Abstract
This paper examines a method to achieve proportional representation (PR) for parties in a legislature that allows the size of the legislature to vary as a function of voting results. The legislature's base consists of one elected candidate from each voting district. Seats are then added to underrepresented parties to approximate their nationwide vote proportions. Additions are governed by rules designed to honor the single-member district concept, to keep the increase manageable, and to satisfy other desirable criteria.
These rules work well in the two-party case although they limit the extent to which true PR is achieved. When there are three or more parties, it is necessary to relax the rules if reasonable moves toward PR are to occur.
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Brams, S.J., Fishburn, P.C. Proportional representation in variable-size legislatures. Soc Choice Welfare 1, 211–229 (1984). https://doi.org/10.1007/BF00433517
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DOI: https://doi.org/10.1007/BF00433517