How Matland’s Party Magnitude Works

In his 1993 paper, Richard Matland argues that party magnitude — the district magnitude divided by the number of parties — is causally closer to levels of political representation than the underlying district magnitude. The concept of party magnitude is used from time to time in the literature, but usually little attention is paid as to how it works.

In addition to the effects of district magnitude, assuming that men are more likely to take the top spot of party lists than women are, where there are fewer parties competing, the likelihood that a woman is elected is increased by reaching further down the party list. Combining the two effects, it is also apparent why, as Matland acknowledges, the effects of party magnitude are temporarily limited. The association is weak where the proportion of women in parliament is low. In this case the likelihood of that a woman is elected is low in any case. As the proportion of women in parliament increases, so does the association. Once women are as common as candidates as men are, and they are equally likely to appear at the top of party lists, the association once again decreases. The likelihood that a woman is elected in this case approaches 50%.

Matland, R. (1993). Institutional variables affecting female representation in national legislatures: The case of Norway. Journal of Politics, 55, 737-55.

Splitting Groups and the Gallagher Index

Measures of (dis-) proportionality are used for many things, including measuring representation (congruence). Many measures exist, and of these Gallagher’s index (1991, 1992) is so widely used and acclaimed that it is easy to forget that it is not perfect. Indeed, there does not appear to be such a thing as the perfect measure in this case (Taagepera and Grofman 2003).
One issue relevant to representation not picked up by Taagepera and Grofman’s paper is that of splitting groups that are not represented. Let’s look at a population with two groups, A and B. Let’s assume the legislature only consists of one group: A. Thus, (1 minus) Gallagher gives 0.8. For comparison the Rose index (i.e. 1 minus Loosemore-Hanby) also gives 0.8. A difference occurs, however, if I then differentiate between subgroups among the B: B1 and B2. The legislature (all A) is unchanged. The resulting value for (1 minus) Gallagher is 0.83, while the Rose index does not change.
By using the Gallagher index, the implication is that having two smaller groups absent in the legislature is somehow preferable to having a larger group absent. It also implies that if we differentiate absent groups conceptually, representation is affected, despite them simply not being represented.
We can also think of this in terms of parties. In the first case, only one of two parties is represented. The implication of using the Gallagher index is, though, that if the party absent from parliament splits into two smaller parties (for whatever reason) the representational situation is slightly improved.
I do not to mean to discourage the use of the Gallagher index, but to highlight the difficulty of measuring proportionality.

The code for doing this is my R-package polrep is as follows:
> pop1 <- c(0.8,0.2,0)
> leg <- c(1,0,0)
> pop2 <- c(0.8,0.1,0.1)
> Gallagher.1(pop1,leg)
[1] 0.8
> Rose(pop1,leg)
[1] 0.8
> Gallagher.1(pop2,leg)
[1] 0.8267949
> Rose(pop2,leg)
[1] 0.8

Gallagher, M. 1991. ‘Proportionality, disproportionality and electoral systems’. Electoral Studies 10(1): 33–51.
———. 1992. ‘Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities’. British Journal of Political Science 22(4): 469–96.
Mackie, T., and R. Rose, eds. 1991. The International Almanac of Electoral History. London: Macmillan.
Taagepera, R., and B. Grofman. 2003. ‘Mapping the indices of seats-votes disproportionality and inter-election volatility’. Party Politics 9(6): 659–77.

Representation of Women in National Legislatures

After a considerable time as an on-line paper, my article on the political representation of women in national legislatures finally appeared in print. I use a large cross-national sample of all free and partly-free countries (according to Freedom House). Like some recent contributions, I find that attitudes toward women as political leaders are a powerful predictor for the share of women in the national legislature. This link was already established by Pippa Norris and Ronald Inglehart, amongst others, but in this article I also consider the role of gender quotas. Once controlling for regional or cultural/attitudinal differences, voluntary party quotas and legislative quotas do not appear to be significant. Obviously there are often implementation issues, but we need to think more carefully about the underlying mechanisms: I argue that cultural variables are probably behind both the share of women in legislatures and the (successful) implementation of quotas.

Norris, P., and R. Inglehart. 2001. “Cultural obstacles to equal representation.” Journal of Democracy 12(3): 126–40.