft balancing—balancing that does not balance at all.” These efforts are counter-productive, since realism and unipolarity are compatible. “Scholars, they advise in conclusion, do not need to desperately search for signs of balancing, they do not need to soften balancing beyond recognition, and they do not need to stand watch for the first glimmering of a new multipolar dawn.”
In “Institutions, Strategic Restraint, and Persistence of American Postwar Order,” John Ikenberry explains why other great powers decided not to balance against the United States after the Cold War ended. In his view, realist predictions of power balancing did not bear fruit because the United States engaged in strategic restraint after World War II, thereby convincing weaker states that it was more interested in cooperation rather than domination. U.S. strategic restraint allowed weaker countries to participate in the make-up of the post-war world order, which limited opportunities for the United States to exploit total power advantages. Ikenberry notes that while the United States could have unilaterally engaged in unfettered power projection, it decided instead to “lock in” its advantage by establishing an enduring institutional order, gave weaker countries a voice, reduced great power uncertainty, and mitigated the security dilemma. The liberal basis of U.S. hegemony—a transparent democratic political system—has made it easier for other countries to accept the post-war order, Ikenberry explains. “American hegemony is reluctant, open, and highly institutionalized—or in a word, liberal” and “short of large-scale war or a global economic crisis, the American hegemonic order appears to be immune to would-be hegemonic challengers.”
In “Command of the Commons: The Military Foundation of U.S. Hegemony,” Barry Posen focuses exclusively on U.S. military capabilities. A key to U.S. preeminence is “command of the commons—command of the sea, space, and air.” But command of the commons and the U.S. persistence in maintaining its near omnipresence raise important questions for U.S. strategy: “Even before the September 11 terrorist attacks, the foreign policy debate had narrowed to a dispute between primacy and selective engagement, between nationalist, unilateralist version of hegemony, and a liberal, multilateral version of hegemony.” U.S. command of the commons, Posen argues, provides a strong case for selective engagement. Posen believes that the Bush Doctrine was problematic because it not only created unease among U.S. allies, but also caused “others to ally against the United States.” Securing the commons through selective engagement is a superior strategy because it is cost effective, secures U.S. interests, and makes the nearly omnipresent U.S. military tolerable because it provides security guarantees to other nations.
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Bipolarity is a distribution of power in which two states have the majority of economic, military, and cultural influence internationally or regionally. Often, spheres of influence would develop. For example, in the Cold War, most Western and capitalist states would fall under the influence of the US, while most Communist states would fall under the influence of the USSR. After this, the two powers will normally maneuver for the support of the unclaimed areas. Which in the case of the Cold War means Africa, etc. (refer to map below).
The bipolar system can be said to extend to much larger systems, such as alliances or organizations, which would not be considered nation-states, but would still have power concentrated in two primary groups.
In both World Wars, much of the world, and especially Europe, the United States and Japan had been divided into two respective spheres – one case being the Axis and Allies of World War II (1939–1945) – and the division of power between the Central Powers and Allied powers during World War I (1914–1918). Neutral nations, however, may have caused what may be assessed as an example of tripolarity as well within both of the conflicts.
Multipolarity is a distribution of power in which more than two nation-states have nearly equal amounts of military, cultural, and economic influence.
Opinions on the stability of multipolarity differ. Classical realist theorists, such as Hans Morgenthau and E. H. Carr, hold that multipolar systems are more stable than bipolar systems, as great powers can gain power through alliances and petty wars that do not directly challenge other powers; in bipolar systems, classical realists argue, this is not possible. On the other hand, the neorealist focuses on security and inverts the formula: states in a multipolar system can focus their fears on any number of other powers and, misjudging the intentions of other states, unnecessarily compromise their security, while states in a bipolar system always focus their fears on one other power, meaning that at worst the powers will miscalculate the force required to counter threats and spend slightly too much on the operation. However, due to the complexity of mutually assured destruction scenarios, with nuclear weapons, multipolar systems may be more stable than bipolar systems even in the neorealist analysis. This system tends to have many shifting alliances until one of two things happens. Either a balance of power is struck, and neither side wants to attack the other, or one side will attack the other because it either fears the potential of the new alliance, or it feels that it can defeat the other side.
One of the major implications of an international system with any number of poles, including a multi polar system, is that international decisions will often be made for strategic reasons to maintain a balance of power rather than out of ideological or historical reasons.
The 'Concert of Europe,' a period from after the Napoleonic Wars to the Crimean War, was an example of peaceful multipolarity (the great powers of Europe assembled regularly to discuss international and domestic issues). World War I, World War II, the Thirty Years War, the Warring States period, the Three Kingdoms period and the tripartite division between Song dynasty/Liao dynasty/Jin dynasty/Yuan dynasty are all examples of a wartime multipolarity.
Nonpolarity is an international system which has been postulated by Richard Haass, featuring numerous centers of power but no center dominating any other center. Centers of power can be nation-states, corporations, non-governmental organizations, terrorist groups, and such. Power is found in many hands and many places. It suffers from attempting to use liberal conceptions of power within a realist paradigm, diluting the meaning of 'polarity', and is not widely found in usual discussions of polarity.
Though usually defined as the decentralization of power within a state, the term devolution, when applied to international relations, describes the process by which economically and militarily emerging states gain greater autonomy in regional affairs but do not achieve global power status. Against the theory that the world is moving from a unipolar order, dominated by the United States, to a multipolar world with various centers of power, Amitai Etzioni argues that, in the foreseeable future, the global redistribution of power is following a different pattern: "the change seems to be toward more regional autonomy, or increased devolution, and greater variety in the relationships between the United States and regional powers." This alternative theory has policy implications as "the desire for more control among rising powers can be more readily accommodated than aspirations to challenge the United States as a global superpower."
The closer the resulting concentration is to zero, the more evenly divided power is. The closer to 1, the more concentrated power is. There is a general but not strict correlation between concentration and polarity. It is rare to find a result over 0.5, but a result between 0.4 and 0.5 usually indicates a unipolar system, while a result between 0.2 and 0.4 usually indicated a bipolar or multipolar system. Concentration can be plotted over time, so that the fluctuations and trends in concentration can be observed.