On the complexity of achieving proportional representation

We demonstrate that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large. On a different note, in settings where the size of the assembly is constant, we show that the problem can be solved in polynomial time.

[1]  Christos H. Papadimitriou,et al.  On the complexity of integer programming , 1981, JACM.

[2]  Burt L. Monroe,et al.  Fully Proportional Representation , 1995, American Political Science Review.

[3]  Peter C. Fishburn,et al.  Chapter 4 Voting procedures , 2002 .

[4]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[5]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[6]  Ariel D. Procaccia,et al.  Junta distributions and the average-case complexity of manipulating elections , 2006, AAMAS '06.

[7]  Steven J. Brams,et al.  Proportional Representation , 1998 .

[8]  Vincent Conitzer,et al.  Complexity of manipulating elections with few candidates , 2002, AAAI/IAAI.

[9]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[10]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[11]  M. Trick,et al.  Voting schemes for which it can be difficult to tell who won the election , 1989 .

[12]  John R. Chamberlin,et al.  Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule , 1983, American Political Science Review.

[13]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[16]  P. Fishburn,et al.  Voting Procedures , 2022 .