Let's define a Basic Post Scarcity Economy as an economic system in which all the basic necessities are provided for free, without requiring any kind of labour in exchange. In this economy working it's entirely optional during the entire lifetime. It is expected that such a lifestyle can be enabled by a widespread automation of the current productive activities. The adjective "basic" is added to discriminate this economy from the related post-scarcity economy in which also luxury goods are widely available.
Additional readings: A curated list of Post-Scarcity resources
When will Basic Post Scarcity Economy be achieved by a nation state?
For the sake of this forecast, these will be the requirements for a Basic Post Scarcity Economy:
-The following basic services and goods should be provided for free to any citizen: Healthcare, Education, Housing, Food, Clothing, Transportation, Internet and Telecommunication, Utilities, Basic household appliances and furniture (e.g. bed, fridge, etc.), basic personal computing (e.g a phone and a computer).
-Such services are available for free for an unlimited time period.
-Such services should be abundant (e.g. a citizen can require an arbitrary amount of surgeries, a heterogeneous diet, transportation replacements in case of broken components, etc.), but they don't need to be unlimited. For instance requests for free housing in specific places or oversized requirements for food supplies may be refused as they are not considered basic.
-The citizens should not be asked to perform any specific labour activity and should be free to decide how to spend their time, have free speech and be free to follow specific religions and ideologies. Minor duties (such as registering IDs, attending some meetings, education requirements, participation in voting) can be still present. Moreover citizens are still required to follow laws and safety regulations.
-Such freedom should be granted to at least 99% of the citizens at any given time. That is a small part of the population can be still required to perform some work activities. If such working population is required, it should not be forced to work for more than 5 years in a lifetime.
-Non basic services and goods should still be available for purchase by any citizen.
The question resolves when a nation state with population greater than 500.000 approves a bill which (combined with previous laws) fulfils the requirements of a Basic Post Scarcity Economy. It resolves ambiguously if such economy is not reached by 2200.
-Notice that the presence of a Universal Basic Income or similar is not required to fullfill the resolution criteria, and it's no substitute to having free access to the services and good mentioned.