Over the centuries, polities have repeatedly consolidated. On the European continent, ancient kingdoms and feudal principalities yielded to city-states, empires, and, ultimately, the modern nation-state system (Tilly, Reference Tilly1990). Although national borders have remained largely fixed since the collapse of the Soviet Union, populations have grown substantially, and governments still redraw local borders. A contested “third wave” of municipal amalgamations is under way in mature democracies (Swianiewicz et al., Reference Swianiewicz, Gendźwiłł and Zardi2017; Erlingsson et al., Reference Erlingsson, Ödalen and Wångmar2020). This enduring push to scale up underscores the continuing importance of the question first posed by Dahl and Tufte (Reference Dahl and Tufte1973): how does polity size affect democratic performance? Previous research links size to democratization, democratic survival, political participation, and more (e.g.,Hadenius, Reference Hadenius1992; Ott, Reference Ott2000; Remmer, Reference Remmer2010; Gerring et al., Reference Gerring, Palmer, Teorell and Zarecki2015; Gerring and Veenendaal, Reference Gerring and Veenendaal2020), yet we still lack evidence on its impact on descriptive representation.Footnote 1
In this paper, we develop and test a novel argument about how polity size affects women’s representation. Our argument builds on insights from two separate literatures. First, from the literature on legislature size, we draw the insight that as polities grow, politicians may respond by expanding the assembly. However, seat expansion is typically subproportional, consistent with Taagepera’s cube-root law (e.g., Taagepera, Reference Taagepera1972; Tufte, Reference Tufte1974; Stigler, Reference Stigler1976; Shugart and Taagepera, Reference Taagepera and Shugart1989; De Santo and Le Maux, Reference De Santo and Le Maux2022). Competitiveness over seats, the number of enfranchised voters per seat, will therefore increase. Second, from the literature on gender and politics, we draw the insight that women’s representation is governed by supply and demand for women candidates (Norris and Lovenduski, Reference Norris and Lovenduski1995) and that these dynamics are shaped by electoral and legislative institutions (Krook, Reference Krook2009). Specifically, we argue that the increased competitiveness over seats associated with large polities may plausibly depress the demand for, and potentially the supply of, women candidates.
While our theoretical argument suggests that polity size will decrease women’s representation, estimating such an effect is challenging. Whether we are considering nations or sub-national units, existing polities are the result of processes of migration and agglomeration, where individuals with differing characteristics and policy preferences sort themselves into different settings (Tiebout, Reference Tiebout1956). Moreover, this selection bias is compounded when polities themselves make the decisions about when to expand (e.g., Alesina et al., Reference Alesina, Baqir and Hoxby2004; Vernby, Reference Vernby2013).
Our strategy for dealing with this follows previous literature that has used amalgamation reforms (when smaller polities are grouped together to form bigger ones) as a source of exogenous variation (e.g., Lassen and Serritzlew, Reference Lassen and Serritzlew2011; Gerring et al., Reference Gerring, Palmer, Teorell and Zarecki2015; Hanes, Reference Hanes2015; Blom-Hansen et al., Reference Blom-Hansen, Houlberg, Serritzlew and Treisman2016). We digitize various statistical yearbooks and archival data to construct a novel dataset on two large reforms that took place in Sweden between 1952 and 1973, both of which fulfill these methodological criteria. Together, the reforms reduced the number of municipalities by almost 90% and dramatically increased average polity size. If our theoretical argument holds, we should expect to observe a relative decrease in women’s representation in amalgamated municipalities, reflecting the heightened competitiveness over assembly seats.
The evidence confirms our theoretical expectations. Relative to stable municipalities, amalgamated units experienced increased seat competitiveness and a markedly slower rise in women’s representation, a result robust to numerous covariates and placebo tests. Decomposing the effect shows that enlarging the population while holding council size constant reduces women’s seats, whereas adding seats moderates—but does not erase—the loss. Because populations grew faster than assemblies, the net impact of both reforms was negative, even though most amalgamated councils became larger than their predecessors.
By linking polity size to women’s descriptive representation, we make three contributions. First, women’s descriptive representation is normatively vital. When women hold office, women’s engagement rises (Wolak, Reference Wolak2020), gender‐salient policy improves (e.g., Bratton and Ray, Reference Bratton and Ray2002; Chattopadhyay and Duflo, Reference Chattopadhyay and Duflo2004; Svaleryd, Reference Svaleryd2009; Halim et al., Reference Halim, Yount, Cunningham and Pande2016), and perceived legitimacy deepens (Phillips, Reference Phillips1998; Mansbridge, Reference Mansbridge1999). Jurisdictional reforms that enlarge polities must therefore weigh potential costs to parity.
Second, we refine the size–democracy debate. While larger units can boost competition and service efficiency (Gerring et al., Reference Gerring, Palmer, Teorell and Zarecki2015; Hanes, Reference Hanes2015), they can also dampen efficacy, turnout, and trust (Mouritzen, Reference Mouritzen1989; Lassen and Serritzlew, Reference Lassen and Serritzlew2011; Hansen, Reference Hansen2013; Roesel, Reference Roesel2017). We add descriptive representation to the list of democratic outcomes that can be adversely affected by polity size.
Third, our theory adds a demographic dimension—the ratio of people to seats—to institutional explanations of descriptive representation. By doing so, it informs current debates on electoral design which have focused on proportional versus majoritarian systems (Profeta and Woodhouse, Reference Profeta and Woodhouse2022), district magnitude (Lucardi and Micozzi, Reference Lucardi and Micozzi2022), and party organization (Aldrich, Reference Aldrich2020). It also complements the redistricting literature on minority representation, which has centered on how boundary changes shift the demographic composition of district electorates (e.g., Canon, Reference Canon2022). Our argument identifies a distinct channel that operates when boundary changes alter the ratio of voters to seats while holding composition constant. This mechanism is more cleanly observed in the case of women, who, unlike many ethnic and racial minorities, are not spatially segregated. How the channel proposed here interacts with the geographic distribution of minorities in jurisdictional mergers is a topic for future research.
1. Women’s representation, seat competitiveness, and polity size
From the literature on gender and politics, we draw the insight that women’s descriptive representation is governed by both the supply of and the demand for women candidates (Norris and Lovenduski, Reference Norris and Lovenduski1995; Lawless and Fox, Reference Lawless and Fox2005), and that these dynamics are shaped by electoral and legislative institutions (Krook, Reference Krook2009). Supply-side factors influence whether women step forward as candidates, while demand-side factors concern party gatekeepers’ willingness to recruit and select women (Norris and Lovenduski, Reference Norris and Lovenduski1995). Studies have rarely theorized the role of polity size in this process. When included, population size typically appears only as an untheorized control or a proxy for factors like urbanization or office desirability (Welch and Karnig, Reference Welch and Karnig1979; Nechemias, Reference Nechemias1985; Darcy et al., Reference Darcy, Welch and Clark1994; Smith et al., Reference Smith, Reingold and Owens2012). In this paper, we argue that polity size can have a direct impact on women’s representation via its effect on competitiveness over legislative seats.
A larger number of seats (whether in a district or in the assembly as a whole) has long been theorized to facilitate the inclusion of women and other underrepresented groups in politics. Often invoking a demand-side logic, the literature argues that when there are more positions to fill, party gatekeepers face weaker zero-sum constraints and can more readily nominate some “non-traditional” candidates without jeopardizing their chances of winning (Rule, Reference Rule1987; Matland and Brown, Reference Matland and Brown1992; Kjaer and Elklit, Reference Kjaer and Elklit2014; Allen and Stoll, Reference Allen and Stoll2023). Empirically, numerous studies find that women’s presence in elected bodies tends to rise with district magnitude or assembly size (e.g.,Rule, Reference Rule1987; Darcy et al., Reference Darcy, Welch and Clark1994; Matland and Studlar, Reference Matland and Studlar1996; Schwindt-Bayer and Mishler, Reference Schwindt-Bayer and Mishler2005). When, on the other hand, few seats are at stake, the dominant group (often men incumbents or insiders) is less willing to share those limited positions.Footnote 2 As Alozie and Manganaro (Reference Alozie and Manganaro1993), p. 386 observed, if there are “only a few slices in the pie,” the majority group is not eager to share them. Likewise, intense intra-party competition for scarce nominations tends to disadvantage candidates who do not fit the prevailing male norm of a political representative. This is especially likely to be true in contexts where male-dominated party committees control selection (Childs and Evans, Reference Childs and Evans2012, p. 744). Consistent with this reasoning, proportional representation electoral systems (characterized by multi-member districts) are generally associated with higher women’s representation than single-member district systems (Norris, Reference Norris1985; Paxton, Reference Paxton1997; Reynolds, Reference Reynolds1999; Paxton et al., Reference Paxton, Hughes and Green2006), though findings are not uniform across all cases (e.g.,Kittilson, Reference Kittilson2006).Footnote 3
We argue that this relationship can be understood through the mechanism of seat competitiveness, which we define as the ratio of potential candidates to available seats. When the pool of aspirants grows large relative to the number of available seats, competition for each seat intensifies, leading to a congestion effect that can harm the prospects of women candidates. Prior research on district magnitude highlights the denominator of this ratio (the number of seats). Our contribution is to emphasize the numerator (the size of the candidate pool). If the number of candidates expands without a proportional increase in seats, candidates must effectively “elbow” past each other to secure their nomination and election. In such crowded contests, (male-dominated) party elites, who often favor experienced or familiar (men) candidates, may be less inclined to take chances on newcomers, including women. It is when seats become scarce that any underlying preference among gatekeepers for men candidates becomes consequential. By contrast, such a preference can be satisfied alongside the nomination of women when seats are more plentiful. Party selection of candidates can in this case work against women due to lack of seniority (Folke and Rickne, Reference Folke and Rickne2016; Cirone et al., Reference Cirone, Cox and Fiva2021) and/or discrimination. Pre-reform selection patterns are consistent with candidates not being selected solely on competence, and suggest that both gender bias and seniority, while difficult to disentangle, are plausible explanations (Besley et al., Reference Besley, Folke, Persson and Rickne2017). High seat competitiveness might also depress the supply of women candidates if potential women aspirants perceive the electoral arena as overly competitive or biased and thus opt not to run (Kanthak and Woon, Reference Kanthak and Woon2015; Preece and Stoddard, Reference Preece and Stoddard2015). In short, greater congestion in the race for office can disadvantage women both by reinforcing gatekeepers’ biases (a demand-side effect) and potentially also by discouraging women’s candidacies (a supply-side effect).
How does polity size factor into this dynamic? The size of the polity is closely related to the pool of potential candidates. Larger populations naturally produce a larger absolute number of politically ambitious individuals. At the same time, although bigger polities tend to have larger legislatures, decades of research show that the growth in assembly size does not keep pace with population growth. Indeed, the sub-proportional response of assembly size to population is one of the most robust stylized facts in comparative politics, with empirical support spanning national legislatures, sub-national councils, and a wide range of institutional contexts (e.g.,Taagepera, Reference Taagepera1972; Tufte, Reference Tufte1974; Shugart and Taagepera, Reference Taagepera and Shugart1989; De Santo and Le Maux, Reference De Santo and Le Maux2022). In practical terms, as population 
$P$ rises, the assembly size 
$A$ usually rises in a less than proportional manner (for example, doubling 
$P$ might lead to only about a 20–50% increase in 
$A$). A rough rule-of-thumb is the “cube root law,” which holds that 
$A \approx P^{1/3}$ (Taagepera, Reference Taagepera1972; Shugart and Taagepera, Reference Taagepera and Shugart1989). The consequence is that larger jurisdictions have more constituents (and potential candidates) per seat than smaller ones. In other words, the aggregate seat competitiveness, approximated by the ratio 
$P/A$, is higher in large polities.Footnote 4
All else equal, we therefore expect women’s representation to decline as polity size increases, because a higher 
$P/A$ (more competition per seat) generates a congestion effect that works to the disadvantage of women candidates. The prediction is signed because the elasticity of assembly size to polity size, 
$\eta$, is generally below unity. This is true both across the range of contexts cited above and in the assembly-size response to the amalgamation reforms studied here (see Panel C of Table 2). As a consequence, the increase in assembly size that typically accompanies population growth is not large enough to offset the rise in seat competitiveness. This logic applies directly to amalgamation reforms, where two or more pre-existing polities are combined into a single larger one. Such reforms abruptly raise 
$P$, and although assembly size also tends to grow, it does so sub-proportionally, leaving seat competitiveness (
$P/A$) higher than before. This constitutes our core theoretical mechanism linking polity size to the underrepresentation of women in legislatures.
Although we predict a short-term dip in women’s representation when seat competition suddenly increases, it does not imply that women’s representation inevitably declines with population growth over the long run. In fact, throughout the 20th and 21st centuries, many countries experienced both significant population growth and substantial gains in women’s political representation. Broader socio-economic developments, including urbanization, educational expansion, and cultural change, have gradually improved the supply of and demand for women in politics. These trends have counteracted the mechanical effect of population on seat competition. Our theory isolates the immediate institutional effect (the “seat congestion” when jurisdictions change or electoral rules shift) while holding constant more slow-moving societal trends. Nothing in our argument precludes the possibility that these broader forces over time can offset an initial drop in women’s representation.
2. Estimating the impact of polity size on women’s representation
What makes for an ideal environment in which to study the impact of polity size and women’s representation? In the following, we first explain why estimates of this effect are especially prone to selection bias. Second, we outline how amalgamation reforms which are imposed by the central government on sub-national units, like the ones carried out in Sweden between 1952 and 1973, can ameliorate this bias.
2.1. Size and selection bias
Several interconnected reasons suggest that a direct analysis of the relationship between polity size and women’s representation is likely to suffer from confounding. First, polity size correlates with numerous factors that also affect women’s representation. Whether at the national or sub-national level, polities are the product of long historical processes of migration and agglomeration, where individuals with different characteristics and preferences sort into different settings (Tiebout, Reference Tiebout1956). As a result, larger polities differ systematically from smaller ones in ways that may influence political outcomes, including women’s representation.
Second, this problem is compounded when polities themselves choose to alter their size. Such decisions are often driven by considerations that also affect political outcomes, introducing further threats to internal validity (e.g., Meyer, Reference Meyer1995). Specifically, changes to the electorate are likely undertaken with their political consequences in mind, raising the possibility of similar bias.
In sum, studies of size face selection bias arising from individual sorting and from polity-level decisions about expansion or division—a process we term political sorting. We now turn to Sweden’s municipal amalgamation reforms (1952–1973) and explain how they can help mitigate this bias.
2.2. The Swedish municipal amalgamation reforms 1952–1973
One way to reduce the selection bias inherent in estimating the effects of polity size is to examine amalgamation reforms (or mergers), that is, instances in which smaller polities are grouped together to form larger ones (see, e.g., Lassen and Serritzlew, Reference Lassen and Serritzlew2011; Gerring et al., Reference Gerring, Palmer, Teorell and Zarecki2015; Hanes, Reference Hanes2015). Depending on the political context and the conditions under which such reforms are implemented, they can offer considerable leverage over the selection problems involved in estimating the impact of polity size. This pertains in particular to when the reforms are (a) forced and (b) initiated for reasons unrelated to the outcome of interest.Footnote 5
We argue that the municipal amalgamation reforms in Sweden fulfill these twin criteria. Sweden’s system of local self-government has deep historical roots but was most importantly enshrined in the 1852 reform, which created a system of some 2,500 municipalities (both urban and rural). This system was largely untouched for more than 80 years, but came under serious pressure with the demographic, socio-economic, and political changes in the inter-war period. Urbanization, migration, and uneven population growth over time caused enormous disparities in size between different municipalities. This had significant consequences for the tax base, making some municipalities highly dependent on government transfers to be able to fulfill their basic functions. Meanwhile, political reforms aiming at expanding the welfare state increased the burden on the municipalities.
To resolve these issues, a government commission in 1945 proposed a radical decrease in the number of rural municipalities, by merging smaller units into larger ones. The proposal, with minor modifications, was accepted by parliament in 1946. Although municipal preferences were heard in the process, the ensuing amalgamation reforms were not voluntary. The county administrative boards (regional branches of the central government) drafted the specific proposals which were then referred to a central government agency for consideration, after which the government itself made the final decision. The reform process was swift: by 1950, all details were finalized, and by 1952 the new set of just over 1,000 municipalities, down from almost 2,500 pre-reform, started to operate (Wallin, Reference Wallin, Wallin, Andersson and Andrén1973). According to our data, 451 municipalities were left untouched by the reform. A close historical study of the process concluded that “the municipal structure was essentially determined early in the planning process and that the municipalities did not influence the amalgamation process to any great extent” (Wångmar, Reference Wångmar2003, as cited in Hanes et al., Reference Hanes, Wikström and Wångmar2012, p. 2738).
Despite this large-scale reform, it was soon deemed insufficient. Therefore, another government commission in 1961 presented the guidelines for a second amalgamation reform, which was adopted by parliament in 1962. The remaining 1,033 municipalities were grouped into 282 “blocs,” largely aligned with geographical circumstances related to industry and the economy and clustered around a central town or village. This time, not only rural municipalities, as in the first reform, were affected, but also smaller and larger cities. Mergers of municipalities within these blocs were originally expected to occur voluntarily, but by 1969 less than 30% of the required mergers had occurred. The government then stepped in and forced through the remaining mergers, against the opposition of approximately half of the municipalities, mostly the smaller ones. The final mergers then occurred between 1971 and 1974 (Wallin, Reference Wallin, Wallin, Andersson and Andrén1973; Brantgärde, Reference Brantgärde1974; Erlingsson et al., Reference Erlingsson, Wångmar and Ödalen2010). As a result, Sweden now had only 278 municipalities, 75 of which were unaffected by the second reform.
As should be clear, both reforms were fairly swift and largely imposed from above, against local resistance. Previous studies show no indications that changes in gender representation were among the motivations behind the reform (Wallin, Reference Wallin, Wallin, Andersson and Andrén1973; Erlingsson et al., Reference Erlingsson, Wångmar and Ödalen2010). Taken together, this should mitigate both the problems of individual and political sorting and, hence, selection bias.
In the period during which the reforms were undertaken, Swedish municipalities used closed-list PR in elections to the municipal assembly, and a systematic study of the 1966 municipal election documents showed that intra-party nomination processes were controlled by a few select gatekeepers, primarily the municipal-level party leadership, who were almost exclusively men. Party members took very little part in the nomination process, especially women party members, and although test ballots put to a membership vote were used, they rarely influenced the outcome. While creating lists representative of the population was a concern, this mostly affected placements in lower list-positions, whereas incumbency and perceived competence primarily determined placements in electable positions (Barkfeldt et al., Reference Barkfeldt, Brändström, Simm and Zanderin1971). Contemporary observers also noted that the parties in the smallest and most peripheral municipalities sometimes struggled to recruit candidates to fill their lists (Sveriges regering, 1978, p. 30). In these municipalities, where the candidate pool was small relative to seats, and gatekeepers were not rationing scarce positions, amalgamation implied increased seat competitiveness.
Total number of politicians/women politicians in Swedish municipal councils 1934–2018.
As shown in Figure 1, reducing the total number of municipalities had large consequences for the number of political representatives. Before the first reform, there were more than 40,000 elected municipal politicians—after the 2 reforms, there were less than 14,000. During the time of the reforms, an overwhelming majority of the politicians were men. At the same time, turning to Figure 2, it is also clear that women’s representation was trending upwards. This is especially true for the period of the second reform, during which women’s representation was on the political agenda for many parties (Freidenvall, Reference Freidenvall2006). The share of women politicians in Swedish municipal councils was thus not lower after than before either of the reforms.
So how did the mergers affect women’s representation? While no large-scale systematic studies exist, the literature on Swedish political history disagrees. Referring exclusively to aggregate trends, Aronsson (Reference Aronsson2001), p. 72 argues that the share of women elected to municipal councils increased despite the decrease in the number of local representatives. But using detailed case studies of six municipal mergers in the second reform phase, Gustafsson (Reference Gustafsson1969), pp. 109–113 instead argues that the mergers decreased the share of women representatives. Gustafsson argues that this was because the competition for a smaller number of elected offices increased, and men candidates prevailed due to their longer experience in previous posts. Our data help reconcile these two perspectives. Because women’s representation was on a strong secular upward trend throughout this period for reasons largely unrelated to the mergers, the relevant question is not whether women’s share fell in absolute terms during the amalgamation reforms (in the aggregate it did not), but whether it grew more slowly in amalgamated municipalities than in comparable non-amalgamated ones. As seen in Figure 2 and the detailed analysis below, our data support the findings from Gustafsson’s case studies. During both reforms, women’s representation grew at a considerably slower rate in municipalities when they were being amalgamated.
Average share of women in Swedish municipal councils, 1938–1979, by reform status.
Figure 2 Long description
A showing a line graph with the vertical axis label, Average share of women representatives and tick labels 2, 4, 6, 8, 10, 12. The horizontal axis shows years with tick labels 1938, 1946, 1954, 1962. A vertical dashed marker is labeled, 1st reform. Legend labels: Not reformed and Reformed. Not reformed coordinate pairs: (1938, 3.4), (1942, 5.0), (1946, 6.6), (1950, 7.9), (1954, 9.2), (1958, 10.0), (1962, 10.5). Reformed coordinate pairs: (1938, 3.1), (1942, 4.1), (1946, 5.4), (1950, 5.8), (1954, 8.1), (1958, 9.2), (1962, 10.2). B showing a line graph with the vertical axis label, Average share of women representatives and tick labels 10, 15, 20, 25, 30, 35. The horizontal axis shows years with tick labels 1958, 1966, 1973, 1979. A vertical dashed marker is labeled, 2nd reform. Legend labels: Not reformed and Reformed. Not reformed coordinate pairs: (1958, 11.2), (1962, 11.2), (1966, 12.7), (1970, 16.4), (1973, 20.7), (1976, 26.2), (1979, 32.2). Reformed coordinate pairs: (1958, 10.0), (1962, 10.8), (1966, 11.9), (1970, 13.5), (1973, 15.9), (1976, 21.8), (1979, 27.2).
3. Research design
3.1. Empirical strategy
Consistent with the objectives of the reforms, municipalities that were merged into larger ones tended to be more rural and economically less developed (Appendix A.5). Simple comparisons of women’s representation in post-reform municipalities would therefore risk conflating the effect of the reform with these pre-existing differences. To study the impact of the two amalgamation reforms on women’s representation (
$W_{jt}$), we therefore estimate the following three-period model for each reform:
\begin{equation}
W_{jt}=\lambda+\theta_0 T_0+\theta_1 T_1+\gamma \times R_j+\gamma_0 T_0 \times R_j+\gamma_1 T_1 \times R_j +u_{jt}
\end{equation}where 
$j$ indicates the post-reform municipality, and 
$R_j$ is the reform intensity variable, which is described in more detail below. Elections are indexed 
$T=-1, 0, 1$, where 
$T_{-1}$ is the penultimate and 
$T_0$ is the last election before the reform, whereas 
$T_1$ is the first election after the reform. The variables 
$T_0$ and 
$T_1$ take on the value of 1 for the pre-reform and post-reform elections, respectively, and 0 otherwise. The differences in women’s representation between municipalities with different values of the reform variable (
$R_j$) across the three elections are captured by 
$\gamma$, 
$\gamma_0$, and 
$\gamma_1$.
Having estimated (1), we can obtain the differences-in-differences (DiD) estimate of the reform effect:
\begin{equation}
W_{j1}-W_{j0}=\alpha_1+\beta_1 R_j +u_{j1}-u_{j0}
\end{equation}where 
$\alpha_1=\theta_1-\theta_0$ is the baseline change and 
$\beta_1=\gamma_1-\gamma_0$ is the main quantity of interest: the effect of the reform on women’s representation. Comparing the reform effect to the baseline change will also provide us with a measure of its substantive impact.
While the DiD design does not require balance on time-invariant covariates, the underlying assumption in any such model is that, in the absence of treatment, the difference between the treated and control groups’ outcomes would have remained constant over time. We follow common practice and test whether trends prior to the reform were parallel. In practice, this means testing whether 
$R_j$ correlates with the pre-treatment trends in the municipalities. Since the data we use to estimate (1) includes two time-points prior to the reforms (
$T=-1$ and 
$T=0$), we perform this test, often referred to as a “placebo test”:
\begin{equation}
W_{j0}-W_{j-1}=\alpha_2+\beta_2 R_j +u_{j0}-u_{j-1}
\end{equation}where 
$\alpha_2 = \theta_0$ is the intercept and 
$\beta_2 = \gamma_0$. Under the assumption that 
$\beta_2$ captures the difference in trends between 
$T=0$ and 
$T=1$ that would have occurred if the amalgamation reform had not been implemented, 
$\beta_2 = 0$ would indicate that the parallel trends assumption holds.Footnote 6
We will apply OLS to estimate (1) and use the estimates to calculate (2) and (3) for both reforms.
3.2. Data and measurement
To measure our main independent and dependent variables, we have constructed a novel data set. Largely, this data builds on a corpus of original documents from the Swedish National Archives. This corpus consists of the handwritten forms that local election officials for a municipality had filled out by hand and sent in to Statistics Sweden for record-keeping. These forms include the number of eligible voters, turnout, election results for the main parties, assembly size, and a headcount of the number of women representatives, and had to be hand-coded.Footnote 7 From the 1950 election onward, the data are more systematically compiled and available in printed reports from Statistics Sweden, which we have digitized and turned into spreadsheet format for the purpose of this project.
3.2.1. Dependent variable
Women’s representation is measured by calculating the percentage share of seats in the municipal council held by women.Footnote 8 To measure the level of pre-reform women’s representation in the amalgamated municipality 
$j$, we use the average women’s representation for those municipalities that were merged together to form 
$j$.Footnote 9
3.2.2. Main independent variable
To create a variable that measures the impact of the reforms on the competitiveness over seats, we would ideally like to have a measure of the number of individuals that are interested in running for office per available seat. While no data on such “latent candidates” exists, their number is strongly related to the size of the polity or, more specifically, to the number of individuals who are eligible to run. Therefore, in line with our theoretical discussion, we measure the competitiveness over seats (
$C_j$) as the number of eligible candidates (i.e., everyone belonging to the electorate) per available seat:
\begin{equation*}
C_j=\frac{P_{j}}{A_{j}}
\end{equation*}where 
$P_{j}$ is the size of the electorate, and 
$A_{j}$ is the number of available council seats in the assembly of municipality 
$j$. In our analyses, we log-transform 
$C_j$, which is heavily skewed, for both reforms. The substantive reason for doing so is that while our theory predicts that party-gatekeepers, when seat competitiveness increases, will be less likely to place women on electable list positions, there are good reasons to assume that in many contexts, including ours, they would prefer to keep at least some women. Although women’s representation was low by current standards during the two reforms we study (see Figure 2), this had been actively debated since the introduction of women’s suffrage. Freidenvall (Reference Freidenvall2006), Ch. 4 has shown that, during our period of study, parties responded to this, not by aiming toward equal representation, but by “tokenism.”
We then create a continuous independent variable that measures the change in seat competitiveness between the pre- and post-reform election (
$C_{j0}$ and 
$C_{j1}$, respectively). When measuring the pre-reform electorate of a municipality 
$j$, we use the average seat competitiveness for those municipalities that were merged:
\begin{equation*}
R_j=C_{j1}-C_{j0}
\end{equation*}This measures how affected seat competitiveness in a municipality was by the amalgamation reform in question. In Appendix A.4 we show that this measure of reform intensity is strongly related to the number of pre-reform municipalities merged into each post-reform unit.Footnote 10
3.2.3. Alternatives to the main independent variable
We also perform a set of analyses where we replace seat competitiveness with a measure that captures the change in the electorate (polity size) between post- and pre-reform. These analyses serve two purposes. First, they allow us to check that the total (or net) effect of reform-induced increases in polity size on women’s representation is indeed negative. Second, the increases in polity size that were induced by the reforms were arguably more exogenous than the increases in seat competitiveness. The reason is that while the increases in polity size were wholly imposed on the municipalities from above, local politicians had some leeway in setting the number of assembly seats. Specifically, while the number of assembly seats a municipality was allowed to have increased with the size of the municipality, for any given population, there was a certain range of required seats from which local politicians could choose (see Appendix A.1 for more information). While the measure that speaks most directly to our theoretical mechanism is seat competitiveness, this additional analysis provides us with further confidence that the effects we are estimating in the main analysis are indeed driven by the amalgamation reforms.
3.2.4. Controls
As discussed above, by studying the Swedish amalgamation reforms we avoid certain types of selection bias. The DiD approach also removes all municipality fixed effects. To further ameliorate selection bias, we also refine our baseline specification by incorporating covariates that are interacted with the time indicators. These are measured prior to the reforms, in order to avoid post-treatment bias (Homola et al., Reference Homola, Pereira and Tavits2024). The initial set of covariates consists of the pre-reform vote shares for the five major parties. For the first reform, these shares are derived from the 1942 municipal election results, while for the second reform, they are based on the 1962 election results. When analyzing the first reform, we also incorporate a variable measuring the proportion of municipalities amalgamated into a specific municipality that practiced direct democracy prior to the reform. This control is necessary because direct democracies were effectively made extinct by the reform: the resulting municipalities were too large to satisfy the legal population threshold for direct democracy, so practically all direct-democracy municipalities were forced into representative democracy.Footnote 11 The second set of covariates consists of pre-reform economic conditions. These include per capita taxable income from labor and capital, the poverty rate, child poverty, population density, and arable land as a percentage share of total land.Footnote 12 Data for these controls were manually coded from the 1942 edition of The Yearbook of Municipal Statistics for the initial reform, and the 1962 edition for the subsequent reform.
3.3. Main results
In Table 1, we show the net effects of the two amalgamation reforms on women’s representation. The DiD estimates for both reforms are negative and significant at conventional levels, suggesting that the increases in seat competitiveness following reform lowered women’s representation. The placebo tests examine the trend between the two elections prior to each reform. With one exception, their estimates are positive, indicating no negative reform effects before enactment. Although two placebo estimates reach statistical significance (
$p \lt 0.10$), they are small in absolute terms. Taken together, the results suggest that the observed reform effects were not the continuation of pre-existing trends in women’s representation in amalgamated municipalities.
Impact of 1946–1973 Amalgamation reforms on women’s representation
Table 1 Long description
Two column groups compare First reform, 1946 to 1952, and Second reform, 1966 to 1973, each with three model columns. For First reform, Reform Effect is minus 1.684 with three stars, minus 1.856 with three stars, and minus 2.182 with three stars, with standard errors 0.395, 0.491, and 0.5. For Second reform, Reform Effect is minus 2.185 with three stars, minus 1.414 with two stars, and minus 1.322 with two stars, with standard errors 0.521, 0.595, and 0.61. Placebo Effect for First reform is minus 0.61 with one star, 0.023, and 0.198, with standard errors 0.37, 0.458, and 0.466; for Second reform it is 0.612 with one star, 0.722 with one star, and 0.598, with standard errors 0.37, 0.399, and 0.411. Baseline Change appears only in the first model of each reform period, with 1.353 for First reform and 6.579 for Second reform. Year effects are Yes in all six models; Cov. Pol. is No then Yes then Yes within each reform period; Cov. Econ. is No, No, Yes within each reform period. R Square values are 0.077, 0.193, and 0.315 for First reform, and 0.227, 0.414, and 0.476 for Second reform. Obs. are 3,064, 3,036, and 2,997 for First reform, and 834, 834, and 825 for Second reform.
Notes: Standard errors, shown in parentheses, allow for clustering at the municipal level. ***/**/*, indicates significance at the 1/5/10% level.
The increases in seat competitiveness that resulted from both reforms also appear to have substantively large effects, especially considering the low levels of women’s representation during the study period. To see this, we can compare the reform effect to the baseline change. According to our baseline model for the first reform, a one-standard-deviation increase in the extent of reform impact (
$sd = 0.33$) caused women’s representation to grow about 40% more slowly than in an unaffected municipality (
$0.33\times-1.684/1.4$). For the second reform, the standard deviation in the extent of reform impact was 0.51, making the corresponding figure about 17% (
$0.51\times-2.185/6.6$).
In Table 1, we also include a number of analyses where we show that the reform effects are robust when we refine our baseline model specifications and incorporate pre-reform political and economic covariates. For the first reform, the addition of these covariates increases the estimated reform effect slightly, whereas for the second reform, their addition reduces the effect. For both reforms, however, the conclusion that the amalgamations lowered women’s representation is robust.
3.4. Disentangling the polity vs. assembly size effects
While we hypothesized that the overall effect of polity size would be to raise seat competitiveness and thereby make it harder for women to gain office, our theoretical discussion suggested that this was in actuality the net of two countervailing effects: (1) A negative effect of an expansion of the size of the electorate, and (2) a positive effect that results from local assemblies increasing their number of seats when the electorate expands. As discussed above, our theory implies that the first effect dominates the second whenever the elasticity of assembly size to polity size is below unity. The negative net effect documented in Table 1 is consistent with this prediction. We now decompose that effect into its constituent parts and confirm that the underlying empirical regularity—the elasticity of assembly size to polity size, 
$\eta$, being below unity—holds in our setting. We also test whether local assemblies did indeed respond to the reform by increasing the number of seats, and whether this dampened the reform’s impact on women’s representation. These analyses build on those in Table 1, but replace seat competitiveness with two variables that measure (1) the change in the electorate between post- and pre-reform and (2) the change in seats between post- and pre-reform.
Specifically, we measure the size of the pre-reform polities and assemblies 
$j$ by taking the average of these two for those municipalities that were merged. The pre-reform measures are denoted 
$P_{j0}$ and 
$A_{j0}$, respectively. The post-reform electorate and assembly seats in the merged municipalities are denoted 
$P_{j1}$ and 
$A_{j1}$, respectively. These measures, in their logged form, are then used to construct the two independent variables:
\begin{align*}
P_j=P_{j1}-P_{j0}\\
A_j=A_{j1}-A_{j0}
\end{align*}where 
$P_j$ will capture the effect of increasing the size of the electorate, and therefore also the pool of candidates, whereas 
$A_j$ will capture the impact of increasing the number of assembly seats.
We then use these variables to perform an analysis where we first estimate a version of our main model that replaces the reform intensity variable, 
$R_j$, with 
$P_j$. The purpose is to find the total (or net) effect of polity size on women’s representation. We then estimate a second model, where we include both polity size, 
$P_j$, and assembly size, 
$A_j$, as independent variables. The purpose of this analysis is to find the partial effects of polity and assembly size, respectively, on women’s representation. The expectation here is that the partial effect of polity size will be more strongly negative than its total effect, because the indirect positive effect that operates through assembly size is now controlled for. Finally, we also use these estimates to infer the elasticity of assembly size with respect to polity size.Footnote 13 This elasticity is the empirical input on which the signing of our theoretical prediction depends. Competitiveness over seats would be unaffected if the relationship between polity and assembly size was proportional (see Appendix A.10 for more details on this analysis).
The results are in Table 2. Beginning with Panel A, which shows the results when only including polity size as an independent variable, the total effect of increasing polity size is negative and statistically significant throughout all specifications. The baseline estimate for the first reform suggests that a one standard deviation (
$sd=0.55$) increase in the electorate causes a 28% drop in women’s representation when compared to an unaffected municipality (
$0.55\times-0.702/1.4$). The corresponding figure for the second reform (where 
$sd=0.70$) is a 16% drop (
$0.70 \times -1.533/6.6$).
Disentangling the effect of increasing polity size from that of increasing assembly size
Table 2 Long description
Three panels report regression results for two periods labeled First reform, 1946 to 1952, and Second reform, 1966 to 1973, each shown across six model columns. Panel A lists Polity Size Effect, its standard error in parentheses, and model features; Polity Size Effect values are minus 0.702, minus 0.815, and minus 0.993 for the first reform, and minus 1.533, minus 0.966, and minus 0.916 for the second reform. Panel A also shows Year effects as Yes in every column, Cov. Pol. as No then Yes then Yes for each reform, Cov. Econ. as No, No, Yes for each reform, R Square as 0.099, 0.194, 0.313 for the first reform and 0.226, 0.415, 0.478 for the second reform, and Obs. as 3064, 3036, 2997 for the first reform and 834, 834, 825 for the second reform. Panel B adds Assembly Size Effect with its standard error in parentheses; Polity Size Effect values are minus 2.449, minus 2.338, and minus 2.676 for the first reform, and minus 2.399, minus 1.488, and minus 1.331 for the second reform. Panel B Assembly Size Effect values are 3.828, 3.624, and 4.021 for the first reform, and 3.103, 1.707, and 1.354 for the second reform, with Year effects again marked Yes in every column and the same Cov. Pol. and Cov. Econ. patterns as Panel A. Panel B R Square values are 0.11, 0.198, 0.317 for the first reform and 0.23, 0.416, 0.479 for the second reform, with Obs. matching Panel A. Panel C lists Estimate values for implied elasticity of assembly size to polity size as 0.46, 0.42, 0.42 for the first reform and 0.28, 0.31, 0.31 for the second reform.
Notes: Standard errors, shown in parentheses, allow for clustering at the municipal level. ***/**/*, indicates significance at the 1/5/10% level. The results in Panel C are derived from the results in Panels A and B (see Appendix A.10).
The partial effects are shown in Panel B of Table 2. One challenge here is that one can expect a very high level of collinearity between polity and assembly size, thus reducing our statistical power considerably.Footnote 14 Despite this, the results are in line with our expectations. First, the partial effects of polity size are negative and, as expected, substantively larger than the total effects shown in Panel A. According to the baseline estimate for the first reform, a one standard deviation (
$sd=0.55$) increase in the variable measuring the expansion of polity size causes a drop of almost 96% in women’s representation compared to an unaffected municipality (
$0.55\times-2.449/1.4$). When adding all controls, the estimates of the polity size effect for the second reform are not significant at conventional levels, likely due to the combination of the smaller sample size and the high degree of collinearity. Substantively, however, they are quite large. The estimate for the model without controls, for instance, implies that a one standard deviation (
$sd=0.70$) increase is associated with 25% lower growth in women’s representation (
$0.70\times-2.399/6.6$), while keeping seats constant. In sum, our estimates suggest that the impact of the amalgamation reforms on women’s representation would have been even more dramatic had the number of council seats held steady.
Turning to the assembly size effect, the estimates are in the expected direction for both reforms and are also substantively large.Footnote 15 For the first reform, a one standard deviation (
$sd=0.28$) increase in seats causes an increase of about 77% in women’s representation compared to an unaffected municipality (
$0.28\times3.828/1.4$). In the baseline model for the second reform, the corresponding figure is 11% (
$0.23\times3.103/6.5$).
Finally, we turn to our estimates of the elasticity of assembly size to polity size, 
$\eta$. As we have already noted, work in the literature pioneered by Taagepera (Reference Taagepera1972) has shown that polity size is one of the strongest predictors of assembly size, and this is true of the cases of reform studied here as well. However, this literature has also argued that assembly size does not respond proportionally to increases in polity size, a regularity that, as we discussed in the theory section, is what allows our prediction to be signed. As long as 
$\eta$ is below one, the rise in polity size dominates and seat competitiveness goes up. Our results, reported in Panel C of Table 2, are in line with the previous literature. The estimates imply an elasticity of around 0.4 for the first reform and 0.3 for the second, the latter close to Taagepera’s Reference Taagepera1972 original cube-root law. Both fall well below unity, confirming that the condition 
$\eta \lt 1$ holds in our setting.
In sum, these results show that in the reformed municipalities the number of assembly seats increased. These increases in assembly size were, however, not proportional to the increase in the size of the electorate and therefore did not manage to nullify or reverse the negative effects of the reforms on women’s representation.
3.5. Additional analyses: mechanism and robustness checks
In this subsection, we examine whether our main results are driven by particular parties, whether they operate through the proposed seat-competitiveness mechanism, and whether they are robust to alternative measurement and modeling choices.
3.5.1. Are our results driven by certain parties?
Our main analysis controls for the pre-reform vote shares of the five major parties, and it is therefore unlikely that our results are driven by differences in partisan composition across reformed and unreformed municipalities. However, in view of research on historical partisan gender gaps (Teele, Reference Teele2024), we analyze whether our results are driven by specific parties. Data on women’s representation for individual parties is only available for the first reform, but as can be seen in Table A.17, women’s representation was low in 1946, ranging from 5.4% in the Agrarians to 8.3% in the Liberals.Footnote 16 When we estimate the reform effects separately for each major party, they are consistently negative (Table A.18). Four out of six of these estimates of the reform effect are statistically significant at conventional levels, despite statistical power being considerably lower in these analyses than in our main analysis.Footnote 17 These results suggest that the negative effect of the reform was not confined to any single party, but rather reflects a broader mechanism whereby heightened competition for a limited number of seats disadvantaged women across the party system.
3.5.2. Does seat competitiveness crowd out women?
If competitiveness over seats is the mechanism at work, women should be more likely than men to lose their seats when municipalities merge. We test this at the individual level using the second merger of the City of Gothenburg, where we observe the council elected just before the amalgamation and follow its members through the reform. Of the cohort elected in 1962, a markedly smaller share of women than of men were still in office by the post-amalgamation election of 1970 (40% versus 56%), even though the two groups entered with very similar levels of prior experience, so seniority differences cannot account for the gap (Table A.23). These findings align with a historical study of six other municipalities that likewise attributes women’s losses to intensified competition for fewer seats (Gustafsson, Reference Gustafsson1969).
3.5.3. Is the effect weaker where gender norms were more egalitarian?
Our scope conditions imply that the reform should bite less where men’s dominance over candidate selection was less entrenched. To probe this, we interact reform intensity, for the second reform, with the municipal rate of women’s participation in the paid labor force in 1960.Footnote 18 The literature treats women’s labor force participation as a marker of more gender-equal norms, which may raise both the supply of women candidates and the demand for them among voters and gatekeepers (Iversen and Rosenbluth, Reference Iversen and Rosenbluth2008; Wängnerud, Reference Wängnerud2009; Stockemer and Byrne, Reference Stockemer and Byrne2012). On either reading, the reform should have less effect where women’s labor force participation was higher. The pattern accords with this expectation. The reform effect is negative at every evaluated point of the participation distribution but decreases as participation rises. With the full set of controls, the reform is no longer statistically distinguishable from zero at the 75th percentile. We do, however, caution against over-interpreting these results, since the interaction term is not statistically significant in any specification (Appendix A.14).
3.5.4. Are the results robust to measurement and modeling choices?
First, we have re-run our analysis, replacing our measure of seat competitiveness with a logged count measure of how many municipalities were merged as our main independent variable.Footnote 19 While this measure is one step removed from our theoretical concept of interest, it is arguably more exogenous than our main measure.Footnote 20 The measure also has a slight advantage over the measure of polity size that was used in the analysis reported in Table 2, since the latter measure could be affected by reform-induced population movements and trends. The estimates using counts as the main indicator of reform intensity are negative and significant at conventional levels, suggesting that women’s representation decreased as the number of municipalities that were merged increased (see Table A.19). Moreover, they are, like our main results, substantively meaningful (see the discussion in Appendix A.13).Footnote 21 To further probe whether the effect of amalgamation varies non-linearly across the treatment distribution, we also estimate dose-specific effects using quartiles of the count measure (Appendix A.8). The estimates are broadly consistent with our main results: the effect of amalgamation grows more negative with treatment intensity, especially at higher levels.
Another measurement issue is how to construct the pre-reform measures of women’s representation and seat competitiveness. In the main analysis, we weighted each to-be-amalgamated municipality equally. One alternative would have been to instead weight municipalities by pre-reform size. As we show in Appendices A.2–A.6, doing so leaves our basic conclusion unchanged: the increased competitiveness over seats resulting from the amalgamation depressed women’s representation.
Finally, we also re-estimate our main specification via a lagged-dependent-variable (regressor-variable) specification (Allison, Reference Allison1990), which produces slightly stronger effects for the first reform and slightly weaker ones for the second (Table A.21).
3.5.5. When do the effects emerge, and how long do they last?
The second amalgamation reform was implemented in two waves. Roughly half of the affected municipalities were amalgamated by the 1970 election, with the rest amalgamated by 1973. This staggered structure allows us to examine both the timing of the reform’s effects and their evolution over time post-reform. Both waves are compared against the municipalities never affected by the second reform, sidestepping a common issue in staggered designs where early-treated units serve as implicit comparisons for later-treated ones (Liu et al., Reference Liu, Wang and Xu2024). Our results show that the negative effect emerges precisely at the first post-amalgamation election for each wave, and not before. The treatment effects are remarkably similar across the two reform waves. This precise timing strengthens the credibility of the claim that the amalgamation reforms drive our results. After the reforms, the effects persist for several elections but also exhibit a trend toward zero over the following fifteen years (Appendix A.12). The results provide further evidence that the reform itself depressed women’s representation, while the gradual decay of the effect suggests that its impact may have reached beyond the councilors who were in office at the time and into the broader pool of potential candidates.
4. Conclusions
Political scientists have a long history of studying polity size and its influence on the quality of democracy. Despite this, studies dealing with the impact of size on the descriptive representation of women have been exceedingly rare. In this paper, we argue that there are strong theoretical reasons to expect such a link. Drawing on the literature on legislative size and the literature on gender and politics, we propose that women’s representation should be negatively related to the ratio of polity size (or the pool of candidates) over the number of elected offices, or what we call competitiveness over seats.
We then move on to test this argument in the empirical context of municipality amalgamation reforms in Sweden between 1952 and 1973, which dramatically reduced the number of municipalities, and hence increased the average population size of these municipalities. In line with our hypothesis, the net effect of competitiveness over seats on women’s representation is negative. Moreover, whereas increasing polity size, while holding assembly size constant, negatively impacts the representation of women, we also estimate that increasing assembly size, while holding polity size constant, increases women’s representation. Our findings thus suggest that the negative impact of the amalgamation reform was softened—but far from nullified—by the increase in assembly size. In short, our evidence confirms the demography-based mechanism we theorize: when the ratio of candidates to seats widened, intensified competition crowded out women.
The generality of our results comes with some important scope conditions. First, the findings from Sweden are drawn from a period when male party gatekeepers dominated nominations for public office, which arguably affected the demand for, and possibly indirectly the supply of, women candidates. Even if in Sweden the gender balance among party gatekeepers is less skewed today, and they no longer express a preference for men candidates (Grahn and Håkansson, Reference Grahn and Håkansson2025), male-dominated gatekeeping remains common across most party systems worldwide. Second, the effect of seat competitiveness depends on how constrained party gatekeepers are. In the extreme and rare situation where party gatekeepers are completely unconstrained and have no interest (for strategic or other reasons) in nominating members from the dominated group, there will be an adequate supply of potential candidates to nominate only men, irrespective of the level of seat competitiveness. By the same token, at the other extreme, when party gatekeepers face very binding constraints, such as strict and ambitious gender quotas, seat competitiveness is also likely to be less consequential for women’s representation. Third, the electoral system may condition the mechanism: although the congestion effects should apply, perhaps even more forcefully, to single-member district systems, the existence of intra-party preference voting or more decentralized candidate nomination systems (such as primaries) might alter how increased competitiveness over seats translates into women’s representation.
While our paper focuses on representational parity for women, future research should investigate the potentially negative effects of increased jurisdictional size on the descriptive representation of other underrepresented groups, such as ethnic and racial minorities, and working-class individuals (e.g., Bloemraad and Schönwälder, Reference Bloemraad and Schönwälder2013; Carnes and Lupu, Reference Carnes and Lupu2023). For spatially concentrated groups, as minorities often are, the seat-competitiveness mechanism we identify will operate alongside changes in the demographic composition of the pre- and post-reform electorates. Disentangling the two channels in such settings will pose distinct empirical challenges.
Finally, our results also bear on institutional design. First, while municipal mergers are common and often justified on efficiency grounds (Blom-Hansen et al., Reference Blom-Hansen, Houlberg, Serritzlew and Treisman2016), they may hinder representational parity unless accompanied by compensatory measures. Increasing council size is one such measure that we have shown partially offsets the seat-competitiveness penalty. However, since assemblies cannot be expanded indefinitely as populations grow, gender quotas are an additional and effective tool that can be adopted alongside amalgamation. As discussed above, they neutralize the gatekeeping dynamics through which seat competitiveness can disadvantage women candidates. Second, similar considerations apply on a larger scale: populations in advanced democracies have nearly doubled since World War II, yet electoral institutions, including legislature size, have remained more static. Scholars should investigate whether this demographic–institutional mismatch has dampened descriptive representation in a broader set of contexts.
Acknowledgements
We wish to thank Jonas Tallberg, seminar participants at Stockholm University, and conference participants at the Council for European Studies 2023 for helpful comments. The authors gratefully acknowledge research assistance by Abrar Bawati, Natalie Hedin, Lo Dahlquist Mörkenstam, Josefine Magnusson, and Agnes Teorell. The authors have used AI tools for proofreading and to assist in the development and debugging of some computer code.
Declaration of interests
The authors declare none.
Funding statement
This work was supported by the Swedish Research Council (grant numbers 2021-00828 and 2019-03153).
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/psrm.2026.10142.
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