A variety of non-mainstream commenters have proposed similar systems for governing a post-centralized world. Though the details of archipelago, patchwork, anarchocapitalism with private law, and other similar ideas vary, they have in common the idea that people should choose their government from among a variety of competing options. Competition would force governments to do well by their citizens, and the availability of options would let people choose a government that fits their values and priorities.
What would working towards archipelago look like? In the US, a top-down approach might focus on weakening the federal government and restoring power to the States. Efforts in this direction have been ineffective and unpopular.
A bottom-up approach would look like withdrawal from mainstream society, building up alternate, more ‘natural’ sources of authority for smaller communities. Religious communities are putting this into practice. The Benedict option is being pursued by Christians who fear persecution and secularization. By relocating to communities of people who share their values, they hope to preserve and pass them on. Similarly, in some Muslim communities voluntary conflict resolution processes based on sharia operate in parallel to official courts. Unfortunately, search results are heavily polluted by arguments around the idea of imposing sharia through official structures, so I don’t have a good link to share.
It’s important to note that these islands don’t see themselves as part of an archipelago. Outgroup homogeneity bias will make each new island in the archipelago appear to its inhabitants as a rebellion against a hostile mainstream culture (that is disappearing, or no longer really exists).
These religious islands are distinct from technolibertarian examples of corporations routing around formal state power, such as the widespread use of contracts that waive rights to trial in favor of private mediation or the endrun that sharing economy companies like Uber and AirBnB have made around entrenched regulatory structures. One difference is that they are authentic communities with specific ideas about the nature and sources of authority; another is that they will not be subsumed by the current formal structures of the authority monopoly. Early islands in the formation of an archipelago must be truly distinct from the mainland.
edit 10/12/2016: While writing a followup relating the current failure of the bipartisan political system (the degree to which the US more closely resembles two one-party states than one two-party states) and the piecewise transition towards archipelago to David Chapman’s countercultural and subcultural modes of meaningness, I found that he had already sketched out this idea and is currently elaborating it further. Highly recommended.