Orit, K.; Harsgor, L.; and R.A.Sheinerman (2015) ‘Are Voters Equal under Proportional Representation?’, American Journal of Political Science, forthcoming, doi: 10.1111/ajps.12225.
Orit, Harsgor and Sheinerman move research on vote-seat disproportionality to the district level by applying the logic of the Lorenz curve of income inequality and the Gini inequality index. While previous studies rely on macro level measures such as the disproportionality index, the authors systematically analyze the vote-seat discrepancy for each party in every district. They map the average vote and seat share graphically and contrast it to perfect representation (the seat share exactly matches the vote share).
The area between the two curves predicts the Representational Inequality Index, with more space suggesting stronger inequality in voters’ representation. Applying this method empirically with data from twenty Western democracies, the authors find that voters casting their ballot in smaller districts are less likely to make a difference on seat distribution and are therefore underrepresented. This disproportionality at the district level translates into an unequal representation of parties along ideological cleavages: Right-wing parties tend to be overrepresented if the Representational Inequality Index is high, because they are usually stronger in more rural areas, which tend to have smaller districts. Thus, they have a competitive advantage in rural areas caused by district magnitude, while winning a proportional vote share in the larger urban districts.
This research improves our understanding of how electoral rules operate at the district level and clarifies how varying district size causes unequal representation of voters within a country. However, there might be a trade-off between ideology- and region-based interests of voters that this model cannot capture. District magnitude does not only foster vote-seat proportionality, but is also a political tool to incorporate regional interests. To ensure a fair say in parliamentary debate, many countries decide to assign a larger proportion of seats to regions with strong geographical interests than they have voters (A good example might be the Faroe Island in Denmark, which have a district magnitude of two). Applying the argument of the authors in this context means: While right-wing voters might be better represented than voters supporting parties at the opposite side of the ideological spectrum in the same district, they are all on average still overrepresented. This leads to the question how voter-seat disproportionality could be incorporated into this model of vote-seat discrepancy.