The so-called principle of the self-determination of peoples or nations has been a sacred cow ever since the administration of Woodrow Wilson. But governments never respect this principle in dealing with their own subjects. The principle is invoked only to support the breakup of other political systems, as when Russia recently took Crimea away from Ukraine.
If a right to self-determination existed, it would be necessary to decide which individuals belong to a particular "people" or nation. One possible way would be for each individual to decide for himself. But today's international law considers the right to exclude undesired individuals to be an inherent right of every nation, no matter how much those individuals would like to become citizens. So decisions on inclusion and exclusion of individuals (as well as where boundaries between countries should be drawn) have to be made collectively.
Most people believe that collective political decisions should be made democratically. But it is impossible to know whether a majority favors some decision until the membership of the group which will vote has been defined. A majority decides, but a majority of whom? A majority in Crimea may be a tiny minority in Ukraine. What principle tells us which population should vote to decide the future of Crimea?
A similar problem can be found in American labor law: determining which workers will be included in a "bargaining unit." The National Labor Relations Act, written by people strongly committed to democracy, requires decisions about designating a sole bargaining agent to be made by voting. But the law does not provide that the membership of the unit of workers to be represented will be determined by an election since a vote cannot determine who is to vote.
American law authorizes the NLRB to listen to arguments about which workers should be included in or excluded from the bargaining unit and determine where the boundaries of the unit will be. This gets the job done. Then voting can proceed. A world government could provide the same service when boundaries between different countries are disputed, just as the U.S. Supreme Court resolves border disputes between the various states.
Given today’s lack of a world government the importance of borders combined with a lack of principled ways to resolve disputes about them is a recipe for major trouble. Borders will continue to change, as they always have. (See any historical atlas if you do not believe me!) But these changes will continue to be made by brute force, or by negotiations backed up by force, as they always have been.
Who governs the Falkland Islands? Great Britain. Why? Because it won the war with Argentina back in 1982. Who will govern what is now the eastern part of Ukraine? Stay tuned for further developments! It may not be pretty.