This question is about rules for apportionment of parliament seats among parties. Many such rules have the property, that a party may gain a seat by splitting into two parties, or two parties may gain a seat by merging into one party.
As a simple example, consider a parliament with 10 seats, and four parties who win 21,22,22,35 votes respectively. The D'Hondt apportionment method would give the parties 2,2,2,4 seats respectively.
However, if the two 22 parties merge into a single party (with 44 votes), then the D'Hondt method gives the parties 2, 5, 3 seats respectively - so the two merged parties gained a seat: they now have 5 seats overall, instead of the 2+2 that they could have without merging.
My question is: is there an apportionment rule in which splitting / merging cannot change the outcome? I.e., if a party that splits into two parties, they get in total the same number of seats as the original one; and if two parties merge into one, it gets in total the same number of seats as the original two?