[Epistemic Status: Unknowledgable, Curious, Doubtful]
It is reasonable to assume that we will eventually colonise space. There are many organizations involved today in (very) early stage projects for space colonization. Their effort might shape how early off-earth civilizations are structured and governed. Far-future civilization may have governance structure (and value system) which may be influenced by these early attempts.
Assuming a longtermist perspective and that humanity will flourish, the value of early off-earth settlers is negligible compared to the enormous amount of valuable lives in the future. Therefore, we can consider the following claim as an important crux when considering whether to work on improving near-term off-earth institutions:
Claim: Future civilization is likely to converge on values and structure which is more influenced by near term space colonization efforts than existing institutions.
My intuition is that this is very unlikely, and that there are crucial-er considerations with respect to anything related to space or governance. Nevertheless, I'll make some preliminary arguments supporting and opposing this claim.
Arguments
1. Governance structures tend to lock in to some equilibrium.
2. Space is a neutral environment, where more peaceful and more globally-minded values are more likely to persist.
3. If, say, a hundred years from now there will be a global benevolent government, it will likely result from a new government as opposed to existing ones. In which case, one coming from a dominating off-earth civilization is likely.
Counter Arguments
1. I find it highly unlikely that such an equilibria from the near future will persist for very long, considering the prospects of AGI and other advancements in the far future. This is very important from the point of view of steering the long term future - Can we expect to impact the governance structure of future civilizations?
2. Errrr, I doubt that space will remain neutral as humanity will be more capable to use off-earth assets, as exemplified in this documentary. In the far future there may be no reason to fight over resources, if they are abundant enough (see for example Paretotopial Goal Alignment), but in the near term I do not see a sufficient reason to view space as the best way to increase peace.
3. I find it more likely that a singleton governance will result out of unification of existing powers or out of some major economic achievement. I don't expect space colonies to have any real power. In fact, it seems more likely that innovations in the near future will still be earth-based, and thus they may not transfer to off-earth settlements. Thus, I'd expect a scenario that resembles the british colonization of the already colonized America - where the superior Earthlings will dominate the Off-Earthers.
- Another reason to focus on off-earth governance is that it can be an interesting route to experiment on different societal structures. This however is probably much easier to do on earth in the coming decades by routes such as charter cities or the Seasteading Institute. Despite that, a case can be made for off-earth governance work by considering the high profile of the first off-earth civilizations (even though Mars one, a program that wanted to fund Mars colonization by filming the process as a reality show, went bankrupt..).
- As space technology improves and becomes cheaper, space becomes more useful: Asteroid mining, ICBMs, Satellites and so on. Regulations in this domain can influence common goods (such as the problem of space junk). Also, disputes over resources and territory can lead to conflicts among major powers.
I'm not optimistic about our ability to influence the distant future in this regard (absent a Singleton), because it seems to me there will be two phases, both with strong but very distinct instrumental pressures for norm convergence.
Initially, space colonisation will be extremely dependant on earth. Earth will be the only source of many raw resources, livestock, manufactured goods, scientific expertise and human capital. Distant travel will be performed by robots, not people, who will be fully controlled from earth. Colonies might be economic through mineral export, but self-sufficiency would at best mean impoverishment and at worst be simply impossible. Even when colonies became more advanced, they could not hope to rival the military capacity of earth. This will naturally encourage a highly centralised form of governance, where key decisions are made on earth, and status is determined by the terrestrial social system.
Eventually however, humans will settle over vast distances, and the description above is reversed. With the colonisation of other habitable planets and construction of vast space stations, there will be rival sources for essentially all goods. Furthermore, speed of light limitations mean that most trade will be impossible, and also most warfare, reducing the ability of earth to influence outer systems in either direction. As such it seems that extreme decentralisation will be the natural form of governance.
... unless the central power in the first stage can prevent this from occurring, by securing their control prior to the second stage, perhaps using cryptographic weapon locks.
I'm not sure it's all a matter of power dynamics, at least not to a first approximation. I can imagine cases where a set of rules, conventions or beliefs is fixed quite early and has a lasting impact far away. Moloch whose fingers are ten armies!