Characterising Global Platforms: Centralised, Decentralised, Federated, and Grassroots

Global digital platforms are software systems designed to serve entire populations, with some already serving billions of people. We propose atomic transactions-based multiagent transition systems and protocols as a formal framework to study them; introduce essential agents -- minimal sets of agents the removal of which makes communication impossible; and show that the cardinality of essential agents partitions all global platforms into four classes: 1. Centralised -- one (the server) 2. Decentralised -- finite $>1$ (bootstrap nodes) 3. Federated -- infinite but not universal (all servers) 4. Grassroots -- universal (all agents) Our illustrative formal example is a global social network, for which we provide centralised, decentralised, federated, and grassroots specifications via multiagent atomic transactions, and prove they all satisfy the same basic correctness properties. We discuss informally additional global platforms -- currencies, ``sharing economy'' apps, AI, and more. While this may be the first characterisation of centralised, decentralised, and federated global platforms, grassroots platforms have been formally defined previously, but using different notions. Here, we prove that their original definition implies that all agents are essential, placing grassroots platforms in a distinct class within the broader formal context that includes all global platforms. This work provides the first mathematical framework for classifying any global platform -- existing or imagined -- by providing a multiagent atomic-transactions specification of it and determining the cardinality of the minimal set of essential agents in the ensuing multiagent protocol. It thus provides a unifying mathematical approach for the study of global digital platforms, perhaps the most important class of computer systems today.