Grassroots platforms with atomic transactions: social graphs, cryptocurrencies, and democratic federations

Grassroots platforms aim to offer an egalitarian alternative to global platforms — centralized/autocratic (Facebook etc.) and decentralized/plutocratic (Bitcoin etc.) alike. Whereas global platforms can have only a single instance—one Facebook, one Bitcoin—grassroots platforms can have multiple instances that emerge and operate independently of each other and of any global resource except the network, and can interoperate and coalesce into ever-larger instances once interconnected, potentially (but not necessarily) forming a single instance. Key grassroots platforms include grassroots social graphs, grassroots social networks, grassroots cryptocurrencies, and grassroots federations. Previously, grassroots platforms were defined formally and proven grassroots using unary transition systems, in which each transition is carried out by a single agent. However, grassroots platforms cater for a more abstract specification using transactions carried out atomically by multiple agents, something that cannot be expressed by unary transition systems. As a result, their original specifications and proofs were unnecessarily cumbersome and opaque. Here, we aim to provide a more suitable formal foundation for grassroots platforms. To do so, we enhance the notion of a multiagent transition system to include atomic transactions and revisit the notion of grassroots platforms within this new foundation. We present concise specifications of key grassroots platforms using atomic transactions: befriending and unfriending for grassroots social graphs, coin swaps for grassroots cryptocurrencies, and communities forming, joining, and leaving a federation for grassroots federations. We prove a general theorem that a platform specified by atomic transactions that are interactive is grassroots; show that the atomic transactions used to specify all three platforms are interactive; and conclude that the platforms thus specified are indeed grassroots. We thus provide a crisp mathematical foundation for grassroots platforms and a solid and clear starting point from which their implementation can commence.