Russell begins his essay, "The Future of Mankind," with three possible scenarios for the future. Note that Russell wrote this essay after World War II and during the rise of the Cold War. (The Cold War defined the antagonism between the Soviet Union, and their allies, and the United States, and their allies. The Cold War followed World War II - 1947 - and lasted until 1991 with the dissolution of the Soviet Union.)
Given that a third world war, erupting from the Cold War, was one of Russell's greatest concerns, his prospects for the future dealt with the possibility of such a war (atomic, no less) or some way to avoid such a war. If such a war were to occur, Russell supposed the destruction of human life, and possibly all life, on the planet. Atomic bombs and their after-effects (radiation clouds, disease, etc.) would decimate and/or eliminate all life.
Russell's second scenario is that the world would revert to a state of barbarism. This too could result from a widespread atomic world war. The only solace is that such outcome leaves open the possibility that humans could return to a civilized state. Russell compares this possibility to the fall of Rome which was followed by a relatively more barbaric time (notably the Dark Ages) but was followed by a Renaissance and eventually a more technological and organized world.
Russell's third scenario is the unification of the world under one united power. Russell adds that such a united power is the most preferable outcome (a more powerful and all-encompassing authority than, say, the United Nations). Russell notes that as long as there at least two supremely powerful states (Soviet Union and United States), the threat of an atomic world war is always possible. And as technology increases, the destructive power of such a war increases. In other words, the more technologically advanced the world becomes, the more destructive our wars become; therefore, Russell believed that a unified world state becomes more and more necessary in order to avoid such a catastrophic war.
Russell hoped that a united world state could be achieved by negotiation and/or the threat of force but he feared that force would be necessary. He also clearly preferred an American victory rather than a Russian victory - whether that be the result of diplomatic relations or the result of a war. He even added that if America were communist and Russia were capitalist, he would still prefer an American victory because there was more intellectual and social freedom in America.
Although a united world state does have problems, Russell believes that under such a state, the threat of war will be lessened or eliminated, leaving humans to put more attention on human happiness. Although Russell presents gloomy potentials for the future, he believes that an immeasurably good outcome can emerge from the third scenario:
What the world most needs is effective laws to control international relations. The first and most difficult step in the creation of such law is the establishment of adequate sanctions, and this is only possible through the creation of a single armed force in control of the whole world.