A formal count of a population is a census.
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A formal order given by a higher authority is called a mandate. This can be an order given by a higher court or a person in higher power within the government.
Census
One factor that determines the number of representatives for a given Congressional District is the distribution of the population with a state. The more populated a state is, the more members that state can have in Congress.
The Three-Fifths Compromise
Yes, Congress counted blacks as 1 third of a person