Abstract
The measurement of disproportionality, volatility and malapportionment often employ similar indices. Yet the debate on the issue of adequate measurement has remained open. We offer a formal and rigorous list of properties that roughly subsume those of Taagepera and Grofman (Party Polit 9(6):659–677, 2003). One of these properties, Dalton’s principle of transfers, is formalized in a manner that resolves the ambiguity associated with it in previous studies. We show that the cosine measure satisfies all the properties. We also show how the Gallagher index can be modified to satisfy all the properties. The cosine measure and the modified Gallagher measure are co-monotone.
Similar content being viewed by others
References
Balinski ML, Young HP (2001) Fair representation: meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, Washington DC
Dalton H (1920) Measurement of the inequality of income. Econ J 30: 348–361. doi:10.2307/2223525
Duncan OD, Duncan B (1955) A methodical analysis of segregation indexes. Am Sociol Rev 20: 210–217. doi:10.2307/2088328
Gallagher M (1991) Proportionality, disproportionality and electoral systems. Elect Stud 10: 33–51. doi:10.1016/0261-3794(91)90004-C
Lijphart A (1994) Electoral systems and party systems. Oxford University Press, New York
Loosemore J, Hanby V (1971) The theoretical limits of maximum distortion: some analytical expressions for electoral systems. Br J Polit Sci 1: 467–477
Monroe BL (1994) Disproportionality and malapportionments: measuring electoral inequity. Elect Stud 13: 132–249
Pedersen MN (1979) The dynamics of European party systems: changing patterns of electoral volatility. Eur J Polit Res 7(1): 1–26. doi:10.1111/j.1475-6765.1979.tb01267.x
Rae DW (1967) The political consequences of electoral laws. Yale University Press, New Haven
Salton G (1971) The SMART retrieval system—experiments in automatic document processing. Prentice-Hall, Englewood Cliffs, NJ
Taagepera R, Grofman B (2003) Mapping the indices of seats–votes disproportionality and inter-election volatility. Party Polit 9(6): 659–677. doi:10.1177/13540688030096001
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koppel, M., Diskin, A. Measuring disproportionality, volatility and malapportionment: axiomatization and solutions. Soc Choice Welf 33, 281–286 (2009). https://doi.org/10.1007/s00355-008-0357-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-008-0357-1