There have been many attempts at a single world government throughout history. The attempts have always followed two paths: military coercion or peaceful persuasion. Military conquests for world domination have existed for as long as human history. Peaceful coalition-forging emerged after the First World War, in the form of the League of Nations. Both methods of world government, however, are doomed to failure.
Belligerent empires are the more obviously flawed. Countries which expand by force create enemies which threaten to destroy them. Nazi Germany and Japan made enemies of the United States, a nation which annihilated them through sheer military muscle. Also, in order to be a belligerent state, one requires a political system which perpetuates instability. To be a belligerent state requires an element of military political power, as we see in every such empire. This ‘power to the generals’ approach incentivises not only inordinate military spending but constant attempts to forcibly seize power through coups. The fear of being deposed causes leaders to institute purges and to destabilize the country further. The culmination of these events is revolution or civil war.
Federational world government is unworkable as well, but less obviously so. The inherent flaw in supranational democracy is human nature. Humans naturally feel the need to form separate groups from others and tend to become polarized within those groups towards hatred of others and seek guidance from radical leaders, developing a Volksgeist: an ethnic ‘spirit’, usually one of prejudice. In the words of sociologist Theodor Adomo, ‘When the leaders become conscious of mass psychology and take it into their own hands, it ceases to exist in a certain sense. … Just as little as people believe in the depth of their hearts that the Jews are the devil, do they completely believe in their leader.’ 
The Volksgeist is the manifestation of basic human instincts, outlined by Roy J. Eidelson and Judy I. Eidelson in volume 58 of American Psychologist . The most important of the five (to us) is Superiority, based on individual ideas of greatness and belief of genetic superiority. Superiority was key to the survival of the genes of our ancestors; the belief in one’s genetic mastery encourages aggressive reproduction. The second most important is Mistrust, a trait which was also important to the survival of our ancestors’ genes. The limited resources in the plains required the strong to form cooperative groups. The proliferation of multiple groups vying for resources meant our ancestors had to be suspicious of other people who had different ways of life to ours. The result of these rational instincts has been human history, or as Karl Marx said, the story of class struggle.
But even if world government is possible, is it desirable? The only two world governments to ever exist are the League of Nations and the United Nations. These institutions were from the beginning restrained to an advisory role. What about a true world federation with real power? What implications would it have for humanity?
A world government would bring alongside it many benefits. For one, most obviously, it would mark the definitive end of organized human conflict. While some areas of the world might occasionally come to blows in the age of a true world government, fought by paramilitary partisans, these conflicts would be almost drained of financial or resource backing, with no strike aircraft, submarines, tanks, missiles, or nuclear weapons. The Second World War was so devastating because entire nations devoted their entire military-industrial complexes to waging war. World government would decisively end this.
The end of state war and the futility and impotence of partisan war would almost completely end the funding of militaries worldwide, unproductive institutions which unsettle regions. In 2018, world military spending totalled $1.8 trillion  and employed 20.5 million people  in 2010. This wasted money could be reinvested into world infrastructure, research and development and increasing worldwide basic health and education levels. The opportunity cost of the military is enormous. We would only need 50% of the modern-day military budget to achieve UN Sustainable Development Goals 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14, providing food, water, basic healthcare, primary and secondary education, heating, access to electricity and heating and sanitation for all people around the world .
A world government would end petty and unproductive ‘trade wars.’ A trade war is, of course, when countries place tariffs on goods from other countries to dissuade doing business in those states to promote home manufacturing. These have been shown to be self-harming and senseless. They are caused by the existence of state lines causing people to fear economic growth in another country and the desire to push reform in another country. The most recent of these has been America’s trade war with China, motivated by fear over China’s intellectual property theft and state subsidized economy. These tariffs, while having the goal of promoting ultimate free trade, have been depressing for the world economy. America has suffered the most. The US Chamber of Commerce predicts the tariffs on EU and Chinese goods would cost the US economy $1 trillion over the next decade .
Most importantly, a world government would effectively end the Volksgeist. History tells us repeatedly that ethnic spirits are founded off states placing legal boundaries between people and forcing them to pick sides. States themselves cause us to form Volker. The state is one large tribe, which is frequently alluded to in nationalist speech. The most famous example of this is the partition of India. For hundreds of years, Hindus and Muslims in peace without ethnic violence in the same cities in India. It was partition which created states, Volker and a need to identify with one. During the mass migration, Hindu partisans murdered at least 800,000 Muslims in Karachi . We see this again in Rwanda, where the legalised divisions between Tutsis and Hutus caused a genocide of epic proportions.
What disadvantages would world government bring? There would be very powerful arguments against a world government. The most obvious would be the emergence of a worldwide police division with unopposed power. This would make a world government seem the end of democracy. But the fact of the matter is that the police state could be avoided as easily as it is in democracies today. Because no state would step in to save American democracy if its military proclaimed a dictatorship tomorrow, we can conclude America is not saved from tyranny by the existence of other states. A strong world constitution with powerful checks and balances could easily hold the world military to account.
A common misunderstanding of world government is that it would be overextended and would overlook the complexities of problems, having to deal with every single one. The obvious solution to this problem would be a state-based world government USA-style. The world government would be split into multiple zones which would have experienced and knowledgeable members forming zone governments. All in all, there is no reason a world government should be overextended.
The most depressing conclusion available to this question: the world would benefit exceedingly from a world government, but human nature prevents us from attaining it. But perhaps the problems a world government would solve are practically things of the past already. Human war has been virtually wiped out in the past fifty years. War deaths have decreased worldwide from half a million a year just after 1945 to 87,000 in 2016 . World trade as a % of GDP increased from 24% in 1960 to 58% in 2017 . While world government would be a positive to the globe, perhaps humanity can do without it.
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2. Eidelson, R. J. & Eidelson, J. I., ‘Dangerous Ideas: Five Beliefs That Propel Groups Toward Conflict’, American Psychologist Vol. 58 No. 3, pp. 182-192.
3. Stockholm International Peace Research Institute, ’World Military Expenditure Grows to $1.8 Trillion in 2018’ , https://www.sipri.org/media/press-release/2019/world-military-expenditure-grows-18-trillion-2018, 2019
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