PROPORTIONAL REPRESENTATION - BROADENING THE OPTIONS

Using a recent article by Monroe as a springboard, we extend and gener alize his system of proportional representation (PR) by developing a g eneral method for determining a set of winners from the ballots. Centr al to our analysis is the use of integer programming, which is a type of linear programming. Under Monroe's system and our generalizations o f it, one minimizes total misrepresentation, where misrepresentation i s based on approval votes, the rankings of candidates, or other ballot information. Our method allows for a variety of PR systems, including those proposed by Monroe, by Chamberlin and Courant, and by Tullock, as well as a new system we call 'hierarchical PR'. Ties, the filling o f vacancies, and certain problems of both large and small electorates are all rendered manageable with integer programming. We discuss nonma nipulability, representative ness, and other criteria for selecting a PR system and conclude with some recommendations.