Apportioning
verb
To divide and distribute portions of a whole.
“The controlling party had apportioned the voting districts such that their party would be favored in the next election.”
Specifically, to do so in a fair and equitable manner; to allocate proportionally.
“The children were required to dump all of their Halloween candy on the table so that their parents could apportion it among them.”
Synonyms: allocate, allot, dispense, parcel out, share out
noun
Apportionment