%0 Journal Article
%@ 0364-765X
%A Balinski, M.L.
%A Young, H.P.
%D 1979
%F iiasa:14051
%I INFORMS
%J Mathematics of Operations Research
%N 1
%P 31-38
%R 10.1287/moor.4.1.31
%T Quotatone Apportionment Methods
%U https://pure.iiasa.ac.at/id/eprint/14051/
%V 4
%X The problem of apportionment is that of allocating an integer number of seats “proportionally” among a set of states or regions as a fraction of their populations. An apportionment method satisfies quota if it accords to each state the exactly proportional (rational) number of seats due it rounded up or rounded down. A method is house monotone if no state’s allocation goes down when the total number of seats to be distributed goes up.    This paper gives a simple characterization of all house monotone methods satisfying quota. Further, a manner of exposition is formulated which unites several key house monotone apportionment methods, thus showing clearly their connections.