Government decisions can be made by divisions that vary in size.
Governments can control jurisdictions that are small or large. This size can be measured in either population or area. Governments can be structured to have multiple levels that govern overlapping jurisdictions of different size.
DEFINITION OF TERMS
The subject here is whether government is centralized or decentralized. A centralized government has most decisions made in one relatively large jurisdiction. A decentralized government has many decisions made in relatively small jurisdictions that subdivide its total territory. Note that while a centralized government may have smaller administrative units, the relevant distinction here is at what level policy decisions are made.
The principle that government should be decentralized can be extended outside the realm of government. In this case, it is sometimes called subsidiarity, and derives from Catholic social teaching. This principle says that decisions should be made at the lowest level practical. The lowest possible level is the individual, followed by the family, private organizations, and local, regional, national, and (theoretically) world government. Decentralization below the level of government is freedom, where everyone can do what they want so long as it does not infringe on the rights of others.
Decentralization is often referred to as federalism, though this term tends to refer more specifically to the American constitutional principle of dual sovereignty between state and national governments. Federalism appears most directly in the Tenth Amendment, and is in turn referred to as "states' rights". This is despite the fact that this term does not appear in the amendment, and that governments do not have rights, they have powers. Thus "states' powers" would be a more accurate term.
SATISFYING POLITICAL DESIRES
Centralization and decentralization have a number of different effects on the actions of government.
One difference between the two is that more people will achieve the outcome they desire for themselves under decentralization than under centralization. It can be shown mathematically that more people will be on the winning sides of an election if a large jurisdiction is broken down into smaller jurisdictions than if a single election applies to everyone. While decentralization guarantees that more people will be on the winning sides, it is true that the winners will not necessarily include all the same people as under centralization.
Note that taking this as far as it will go leads to everyone having his own jurisdiction and everyone being on the winning sides. This is freedom.
On issues for which there is no inherently right or wrong position, this is clearly beneficial, since more people can get their way. Which issues fall into this category is likely to be contested, but it should include such things as state birds and flags at the least.
What about issues where there are inherently right and wrong sides? There is no guarantee that the right side will win under centralization, but decentralization guarantees that fewer people will be coerced. This approaches the ideal of freedom under which nobody is coerced and policy positions simply become personal choices. Personal choices may still be immoral, but personal immorality is different from the immorality of coercion.
Whether or not decentralization leads to good policies, it will at least reduce the potential for civil strife, since more people can have their way at the same time.
Another difference between centralization and decentralization is that under decentralization it is easier for people to avoid policies that are destructive or distasteful. Specifically, they can move to a different jurisdiction. This is easier when jurisdictions are smaller, since smaller jurisdictions are more likely to have the same language, similar culture, and be closer to family.
Similarly, when people are looking to move somewhere, they will have more choices of different policies. Thus they will be more likely to find suitable policies.
This further implies that people will tend to gravitate toward jurisdictions that have better policies and avoid jurisdictions that have bad policies. The latter jurisdictions will receive less tax revenue, and will be forced to contract. Thus decentralization creates a sort of 'natural selection' amongst political jurisdictions that encourages good policies and discourages bad policies.
Political leaders are capable of recognizing this process in action. They can then act to eliminate bad policies and implement good policies. This is true even if they would prefer not to do so otherwise, due to ideology or political pressures.
Decentralization makes reliable comparison of different policies possible. Determining the effects of a particular policy is often difficult. How do you know whether a policy causes a particular result or they are unrelated? In a single jurisdiction it is difficult to tell. But comparing the conditions before and after policy changes (or not) in multiple jurisdictions makes statistically significant analysis possible. Some jurisdictions can serve as a 'control' while others are an 'experimental' group.
Having different policies in different jurisdictions creates data on a greater number of policy options. Being able to compare different policies in different jurisdictions makes it more likely that good ones will be chosen.
Having smaller jurisdictions makes experimentation easier and less costly. It is easier because people need only convince political leaders in a small jurisdiction to try a given policy. With more jurisdictions to choose from, it is more likely that they will find a jurisdiction that is willing to try something new. If the policy succeeds, other jurisdictions may follow along, until the policy becomes widespread. In contrast, if people need to convince political leaders in a single large jurisdiction to try a policy, they may be unable to. A policy that would have been successful may never be implemented.
Smaller jurisdictions also make experimentation less costly, since fewer people will be hurt if a new policy fails than if it is tried in a large jurisdiction.
Decentralization makes it easier to organize resistance to bad policies. A citizen may be able to rouse enough others to create the political pressure needed to change a policy of a town or school board. But a single citizen has no hope of organizing enough people to change a policy in a very large jurisdiction. Effecting that sort of change takes a great deal of organization, which is difficult to create and maintain. It can be co-opted, and even then there is no guarantee of success.
Another benefit of decentralization is that it avoids faction. That is, it is more difficult for a person or group to take control of an entire country and overthrow its political system. In a centralized country, if such a group takes control of the central government, there may not be any institutions capable of resistance. But in a decentralized country, the central government would have less power, and regional jurisdictions could serve as centers of resistance to the faction.
One implication of this analysis of centralization and decentralization is that world government would lead to more government coercion, less satisfaction of people's political desires, and worse policies through less political competition. It would create a great danger of tyranny.
The chief objection to decentralization is that sometimes small jurisdictions may have bad polices. In this case, the central government can overrule them and impose good policies. This is certainly possible. It is possible for either a small jurisdiction to have a better policy than a large one or a large jurisdiction to have a better policy than a small one. The relevant question is which is more likely. For all of the reasons above, the former is more likely than the latter.
Note that this question cannot be settled on a case by case basis. There must be some final authority, whether it is the central or regional government. For decentralization to succeed, some bad policies must be tolerated. Attempting to correct them through centralization would undermine decentralization and lead to worse policies overall.
Centralization leads to more government coercion and less satisfaction of people's political desires. It leads to worse policies through less political competition. It creates a greater danger that a faction could seize power. In contrast, decentralization implies less coercion, better policies, and less danger of faction.
Now, decentralization is not always possible, as in the case of national defense. But whenever possible, government power must be decentralized.