@article{iiasa14051,
          volume = {4},
          number = {1},
           month = {February},
           title = {Quotatone Apportionment Methods},
       publisher = {INFORMS},
            year = {1979},
         journal = {Mathematics of Operations Research},
             doi = {10.1287/moor.4.1.31},
           pages = {31--38},
             url = {https://pure.iiasa.ac.at/id/eprint/14051/},
            issn = {0364-765X},
        abstract = {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.},
          author = {Balinski, M. L. and Young, H. P.}
}