Sunday, September 25, 2022

Engineered Majorities: U.S. Senate Malapportionment in Comparative Context

Guest Blogger

This post was prepared for a roundtable on Comparative Constitutional Design, convened as part of LevinsonFest 2022—a year-long series gathering scholars from diverse disciplines and viewpoints to reflect on Sandy Levinson’s influential work in constitutional law. 

Ashley Moran 

One of the central takeaways from my early interactions with Sandy was his appreciation for the myriad paths constitutional design can take in addressing a given democratic aim and his discerning eye for assessing the implications of these choices. It’s a point that has invigorated my own work since, particularly in the comparative sphere. And it’s in this spirit that I explore a compelling argument Sandy has raised (among many) in his critique of the U.S. Senate: today a majority of the U.S. population, concentrated in 9 states, is represented by a very small minority of 18% of Senate seats (Levinson 2010; Levinson and Levinson 2019, 39; Levinson and Balkin 2019, 178). My comparative bent wondered how such relegation of the majority compares globally. The topic would seem ripe for comparative exploration, since upper chambers are known for overrepresenting select groups and subnational units (Samuels and Snyder 2001, 658), yet there is relatively little comparative research on malapportionment in upper chambers. 

The topic of malapportionment is well-trodden ground, with established measures borne both of legal necessity following Baker v. Carr and academic study of the causes and consequences of malapportionment. Most of these measures, however, have not been applied to comparative contexts or upper chambers. A robust set of studies focuses on malapportionment in the United States (e.g., Schubert and Press 1962; Balinksi and Young 2001; Ansolabehere and Snyder 2008; Ladewig 2011; Cervas and Grofman 2020). Broad cross-national studies are far less common and focus almost exclusively on lower chambers (e.g., Bruhn et al. 2010; Kamahara and Kasuya 2014; Ong et al. 2017), with the notable exception of groundbreaking work from Samuels and Snyder (2001) that includes 25 upper chambers. In this post,[1] I apply a broader set of established measures than those seen in prior comparative studies of malapportionment, include a larger set of 49 upper chambers, and develop a new measure to explore Sandy’s critique of the U.S. Senate and compare majority relegation in upper chambers globally.[2] 

The Challenge of Malapportionment 

Creation of an upper chamber in the legislature can be a key strategy for diversifying the avenues and actors involved in policymaking. The number of countries providing for bicameralism in their constitutions has nearly doubled in the last 50 years, from 44 countries in 1970 to 84 today (Elkins and Ginsburg 2021). Yet bicameralism still isn’t nearly as widespread a mechanism of dividing power as, say, the dual executive—seen in 126 countries today (Elkins and Ginsburg 2021)—leaving bicameralism room to expand and putting questions of upper house design squarely on the drafting table. 

Upper chambers are often created as a mechanism to represent territorial and group interests, putting them at particular risk of malapportionment—and the democratic and economic hazards that come with it. In addition to violating the cornerstone democratic principle of one-person one-vote, malapportionment is associated with a variety of democratic dysfunctions, from under-representation of racial minorities (Baker and Dinkin 1997) to bias in favor of incumbents (Snyder and Samuels 2001; Boone and Wahman 2015). Malapportionment is also associated with disparate allocation of government resources in favor of overrepresented areas (Baker and Dinkin 1997; Ansolabehere et al. 2002; Horiuchi and Saito 2003; Gibson et al. 2004; Bruhn et al. 2010; Maaser and Stratmann 2016) and less progressive tax structures that reinforce economic inequality (Ardanaz and Scartascini 2013). 

The scope of malapportionment in a given system can be captured in several ways. Average malapportionment assesses the overall disparity between vote and seat shares across all districts in a system. Measures of malapportionment at the extremes assess how under- and over-represented constituents are in the most malapportioned districts in a system. Measures of malapportionment capacity to shape policy assess when a system has the capacity to engineer majorities where they don’t otherwise exist and when a system can relegate an actual population majority to an engineered minority status. I take these facets of malapportionment in turn, comparing the U.S. Senate to other upper chambers globally. 

Average Malapportionment 

The widely used Loosemore-Hanby Index (LHI) captures average malapportionment as differences in the shares of seats and voters across all districts (Loosemore and Hanby 1971). The result conveys the portion of seats in a system that are not apportioned equitably. This is the measure used in the largest prior cross-national study with a focus on upper chambers (Samuels and Snyder 2001), but it has not been applied comparatively to upper houses since. Today, 36% of U.S. Senate seats are malapportioned, as Table 1 shows. This is comparatively high, ranking ninth highest globally. Notable at the other end of the rankings are countries with zero malapportionment because the upper chamber is selected by a single national constituency—as in Colombia, Palau, Paraguay, the Philippines, and Uruguay—or a single national body, as in Cambodia and Eswatini. 

Table 1. Average Seat Malapportionment in Upper Chambers


Malapportionment at the Extremes 

Two additional measures provide a view of how under- and over-represented constituents are at the extremes. The voter equivalency ratio (VER) conveys the number of people in the most-populous district that equates—in apportionment terms—to a single person in the least-populous district. This has been used to highlight the deep disparities in voter representation in the U.S. Senate (Tyler 1962; Ladewig 2011; Cervas and Grofman 2020), but it has not been used extensively in comparative contexts. Comparing this aspect of U.S. apportionment globally highlights that the U.S. Senate ranks even higher in malapportionment at the extremes. One person in the least-populous U.S. Senate district has the same voting power as 74 people in the most-populous district, ranking the United States fifth highest in this facet of malapportionment, as Table 2 shows. 

A second measure of malapportionment at the extremes—the maximum population deviation (MPD)—conveys the disparity between populations in the most- and least-populous districts, relative to an ideally populated district under perfect apportionment. This provides a sense of how many seats the malapportioned population is being short-changed. Again this measure has been used to assess U.S. apportionment to great effect (Ladewig 2011; Cervas and Grofman 2020), but has not been deployed in global comparative analysis. 

Based on maximum population deviation, the U.S. Senate again shows higher levels of malapportionment than most other upper chambers included here. In the United States, the difference between the most- and least-populous seats reflects a population over six times larger than the size of a single ideally populated district, as the 6.26 MPD score shows in Table 3. In other words, if the system were perfectly apportioned, the size of the population that is currently malapportioned in the most-populous U.S. Senate district (California) would instead be represented by six Senate seats for each single seat it elects under the current system. 

Table 2. Voter Equivalence in the Most- and Least-Populous Districts for Upper Chambers


Table 3. Maximum Population Deviation in Districts for Upper Chambers


Comparing global malapportionment at the extremes, it is clear the U.S. Senate is exceedingly malapportioned—even by upper chamber standards that largely accept a degree of malapportionment to accommodate diverse territorial or group interests. Only four countries have more extreme disparities in voter representation across the most under- and over-represented districts, as Table 2 shows. And only five (slightly different) countries have higher deviations from the ideal district size, as Table 3 shows. 

Globally, some countries’ malapportionment is mostly at the extremes. Algeria, Cameroon, and Kazakhstan, for example, have high malapportionment in terms of extreme disparity between districts and deviations from ideal district size (shown in the VER and MPD metrics), but not in terms of average malapportionment across all districts (shown in the LHI). Other countries have the opposite. Haiti and the Republic of the Congo, for example, have very high average malapportionment across districts and much lower malapportionment at the extremes. The United States, however, is among a handful of countries that have both. Along with Argentina, Brazil, the Dominican Republic, Indonesia, and Spain, the United States has very high levels of both average and extreme malapportionment, as Tables 1-3 convey. Of these, all but Indonesia are constitutionally mandated to allocate an enumerated number of seats to existing subnational units like regions rather than, say, election districts that can be reapportioned. Indonesia, too, is constitutionally mandated to allocate seats by region, but the constitution does not specify the number or equal distribution of seats per region. These three factors—constitutional mandate, fixed seat numbers, and fixed district boundaries—restrict countries’ abilities to reapportion seats to adjust to demographic shifts. 

Malapportionment Capacity to Shape Policy 

Assessments of average and extreme malapportionment make clear that the United States and a few other countries are outliers in their uniformly high levels of malapportionment in each of these areas. The practical import of this is made clear by the last two measures I compile below: the minimum population share needed to elect a legislative majority and the minimum seat share held by a population majority. These two measures identify when a system has the capacity to engineer majorities where they don’t otherwise exist, and when a system can relegate an actual population majority to an engineered minority status. These have clear implications for policymaking in any state. 

The minimum population share to elect a legislative majority (MPS) identifies the smallest possible portion of a population that can select a majority of a legislative chamber. It does this by ordering districts from smallest to largest populations, summing the smallest district populations for seats that reflect 50% plus one of the seats, then dividing by the total population to get the share of the population that elected that legislative majority. This hinges on identifying the least-populous districts up to the one that elects the last member needed to form a legislative majority. The U.S. Senate has well-documented, high levels of malapportionment in this area (Tyler 1962; Cervas and Grofman 2020), and again this new global comparison finds this facet of U.S. malapportionment is higher than most other upper chambers globally, as Table 4 shows. 

What I’ll call the minimum seat share held by a population majority (MSS) is the measure inspired by Sandy’s analysis of disparities in state populations’ voting strength in U.S. Senate elections (Levinson 2010). It identifies the smallest portion of seats that can be received by a majority of the population. It does so by ordering districts from largest to smallest populations, summing the seats that reflect 50% plus one of the largest district populations, then dividing by the total number of seats to get the share of seats assigned to that population majority. Outside of Sandy’s discussion of this issue in relation to the U.S. Senate, I have not seen this aspect of malapportionment tracked across cases. Table 5 compiles this minimum seat share measure for just over four dozen cases globally. 

Table 4. Minimum Population Share to Elect a Majority in Upper Chambers


Table 5. Minimum Seat Share Held by a Population Majority in Upper Chambers


The first takeaway regarding these measures that capture the policy implications of malapportionment is that the U.S. Senate again has some of the worst malapportionment globally—and this is even more pronounced in the new measure of minimum seat share given to a popular majority. On this, the United States ranks fifth globally, following only Indonesia, Argentina, the Dominican Republic, and the Republic of the Congo as the top states that relegate popular majorities to the smallest minorities in the upper chamber. In these states, a majority of the population can be relegated to only 12% of the seats in the Indonesian upper house and 18% of seats in the U.S. Senate, as Table 5 shows. 

The second takeaway relates to how average and extreme malapportionment can shape the capacity of malapportionment to in turn affect policy. As noted previously, Algeria, Cameroon, and Kazakhstan have very high malapportionment at the extremes, yet they have lower average malapportionment. This leads to less distortion in majority voting power overall (at least in terms of malapportionment). This is seen in their relatively higher minimum population shares needed to elect a majority and minimum seat shares allocated to a majority. On the other hand, Haiti and the Republic of the Congo have notably high average malapportionment and relatively low malapportionment at the extremes, yet they face substantial distortions in majority voting power, as Tables 4 and 5 show. Average malapportionment clearly has a more pernicious impact on the majority-distorting features of a system that can shape public policy. 

The data also reveal countries at the other end of the spectrum—like the Czech Republic, India, Romania, and Zimbabwe—where the minimum population needed to control the chamber, and the minimum seats awarded to a majority, are both much closer to the 51% threshold they would be in perfect apportionment. Also at this end of the spectrum are countries like Colombia, Palau, and Uruguay that altogether avoid the majority voting distortions caused by apportionment by instead using a single national constituency. 

MPS and MSS further reveal countries—notably those adopting their constitutions after ethnic conflict, like Bosnia and Herzegovina (BiH) and Rwanda—that have well-apportioned systems but also higher barriers to minority control. This is seen in very high population shares needed to elect a legislative majority and equal or high minimum seat shares awarded to majorities. In these counties, malapportionment across seats is minimal due to multi-member districts based roughly on population. However, the small number and disproportionate size of the districts electing these seats shape the (theoretical) power of each district voting bloc. In BiH, for example, the minimum population share of 64% conveys that no single national community (meaning, the Bosniac, Croat, and Serb populations, which each elect 1/3 of the country’s seats) can form a legislative majority without votes controlled by another community. Similarly, the BiH minimum seat share of 67% conveys that a popular majority cannot be relegated to a legislative minority. 

This brief, but more extensive, look at upper houses globally provides new data on the propensity of constitutional designs to engineer majorities (and minorities). It is the tip of the iceberg in terms of the proper deep dive that would be needed to identify constitutional design recommendations for this challenge. But it speaks to a particular aspect of the perennial design question of what to entrench (or not) in a constitution. Samuels and Snyder (2001) find that malapportionment can play an important role in aiding democratic transitions. It can do so by providing guarantees for minority groups whose agreement is key to the constitutional settlement—as it surely did in the early days of the United States. But we also know that malapportionment tends to persist (Bruhn et al. 2010) and worsen over time (Snyder and Samuels 2004; Cervas and Grofman 2020) since underrepresentation of more populous places is exacerbated by disparate growth rates. These two sets of findings highlight the incentives and the risks of entrenching features like ‘equal’ geographic apportionment that continue to roil modern U.S. constitutional democracy. In doing so they highlight apportionment as one of the pivotal areas where constitutional design must walk the fine line of both accommodating disparate interests in the short term to secure the constitutional compact, while also providing mechanisms—in the constitution or through the courts—to transition away from these rigid aspects of the constitutional settlement over time. 

Ashley Moran is a Postdoctoral Fellow with the Comparative Constitutions Project at the University of Texas at Austin. You can contact her at

[1] This is an early iteration of this research, and feedback is very much appreciated.

[2] Country data, apportionment calculations, and data sources compiled for this analysis are available upon request. This includes 49 upper chambers with seats elected by citizens or elite groups. This excludes 19 upper chambers wholly composed by appointment and/or hereditary entitlements, four countries where an upper chamber is envisioned in the constitution but not yet formed, and 12 upper chambers that have multi-tier elections.

Older Posts
Newer Posts