Algorithmic Citizenship is a new form of citizenship, one where your citizenship, and therefore both your allegiances and your rights, are constantly being questioned, calculated, and rewritten.
Most people are assigned a citizenship at birth, in one of two ways. You may receive your citizenship from the place you're born, which is called jus soli, or the right of soil. If you're born in a place, that's where you're a citizen of. This is true in a lot of North and South America, for example - but not much of the rest of the world. You may get your citizenship based on where your parents are citizens of, which is called jus sanguinis, or the right of blood. Everybody is supposed to have a citizenship, although millions of stateless people do not, as a result of war, migration or the collapse of existing states. Many people also change citizenship over the course of their life, through various legal mechanisms. Some countries allow you to hold more than one citizenship at once, and some do not.
Having a citizenship means that you have a place in the world, an allegiance to a state. That state is supposed to guarantee you certain rights, like freedom from arrest, imprisonment, torture, or surveillance - depending on which state you belong to. Hannah Arendt famously said that "citizenship is the right to have rights". To tamper with ones citizenship is to endanger ones most fundamental rights. Without citizenship, we have no rights at all.
Algorithmic Citizenship is a form of citizenship which is not assigned at birth, or through complex legal documents, but through data. Like other computerised processes, it can happen at the speed of light, and it can happen over and over again, constantly revising and recalculating. It can split a single citizenship into an infinite number of sub-citizenships, and count and weight them over time to produce combinations of affiliations to different states.
Citizen Ex calculates your Algorithmic Citizenship based on where you go online. Every site you visit is counted as evidence of your affiliation to a particular place, and added to your constantly revised Algorithmic Citizenship. Because the internet is everywhere, you can go anywhere - but because the internet is real, this also has consequences.