What Is the Role of District Magnitude in When Women Represent Women?

Electoral systems impose incentives for how reelection-seeking candidates should go about building reputations. Across most systems, as the number of seats to be distributed in a district increases, the proportion of the vote that a candidate needs to get elected decreases.

In order to generate support from the majority of voters, candidates and their parties tend to focus on policies that are appealing to the median voter (Downs Reference Downs1957). As district magnitude (M) increases, voters will calculate that they can safely distribute their votes across more candidates without their votes being “wasted” on candidates who are not viable (Cox Reference Cox1987; Duverger Reference Duverger1954; Leys Reference Leys1959; Sartori Reference Sartori, Montgomery and Hirschman1968). Parties can even seek to assemble a slate of candidates, each of whom is likely to appeal to a distinct subset of voters (Kweon and Ryan Reference Kweon and Ryan2021; Shugart, Valdini, and Suominen Reference Shugart, Valdini and Suominen2005; Taylor-Robinson Reference Taylor-Robinson, Martin, Saalfeld and Kaare2014). Facing such incentives, instead of perceiving themselves as responsible for the interests of at least 50 per cent + 1 of the constituents in their districts, legislators may feel they can specialize (Coffe Reference Coffe2018; MacDonald and O'Brien Reference MacDonald and O'Brien2011; Thomas Reference Thomas1994; Thomas and Welch Reference Thomas, Welch and Carroll2001; Tremblay Reference Tremblay2005).

Research Design

Virtually all of the existing literature in this area is dependent on observational data—with all the challenges to causal inference that entails. While the vast majority of the works we have already cited are careful to minimize disjunctures between their theorizing and their empirical tests, some scholars working with observational data have sought to address issues of causal inference more directly. Examples of a few works that have employed innovative research designs include Clark and Caro (Reference Clark and Caro2013), Hoehmann (Reference Hoehmann2020), and MacDonald and O'Brien (Reference MacDonald and O'Brien2011). We see our work as a contribution to this thread of literature that seeks creative ways to exploit observational data.

In this letter, we capitalize on an instance of reform, its timing, and the nature of the post-reform system to take several turns at modeling select observations (see Figure 1). Our strategy could be applied in any context in which an electoral reform is adopted in one legislative term and then first applied for the selection of the subsequent legislature—the way most reforms are likely adopted.

Fig. 1. Modeling strategies.

As a first cut, we look at cosponsorship patterns in the last pre-reform legislative term, the term in which the reform was adopted, and the first post-reform legislative term together. Initially, we code members serving in the term in which the reform was adopted as having the incentives imposed by the pre-reform rules, under which they were elected, throughout the entire term (Model 1). We then split those reform-term members based on the precise date of the reform, giving them M = 2 prior to the reform and the magnitude they would face in 2018 if they were to seek reelection (Model 2). This was possible because the post-reform districts were either identical to a pre-reform district or were some combination of whole pre-reform districts.Footnote ¹ We then drop observations from the term in which the reform was adopted all together to rule out the possibility that our results are somehow tainted by observations when electoral incentives were in flux (Model 3). Then, we analyze sponsorship patterns of members only during the term in which the reform was adopted, looking at them before and after its approval (Model 4).Footnote ² For a comparative depiction of Models 1 through 4, see Figure 1.

In a second cut at the question, we seek to address any concern regarding different individual representatives, with unique policy priorities, serving across different terms. It is possible that candidates, especially women candidates, who entered in the later congress were more attuned to women's issues than candidates who ran previously. As a result, we might confound this change in the candidate pool with the effects of electoral incentives. In an effort to address such concerns, we limit our observations to only members who served both before and after the reform. On this subset of the data, we repeat the first three modeling strategies outlined earlier: members from all three terms, with reform-term members coded as having only pre-reform incentives (Model 5) and then as facing two different sets of incentives (Model 6); and then only members in the full pre-reform term and the post-reform term (Model 7). For a comparative depiction of Models 5 through 7, see Figure 1.

Finally, one might be concerned that due to some kind of ideological shift, women's issues became increasingly salient over time. Thus, even members who had not focused on them in prior terms might focus on them with greater frequency more recently. Again, we might confound this changing milieu of awareness with a change in electoral incentives. To deal with this, in a third cut at the question, we limit ourselves to examining the effect of the interaction between MC gender and district magnitude in only the post-reform term, where district magnitude varies from three to eight seats but issue salience would be more or less constant (Model 8). For a depiction of Model 8, see Figure 1.

Our ability to parse our data into the eight models described earlier allows us to address multiple concerns that might otherwise typically arise in an observational study unable to capitalize on the timing of an institutional change. That said, despite our repeated shuffling of observations, we are not claiming that we have “as if” random assignment of district magnitude as a treatment.

Data and Methods

We use data from the 2010–14, 2014–18, and 2018–22 Chilean Cámara de Diputadas y Diputados. We collected all bills (mociónes) introduced by legislators.Footnote ³ In total, our data include 4,481 bills sponsored by 255 unique legislators. Of these, 3,307 bills were co-sponsored by at least one of the fifty-five women elected during this period.

We recognize that defining “women's issues” is not without controversy. In terms of breadth, we take a relatively conservative definition (Funk and Philips Reference Funk and Philips2019)—that is, a relatively narrow definition focused on women's rights and equality. A middling definition adds to these children and family issues and anti-poverty policies. An even broader definition adds to these issues that correspond to women's traditional social roles. While we prefer the first of the three, the bulk of our findings are robust to the use of multiple, possibly competing, sets of keywords for identifying issues.

We combined two approaches to code bills about women's issues. First, we utilized a dictionary-based approach to automatically code the bills as (potentially) addressing a women's issue. We classified bills using Barnes' (Reference Barnes2016) and Htun, Lacalle, and Micozzi's (Reference Htun, Lacalle and Micozzi2013) dictionaries. Barnes (Reference Barnes2016) was interested in determining when women would represent women, and Htun, Lacalle, and Micozzi (Reference Htun, Lacalle and Micozzi2013) were interested in whether the increasing presence of women in a chamber resulted in more substantive representation. Ideal for our purposes, both dictionaries contain terms related to women's rights (that is, reproductive rights, gender equality in pay, equal representation, access to childcare, and so on) and women's health, but they differ in how they were built. Barnes (Reference Barnes2016) created her dictionary by reading through bills, while Htun, Lacalle, and Micozzi (Reference Htun, Lacalle and Micozzi2013) defined their set of keywords a priori.Footnote ⁴ Both were designed for application to the Argentine case at a given point in time. As a result, they may miss nuances in language usage between the two countries. For example, Chileans use the term “intrafamiliar” (“intrafamily”) when discussing domestic violence but Argentines apparently do not. Moreover, since they were created to code bills mostly introduced before 2012, they may not contain keywords on women's issues that have received more attention recently. For example, none of the dictionaries contain the term “femicidio” (“femicide”), which, according to Google search trends for Chile, has become more widely used in recent years.

We initially used both dictionaries to split the bills into those that were (potentially) related to women's issues and those that were not. Then, we read the titles of the bills to identify false positives and false negatives. In doing this second step, we coded as focused on women's issues, for example, bills about intrafamily violence (violencia intrafamiliar), femicide (feminicidio), and violence against children and teenagers (an issue that disproportionately affects girls in Chile) that were missed by the original dictionaries. Our reading of the titles allowed us to remove bills about the environment (madre Tierra [“mother Earth”]), stem cells (células madre), and gender identity that the original two dictionaries included among the bills on women's issues. In total, we coded 250 bills as being about women's issues.Footnote ⁵

As we explained in the previous section, we use a variety of modeling strategies to test our hypothesis. In all these models, the dependent variable is the percentage of the legislator's portfolio that relates to women's issues (Women's issues) and our unit of analysis is the legislator-term (or legislator-term-reform date in the case of Models 2 and 6).

We utilize two explanatory variables in the models, Woman and Magnitude (or M).Footnote ⁶ For the 2013–14 and 2018–22 terms, M is the district magnitude used in the previous election (M = 2 for the 2013–14 term and 3 ≤ M ≤ 8 for the 2018–22 term). For the 2014–18 term, M is set equal to 2 in Models 1 and 5. In Models 2, 4, and 6, M = 2 for the period between March 11, 2014, and April 27, 2015, and the M established by the reform in the remainder of the term.Footnote ⁷ Given that we are interested in learning whether women introduce more women's issues bills as a function of the magnitude of the district in which they were elected, we include an interaction between Woman and M in all models.

Finally, we fit our models using the ordinary least-squared estimator. We opted for this modeling strategy because of its flexibility when handling fixed effects and its easiness of interpretation when including interaction terms.Footnote ⁸