Does Proportionality Increase Turnout? A Study of Adaptation to Oscillating Electoral Systems

Abstract

Does proportionality increase turnout? This article studies a national electoral reform in early twentieth-century Argentina that was implemented asymmetrically across districts, creating a natural laboratory in which some districts oscillated between electoral systems across elections. Leveraging this unusual variation in a difference-in-differences design, this article shows that a shift from multi-member plurality rules towards a slightly more proportional system—which removed one-third of the contested seats from the grasp of the dominant party—led to a four percentage point increase in turnout. An investigation into causal mechanisms indicates that more proportional rules, by increasing the odds that smaller parties obtain seats, promoted strategic party entry and intensified electoral competition, both between and within parties. These findings complement existing quasi-experimental results that focus exclusively on elections in European democracies, confirm that parties are able to adapt immediately to changes in electoral rules, and refute the belief that proportionality does not affect turnout in Latin America.

Keywords

electoral system turnout proportionality electoral reforms

Introduction

Few issues have motivated as much research in comparative politics as the consequences of electoral systems—the rules that define how votes translate into legislative seats. Electoral systems affect politics by shaping the incentives for strategic coordination of parties and voters (see, e.g., Cox, 1997; Cox, 2015). Theoretical models show that proportional representation (PR), by making smaller parties more likely to secure seats, stimulates electoral competition, incentivizes parties to mobilize voters, and consequently increases turnout.¹ Consistent with these models, a meta-analysis of existing research has shown that PR systems, on average, have a 5.2 percentage point higher turnout in national elections (Frank & Martínez i Coma, 2023), while another has shown that PR and turnout are typically positively associated in subnational elections (Cancela & Geys, 2016).

Yet estimating the effect of PR on turnout presents a difficult empirical challenge because, as several studies have shown, PR systems are the result of strategic choices (e.g., Boix, 1999; Calvo, 2009; Cox et al., 2019; Emmenegger & Walter, 2021; Leeman & Mares, 2014; Schröder & Manow, 2020). While a positive correlation between PR and turnout might suggest a causal relationship, it could also be a result of unconsidered factors influencing both the adoption of PR rules and voter turnout, such as the strength of socialist parties (e.g., Boix, 1999) or the electoral gains that PR affords to major parties (e.g., Calvo, 2009). Acknowledging these concerns, Shugart (2005, p. 34) encouraged scholars of electoral systems to look for “crucial experiments,” defined as “case studies in which the effects of specific electoral rules can be isolated from other variables,” arguing that repeating this type of study could eventually “lead to accumulation of knowledge.”

A small set of papers has harnessed quasi-experimental research designs to overcome endogeneity concerns (see, e.g., Fauvelle-Aymar & Lewis-Beck, 2008; Eggers, 2015; Cox et al., 2016; Skorge, 2021; Teele, 2023; Paulsen, 2022). This article contributes to this collective enterprise while also diverging from prior studies in two ways. First, previous studies have focused exclusively on Europe. Meanwhile, correlational research has argued that Latin America might be an exceptional region in which electoral systems and turnout are unrelated (e.g., Fornos et al., 2004; Perez-Liñán, 2001). This article studies exogenous variation in electoral systems in a Latin American case—early twentieth-century Argentina—bringing new data to this open debate. Second, this article explores a historical case that provides advantages for studying whether parties, when making decisions about voter mobilization, adapt immediately to electoral systems (e.g., Crisp & Demirkaya, 2020; Fiva & Hix, 2021; Lago, 2019) or, instead, if adaptation takes time (e.g., Gallego et al., 2012; Taagepera, 1998).

I study a quasi-experiment that provides an ideal context for estimating the impact on turnout of a shift away from a purely majoritarian system. In 1912, partly as a result of a struggle between factions of the ruling conservative party, a national electoral reform altered the method of electing members of Congress in Argentina’s 15 districts (Castro, 2012). Until 1912, the electoral system featured multi-member provincial districts and simple plurality rules. The usual outcome of this electoral system, which was widespread in the 19th century, was that hegemonic parties obtained all the contested seats (Colomer, 2007). The electoral reform made provinces transition into a relatively less majoritarian system that favored smaller parties by introducing limited voting—citizens could only cast votes for two-thirds of the contested seats. This system, known as the “incomplete list,” effectively reserved a third of the seats for minority parties (Heaps-Nelson, 1978). An interesting aspect of the new electoral rules is that they could only be implemented in elections in which districts contested at least three seats. As provinces elected half of their congressional delegation every two years, those with a total of five seats repeatedly alternated between electing three seats through the more proportional system in one election, and electing two seats through multi-member plurality rules in another. The unconventional rollout of this reform provides an ideal setting for a differences-in-differences design.²

Using panel data covering all the regular legislative elections from 1912 until a coup d’etat that interrupted free elections in 1930, this article estimates that the transition from multi-member plurality to the more proportional system led to an average increase in turnout of four percentage points (from a baseline of 60.4%). The immediate effect is positive and statistically significant—noticeable in the first election after a district transitions into a new electoral system. After establishing this main result, I then explore mechanisms and show that higher proportionality increased the effective number of parties (ENP), the probability of party splinters, and overall electoral competitiveness. Previous works have argued that if the mechanism connecting proportionality and turnout is party mobilization, then the effect of a transition into a more proportional system should be more pronounced in districts that were previously uncompetitive under majoritarian rules (e.g., Cox et al., 2016); the evidence in this study confirms this prediction.

Altogether, the results suggest that a transition away from a severely majoritarian system into a more proportional one encourages party entry, electoral mobilization, and, consequently, voter turnout. These findings complement existing quasi-experimental results that focus exclusively on elections in European democracies, confirm that parties can adapt immediately to changes in electoral rules, and refute the belief that proportionality does not affect turnout in Latin America.

More broadly, this article complements quasi-experimental research about the causal effect of other aspects of the electoral system besides proportionality, such as district magnitude (e.g., Lucardi, 2019; Lucardi & Micozzi, 2022), open-list systems (e.g., Sanz, 2017), the number of candidates (e.g., Pons & Tricaud, 2018), runoff versus single-round elections (e.g., Bordignon et al., 2016), compulsory voting (e.g., Cox & Gonzalez, 2022), fines on non-voters (e.g., Feierherd et al., 2022), and the combination of district magnitude and the number of votes that citizens can cast (e.g., Crisp & Demirkaya, 2020). It also speaks to works that estimate the effect of proportionality on other outcomes besides turnout, such as the fragmentation of the party system (e.g., Fiva & Hix, 2021), the vote share of right-wing populists (e.g., Bechter et al., 2023), or the frequency of invalid votes (e.g., Cox & Le Foulon, 2024).

The Effect of Proportionality on Turnout

Does Proportionality Increase Turnout?

A large theoretical literature in comparative politics has studied the political effects of different electoral systems (e.g., Cox, 1997). The link between proportionality and turnout, in particular, has been extensively theorized. Some theories highlight mechanisms based on voter decisions, and others focus on party mobilization (see Smith, 2018 for a review). On the empirical front, several works have attempted to test the hypothesis that proportionality increases turnout. A meta-analysis by Cancela and Geys (2016, p. 267) includes 51 such studies—most of which estimate a positive correlation.

Despite many works testing the hypothesis that proportionality leads to higher turnout, meta-analyses are “only as good as the individual studies that go into the sample” (Smith, 2018, p. 197). Indeed, correlations between electoral systems and turnout in observational research might be spurious, as the factors that affect the choice of electoral systems might also independently affect turnout (Eggers, 2015).

This paper avoids this pitfall by focusing on a setting that provides exogenous variation in electoral systems within districts over time. I study an electoral reform in Argentina, described in detail in the next section, that made some districts alternate between two electoral systems (one more proportional than the other). This setting allows me to study, in a difference-in-differences design, how turnout changed in districts that transitioned into a more proportional system while comparing them with the evolution of turnout in districts whose electoral systems did not change in the same period.

This is not the first article to estimate the effect of proportionality on turnout. Studying Norwegian municipalities between 1910 and 1922, Paulsen (2022) shows with a difference-in-differences design that transitioning from multi-member plurality to PR increases turnout by 7.16 percentage points. Studying French municipalities between 2001 and 2008 in a population-based regression discontinuity design, Eggers (2015) estimates that moving from a multi-member plurality system into a diminished form of PR (with a 50% bonus for the winning party) causes a one percentage point increase in turnout. Fauvelle-Aymar and Lewis-Beck (2008) take advantage of the fact that France uses different electoral systems for cantonal and regional elections and find that between 1992 and 2004, PR rules caused a 0.5 percentage point increase in turnout compared to two-round elections.

Other works study how proportionality affects other aspects of turnout. Cox et al. (2016) examine a national electoral reform in Norway, demonstrating that the shift from a two-round system in single-member districts to multi-member districts with PR results in a contraction of turnout rates across districts: while the reform increased turnout in districts where elections were previously less contested, it reduced turnout in those where elections were previously more competitive. Relatedly, Skorge (2021) and Teele (2023) analyze elections in Norway and show that transitions to proportional representation reduced the gender gap in turnout.

This article contributes a new study to this collective enterprise. In the future, the accumulation of similar studies might allow a meta-analysis that exclusively includes quasi-experimental estimates.

Does Proportionality Affect Turnout in Latin America?

In addition to contributing one further study to the research on proportionality’s effect on turnout, a characteristic that sets this article apart is that it studies the effect of proportionality on turnout in a Latin American democracy—a type of case that has been neglected by the quasi-experimental literature, which has focused exclusively on Europe.

Observational works have argued that proportionality does not affect turnout in Latin America (Fornos et al., 2004; Perez-Liñán, 2001). These previous works have been empirical explorations that use small cross-sectional samples and offer no theoretical scope conditions to justify the non-significant correlations. Perez-Liñán (2001, p. 285), for instance, interprets null findings only as suggestive that “institutional effects may take a distinctive form in new democracies” and recommends “further replication attempts.”

Despite the exploratory nature of existing findings on proportionality and turnout in Latin America, subsequent research in the literature commonly mentions Latin America’s exceptionalism, even if sometimes merely in passing. For example, Cox et al. (2016, p. 1250) write: “The relationship between proportionality and turnout is also less consistent in new and developing democracies; ” discussing the association between PR and turnout, Herrera et al. (2014, p. 132) write: “Evidence from Latin America also runs counter to folk wisdom; ” and Gallego et al. (2012, p. 159) state that the relationship between proportionality and turnout “does not hold in Latin America.”

One possible explanation for the null association between proportionality and turnout in Latin America is that there exist scope conditions under which electoral systems affect turnout, and those conditions are not met in the region. An alternative explanation is that previous correlational research failed to detect a significant correlation for purely methodological reasons. For instance, the sample sizes of previous studies might have been too small, such that the studies were underpowered.³ Similarly, it is also likely that cross-country samples did not feature enough variation in electoral systems to precisely estimate a correlation. Indeed, Fornos et al. (2004, p. 933) note that in Latin America “nearly every country uses PR in either large or nationwide districts,” and, therefore, “there is simply very little variance on this independent variable.”

Although there could be methodological explanations for the null correlation between proportionality and turnout in Latin America, subsequent works have proposed theories to explain it. Gallego et al. (2012), for instance, theorizes that proportionality does not affect turnout in new democracies because it takes time for parties and voters to learn how to behave strategically. Alternatively, Endersby and Krieckhaus (2008) argue that electoral systems only affect turnout in fully democratic countries—where voters believe that their votes matter.

In this paper, I study the effect of proportionality and turnout in Argentina (1912–1930), which is a place where existing theories predict null effects: a new partial democracy in Latin America. Unlike previous observational research (Fornos et al., 2004; Perez-Liñán, 2001), this case offers plenty of exogenous variation in electoral systems across districts and within districts over time and allows me to estimate a positive and significant effect. This result contradicts the conventional wisdom about the effect of electoral systems on turnout in Latin America and new democracies.

Are the Effects Immediate?

Another distinctive characteristic of this article’s case study is that it features districts in the same country that switched not once, but repeatedly, back and forth between different electoral systems over time. Studying oscillating electoral systems has methodological advantages. Only some districts alternated between a more proportional and a less proportional electoral system while other districts did not—allowing a difference-in-differences design. Moreover, the multiple switches generate many observations of the first period after a transition, which are useful to estimate immediate effects with recently developed methods (de Chaisemartin & D’Haultfœuille, 2020).

Some works have cast doubt on the existence of short-term effects of electoral system change. Renwick (2018, p. 14), for example, argues that it is possible that “some effects of electoral systems may take multiple electoral cycles to emerge; ” Taagepera (1998, p. 85) that parties and voters need “at least three elections” to learn how to use electoral rules to their advantage; and Gallego et al. (2012, p. 156) that “time is needed before the consequences of electoral systems are fully revealed.” Others have found mixed evidence for short-term effects (e.g., Lago & Martínez i Coma, 2023). These studies hypothesize that changes in the electoral system represent a cognitive burden to which voters adapt over time, which explains the absence of short-term effects. Yet it is also possible that short-term effects exist, but the same factors that motivate changes in electoral law—such as political strife or new party coalition—themselves offset the effects of the electoral system on turnout in the short term.

If one were to study the immediate effect of electoral reforms using cross-country data (e.g., Lago & Martínez i Coma, 2023) or a case where the electoral system changes because parties make reforms for short-term electoral gain (e.g., Bowler & Donovan, 2013), then it would be difficult to untangle the immediate effect of the electoral system from that of the underlying political factors that motivated the reforms (e.g., Baldini, 2012; Bowler & Donovan, 2013). This article’s case study not only offers many episodes of electoral system change, but these changes are also exogenous to party competition. This extremely unusual setup allows me to avoid the aforementioned pitfall, joining other works that also use exogenous variation in electoral systems and have detected immediate adaptation to electoral rules, both after a one-off change (e.g., Fiva & Hix, 2021) and with alternating electoral systems (e.g., Crisp & Demirkaya, 2020).

At a minimum, therefore, this article detects short-term effects of proportionality on turnout—adding new evidence against previous claims that it takes time for the effects to arise. While previous research has estimated immediate effects of electoral systems in Norway, it called for further research to determine whether “the speed of …adaptation …is generalizable to other cases” (Fiva & Hix, 2021, p. 1790). This paper suggests that it is. Immediate effects, of course, do not refute long-term effects.

Taking interpretation of these results a step further, one might argue that the existence of short-term effects has implications for our understanding of causal mechanisms. If immediate effects exist, as this article will show, then either: (a) voters do not need that long to learn how to use electoral rules strategically, or (b) the mechanism linking proportionality and turnout in the short term is not based mainly on voter decisions but on party mobilization decisions. I provide further evidence for the party mobilization mechanism in the results section.

Research Design

To estimate the effect of proportionality on turnout, I study variation in electoral systems over time within provinces in Argentina from 1912 to 1930. This unusual variation was introduced by an electoral reform in 1912 during Argentina’s transition into a system of competitive elections.

Historical Context and the 1912 Electoral Reform

From 1880 to 1912, Argentina was governed by a confederation of local conservative “parties” under the broad label Partido Autonomista Nacional. All adult native-born men had suffrage, but voting was non-secret and voluntary, which led to widespread vote buying and voter intimidation (Botana, 1977). National legislators were elected to four-year terms in 15 provincial districts, with each province electing half of its congressional delegation every two years using multi-member plurality rules. Under this electoral system, each voter could cast votes for the same number of candidates as seats contested in each multi-member district. The candidates who received the most votes obtained seats. Even though the electoral law did not explicitly require closed lists, the established practice was for parties to distribute predefined lists to the voters they mobilized. Therefore, the usual electoral outcome was that the dominant party in each district obtained all the contested seats (Heaps-Nelson, 1978).⁴

In 1912, internal factional strife within the conservative party prompted an electoral reform (Castro, 2012; Madrid, 2019). While this reform is primarily recognized for introducing secret and mandatory voting, it also modified the electoral system.⁵ The reformers abolished multi-member plurality rules for legislative elections and introduced a less majoritarian system known as the “incomplete list” system. According to this system, known in the political science literature as the limited vote (see, e.g., Norris, 2004, p. 48), voters could only cast votes for a number of candidates equal to two-thirds of the number of contested seats, which limited the number of seats that dominant parties could obtain by mobilizing voters. The median provincial election between 1912 and 1930 had a district magnitude of 3 (and the average provincial election a magnitude of 5.7), so a typical scenario would be that voters could cast two votes for three seats (or four votes for six seats).

Table 1 describes how the reform changed the electoral system. Compared to the multi-member plurality rules in place before 1912, the incomplete list system was more permissive. It encouraged the entry of minority parties by limiting the electoral prize that dominant parties could reap to two-thirds of the disputed seats.

Table 1.

Schematic Representation of the 1912 Electoral Reform.

	After 1912:	Before 1912:
	Incomplete List/Limited Vote	Multi-member Plurality
Magnitude	M $\geq$ 1	M $\geq$ 1
Formula	M most voted candidates elected	M most voted candidates elected
Votes per voter	2/3 M	M
Typical outcome	2/3 of the seats to largest party;	Dominant party sweep
Typical outcome	1/3 of the seats to minority party	Dominant party sweep

One might think of the electoral reform as introducing a weak “dose” of proportionality in what was previously an extremely majoritarian system (see, e.g., Eggers, 2015). The electoral reform bill that President Saenz Peña sent to Congress included an opening letter that argued that the incomplete list system would be a “rehearsal for a definitive [PR] reform” (HCDN 47-PE-1911). This is also how pundits interpreted the reform at the time. Rodolfo Rivarola, the founder of the first political science journal in Argentina (the Revista Argentina de Ciencia Política) fielded a public opinion survey in 1911 to ask respondents about their preferred electoral system, and the close-ended questionnaire classified the incomplete list as a proportional system (Cantón, 1967, p. 22).⁶

Before the electoral reform of 1912, elections in Argentina were not competitive, so the emerging mass party Unión Cívica Radical (UCR) frequently abstained from electoral competition. It is particularly in these non-competitive settings, where majoritarian rules discourage entry, that shifts toward higher levels of proportionality should boost competition and turnout the most (Cox et al., 2016; Herrera et al., 2014). The architects of the 1912 reform were aware that, by permitting minority parties to secure representation, the reform would lift them from electoral abstention. In a legislative debate in Argentina’s lower house, the Minister of the Interior and advocate of the reform, Indalecio Gómez, contended that by placing one-third of the seats beyond the reach of the ruling party’s political machine, the incomplete list system would stimulate electoral opposition by increasing the likelihood that smaller parties obtain seats.⁷

The Natural Experiment

The electoral reform was enacted with the explicit goal of promoting voter turnout. Therefore, a simple before-and-after comparison of changes in turnout at the national level would elicit the obvious concern that turnout could have increased after the reform for some underlying political reason that also motivated the reform. Fortunately, however, for arbitrary reasons, a group of provinces had to implement the incomplete list system in certain elections while maintaining the multi-member plurality system in others. Due to their smaller district magnitudes and the Argentine practice of each province electing only half of its congressional delegation in each election, some provinces encountered electoral cycles during which they were exempt from the electoral reform because they contested fewer than three seats, making it impossible to limit voting to two-thirds of the number of seats contested.

As shown in Figure 1, a group of always-treated provinces used the incomplete list in all elections (Buenos Aires, Capital Federal, Córdoba, Corrientes, San Luis, and Santa Fe), another group of never-treated units never used the incomplete list (Jujuy, Catamarca, and La Rioja), and a third group of switchers sometimes used the incomplete list and sometimes used the old multi-member plurality system (Entre Ríos, Mendoza, Salta, San Juan, Santiago del Estero, and Tucumán).

Figure 1.

The 1912 electoral reform and its application across provinces. Notes. The graph shows which provinces had elections under the incomplete list electoral system (dark gray cells), elections under the multi-member plurality system (black cells), or no elections (light gray cells) between 1912 and 1930. Some years had no elections for idiosyncratic reasons (described in Supplemental Appendix A).

The most valuable source of variation for causal identification comes from the third group of provinces that alternated between conducting elections under the multi-member plurality system and the incomplete list system. The variation used for estimation comes from two types of switchers: (1) districts that switch from multi-member plurality to the incomplete list system (switchers-in); and (2) districts that revert to multi-member plurality from the incomplete list system (switchers-out).

There were 18 instances of electoral system switching between 1912 and 1930. Table 2 shows how turnout changed in each case of electoral system switching. In seven cases, the electoral system became less proportional (the province transitioned from the incomplete list to multi-member plurality), while in eleven cases, the electoral system became more proportional (the province transitioned from multi-member plurality to the incomplete list). On average, when the electoral system became less proportional, turnout decreased by 7.27 percentage points relative to the election immediately before. In contrast, provinces that switched from multi-member plurality to the incomplete list, on average, experienced a one percentage point increase in turnout. While suggestive that proportionality increased turnout, these average changes cannot be interpreted causally because the before-and-after comparisons lack a control group—namely, provinces that did not switch electoral systems in the same period.

Table 2.

Change in Turnout after the 18 Instances of Electoral System “Switching”.

Province	Year	Type of Electoral System Switch	Δ Turnout (%)
Entre Rios	1916	Incomplete list → multi-member plurality	−5.85
Entre Rios	1920	Incomplete list → multi-member plurality	−12.16
Mendoza	1916	Incomplete list → multi-member plurality	1.86
Santiago del Estero	1914	Incomplete list → multi-member plurality	−18.88
Santiago del Estero	1918	Incomplete list → multi-member plurality	−10.68
Tucumán	1916	Incomplete list → multi-member plurality	−2.33
Tucumán	1920	Incomplete list → multi-member plurality	−7.53
Average Δ Turnout — Incomplete list to Multi-member plurality: -7.27 pp. turnout
Entre Rios	1918	Multi-member plurality → incomplete list	−0.52
Entre Rios	1922	Multi-member plurality → incomplete list	19.08
Mendoza	1914	Multi-member plurality → incomplete list	−5.69
Mendoza	1918	Multi-member plurality → incomplete list	−8.14
Salta	1922	Multi-member plurality → incomplete list	4.73
San Juan	1922	Multi-member plurality → incomplete list	−2.65
Santiago del Estero	1916	Multi-member plurality → incomplete list	8.57
Santiago del Estero	1920	Multi-member plurality → incomplete list	3.47
Tucumán	1914	Multi-member plurality → incomplete list	−4.06
Tucumán	1918	Multi-member plurality → incomplete list	−6.97
Tucumán	1922	Multi-member plurality → incomplete list	3.16
Average Δ Turnout — Multi-member plurality to Incomplete list: +1 pp. turnout.

As only some provinces oscillated between electoral systems, one can study changes in turnout over time in the provinces that switched electoral systems, as in Table 2, while comparing them with changes in turnout in provinces whose electoral systems did not change. Naturally, if provinces could choose their electoral system, this empirical strategy would elicit the obvious concern that parties strategically choose electoral systems for short-term partisan gain. But this is not the case in this particular setting because the electoral systems that provinces used were a function of the number of seats they had to elect—a number over which provinces exerted no unilateral control.

The assignment of provinces to electoral systems in each election depended exclusively on the number of seats contested. The instances of within-province switching between multi-member plurality and incomplete list systems can be ascribed to various factors. First, provinces with five legislative seats elected three seats in some elections (with the incomplete list system) and two seats in others (employing the multi-member plurality system). Second, provinces that, owing to population growth, increased their seat count from five (or fewer) to six (or more) permanently transitioned into the incomplete list system, electing more than three seats every two years.

Members of Congress from a specific province could, in rare circumstances, force the next election to be conducted under the incomplete list system. If the upcoming election was set to have a district magnitude of two, a seating member of Congress from that district’s delegation could strategically resign, increasing the district magnitude in the next election to three, which would require incomplete list rules. However, it was not in the legislators’ best interest to do this. This move would only make sense if the legislator anticipated that his party would place second in the election (if the legislator anticipated that his party would place first, he would prefer plurality rules). But the electoral prize of the second most-voted party in an election of district magnitude equal to three with the incomplete list system is just one seat. Thus, strategic resignations mean surrendering one seat with certainty in exchange for some probability of gaining just one seat, which would be irrational. There is no evidence that legislators strategically resigned between 1912 and 1930.

Econometric Specification

To estimate the effect of the (more proportional) incomplete list system on turnout, I use the following two-way fixed-effects specification:

T u r n o u t_{i t} = β_{1} {Incomplete list}_{i t} + α_{i} + θ_{t} + u_{i t}

(1)

where Turnout_it is the percentage of registered voters who cast a ballot in province i in year t, Incomplete list_it is an indicator that province i held elections under the incomplete list rules in year t, and α_i and θ_t are province and year fixed effects. β₁ is the two-way fixed effects estimator of the effect of proportionality on turnout. I estimate equation (1) with OLS and cluster standard errors by province.

In addition to the baseline two-way fixed effects specification (1), I also study the immediate effect of transitions from multi-member plurality rules into the incomplete list system using de Chaisemartin and D’Haultfœuille’s (2020) DID_M estimator.⁸ This recently developed differences-in-differences estimator captures the effect of switching to the incomplete list system on turnout in the districts whose electoral system switches from time t − 1 to t. The control units are those districts that did not switch electoral systems between t − 1 and t.

Data

To estimate equations (1), I build a panel database of the universe of regular elections between 1912 and 1930 in Argentina’s 15 districts (14 provinces and the City of Buenos Aires). The panel begins in 1912 with Argentina’s first competitive elections and ends in 1930 with a coup d’etat that inaugurated a decade that was infamous for its high levels of electoral fraud. Each district experienced between 5 and 10 elections in this period, so my panel has 134 observations (election-districts).

I used electoral data from Cantón (1968, pp. 81–106) and official records of Argentina’s lower chamber.⁹ The two main variables are a measure of turnout (the number of persons who cast a ballot as a fraction of registered voters) and an indicator that a province used the incomplete list system in an election.¹⁰

To investigate mechanisms, I also create measures of the fragmentation of the party system and its degree of competitiveness. To measure the fragmentation of the party system, I compute the ENP in each election, defined as $1 / \sum v_{k}^{2}$ , where v_k is the vote share of party k (Laakso & Taagepera, 1979). I interpret a higher number of competing parties as an indicator of the willingness of non-dominant parties to compete in elections. I also code an indicator of party splinters in province i in year t (defined as parties with the same name as another plus a distinctive noun or adjective). Finally, I calculate three measures of electoral competitiveness: the difference in the vote shares of the first and second most voted parties; the total vote share of the most voted party; and the minimum gain in vote share that would afford a party at least one additional legislative seat given the electoral rules (see, e.g., Cox et al., 2020). Higher values indicate lower competition.¹¹

Empirical Results

This section presents the empirical results. First, it shows that elections under the incomplete list system score higher in terms of common measures of proportionality than elections with multi-member plurality rules. Second, it shows that the incomplete list system increased turnout and that the effect was immediate—detectable in the first election with the new electoral system. Third, it explores mechanisms and shows that elections with the more proportional incomplete list system incentivized party entry and increased several measures of electoral competitiveness—factors that promoted electoral mobilization. Finally, this section illustrates the study’s findings with a concrete empirical case, describing the dynamics of party competition and mobilization in the province of Santiago del Estero, which had alternating electoral systems between 1916 and 1920.

Elections with the Incomplete List Were More Proportional

I have argued that the transition from multi-member plurality rules to the incomplete list system represented a shift towards greater proportionality (or, equivalently, lower dis-proportionality). The incomplete list system attenuated the winner-takes-all effect of the majoritarian formula by reserving a third of the disputed seats for minority groups that would not have obtained any seats under multi-member plurality rules. In expectation, reserving seats for a minority party increased the degree to which parties obtained a number of seats proportional to their popularity.¹²

Other comparative works also consider the incomplete list more proportional (or less majoritarian) than multi-member plurality. For example, Norris (1997, p. 299) classifies the limited vote as a “semi-proportional” system. Furthermore, Norris (2004, p. 91) shows empirically that multi-member plurality, sometimes called the “bloc vote,” is the electoral system that produces the least proportional seats-to-votes allocation.

Supplemental Appendix B shows that, in addition to being more proportional than multi-member plurality in expectation, the incomplete list system, on average, produced a more proportional seats-to-votes allocation in Argentina from 1912 to 1930.

The Effect of Proportionality on Turnout

I now turn to estimating the effect of the incomplete list system on voter turnout. Table 3 displays the estimates of the baseline two-way fixed-effects equation (1). The specification in Column 1 shows that the incomplete list system, on average, led to a four percentage point increase in turnout compared to multi-member plurality electoral rules.¹³ This represents a 6.6 percentage point increase relative to a baseline average turnout of 60%. Given that clustered standard errors can be biased downwards when the number of clusters is small, as in this application, I also compute p-values using wild cluster bootstrap (Cameron et al., 2008), obtaining statistically significant results.¹⁴

Table 3.

Estimates of the Effect of Proportionality on Turnout.

	(1)	(2)	(3)
	Turnout	Turnout	Estimate of Immediate Effect
Incomplete list	4.088*	4.211*	DID _M = 5.089*
	(1.483)	(1.658)	95%CI = [0.698, 9.479]
District magnitude		−0.074	N = 61; switchers = 18
		(0.340)
			DID _l = 6.400^†
Wild cluster bootstrap p-value	0.040	0.036	95% CI = [-0.471,13.270]
			N = 24; switchers = 6
Mean of control group	59.9	59.9
Province FE	Yes	Yes
Year FE	Yes	Yes
Observations	134	134
R-squared	0.83	0.83
Number of provinces	15	15

Notes: † Significant at 90% level, * Significant at 95% level. Results in columns 1 and 2 are two-way fixed-effects estimates, estimated by OLS. Robust standard errors clustered at provincial level in parentheses. Results in column 3 estimated using DID_M and DID_l estimators and statistical software developed by de Chaisemartin and D’Haultfœuille (2020), with standard errors clustered at provincial level.

It should be noted that the treatment under study is a compound one. Districts that used the incomplete list system also had a higher district magnitude: districts used multi-member plurality when they elected one or two seats, and the incomplete list when they elected three seats or more. Lucardi (2019) has shown quasi-experimentally that district magnitude affects patterns of electoral competition. Column 2 shows that the estimated effect of the incomplete list on turnout increases slightly when I control for district magnitude. The coefficient for district magnitude is not statistically significant.

To study the immediate effect of the incomplete list in provinces that switch electoral systems, which taps into whether parties can flexibly adapt their mobilization strategies to oscillations in the electoral system, I rely on de Chaisemartin and D’Haultfœuille’s (2020) DID_M estimator. This estimator, part of a recent wave of new difference-in-differences estimators (Roth et al., 2023), is particularly suitable for contexts where treatment status switches on and off over time within units. The DID_M estimator compares the evolution of turnout in districts that switch electoral systems between periods t − 1 and t with the changes in turnout in districts that did not switch electoral systems in that same period.

As shown in Column 3, the estimated effect of switching from a multi-member plurality to an incomplete list system is positive and statistically significant, allowing me to reject the null hypothesis of no immediate effect of switching electoral systems. Using the incomplete list leads to an immediate five percentage point increase in turnout. The 95% confidence interval for this estimate ranges from 0.7 to 9.5 percentage points—based on 1000 bootstrap permutations. I also report an estimate of the DID_l estimator, which focuses only on the immediate effect of the first instance of switching in each province (n = 6). This estimate is positive and statistically significant at the 10% level, but the estimate is less precise because of the smaller number of first-time switchers.

The estimated size of the effect of proportionality on voter turnout is similar to previous quasi-experimental estimates for European cases: Paulsen (2022) estimates an effect of 7 percentage points in early twentieth-century Norway; and in contemporary France, using different methods, Fauvelle-Aymar and Lewis-Beck (2008) and Eggers (2015) estimate effects of approximately 0.5 and one percentage points, respectively. It is also similar to the 5.2 percentage point estimate obtained through a meta-analysis of cross-national observational research (Frank & Martínez i Coma, 2023, p. 624). The positive estimated effect of proportionality on turnout in my sample of Argentine provinces contradicts previous correlational null findings on Latin American samples (Fornos et al., 2004; Perez-Liñán, 2001) and suggests that the belief that electoral systems do not affect turnout in new democracies should be revised.

Parallel Trends

An assumption of the difference-in-differences estimator is that turnout in the treated and control groups would have evolved on parallel trends had the former not transitioned into the incomplete list system. This assumption is about a counterfactual and cannot be tested. An indirect way of gauging its plausibility is to test whether experimental groups were evolving on parallel trends before one group was treated. While the fact that districts in my sample oscillated between multi-member plurality rules and the incomplete list system has the advantage of allowing me to estimate with accuracy the immediate effect of switching electoral systems, this advantage comes at the cost of losing pre-treatment periods needed to study pre-trends.

To assess the validity of the parallel trends assumption, I compare the evolution of turnout from period t − 2 to t − 1 in provinces that switched and did not switch electoral systems between t − 1 and t, in the (admittedly small) sample of provinces that did not switch between t − 2 and t − 1 (N = 10; Switchers = 3) (see de Chaisemartin & D’Haultfœuille, 2020). Although the small sample size for this test makes the estimate not precise (DID_P = −2.3, 95% CI from −18.7 to 14.1), the estimated placebo effect is negative and not statistically significant, suggesting an absence of anticipation effects.¹⁵

Mechanisms: Proportionality, Strategic Entry, and Voter Mobilization

What explains the positive effect of the incomplete list system on turnout? The theoretical literature has proposed two non-exclusive mechanisms connecting proportionality and turnout: (i) mechanisms focusing on voters, and (ii) mobilizational mechanisms focusing on parties. I cannot conclusively adjudicate between these two mechanisms. Nonetheless, some characteristics of Argentina between 1912 and 1930 suggest that it is less likely that voter-based mechanisms explain the results than mobilization-based mechanisms.

Voter-based mechanisms focus on voter preferences, strategic behavior, and feelings of efficacy. If one accepts the premise that it takes time for voters to learn how to strategically use electoral systems (e.g., Gallego et al., 2012), and that electoral systems determine turnout through their effects on feelings of voter efficacy (e.g., Endersby & Krieckhaus, 2008), then it is unlikely that the incomplete list system increased turnout mainly because of voter behavior. Between 1912 and 1930, Argentina was a new democracy. Elections before 1912 had low participation rates and were orchestrated by political parties, so voters after 1912 were inexperienced. Senator Joaquín V. González keenly expressed this idea during the debate about the electoral reform, saying, “This country …has never voted before.”¹⁶ Moreover, although political machines were weakened by secret voting, they continued playing a decisive role in elections (Persello, 2001, pp. 128–133). It is thus improbable that the incomplete list substantively increased feelings of voter efficacy.

Political parties, on the other hand, had accumulated vast experience mobilizing voters in the decades before 1912 (Castro, 2012; Sabato, 1998). The congressional debates about the electoral reform also reveal that politicians were aware of how the incomplete list would affect the party system and patterns of competition (De Privitellio, 2011). Indeed, favoring the formation of an “opposition party” was an explicit goal of those who proposed the incomplete list system (Heaps-Nelson, 1978).

Considering the heterogeneous situation of voters and parties at the onset of the electoral reform (with experienced parties and inexperienced voters), it is more likely that the incomplete list system increased turnout because it increased the probability that electoral mobilization generated seats for minority parties than because it affected feelings of voter efficacy.¹⁷ In this section, I show additional evidence consistent with a party-based mechanism. I show that the incomplete list made more parties campaign, that it allowed parties to split into factions and compete with one another, and that it made elections more competitive. Finally, I also verify an observational implication of the party-mobilization hypothesis proposed by Cox et al. (2016): that the effect of the incomplete list is bigger in districts where elections under the plurality system were less competitive.

Party Entry

To study mechanisms, Table 4 shows estimates of the effect of the incomplete list system on different outcome variables. Column 1 focuses on the ENP that competed in elections. The incomplete list system, on average, led to the entry of 0.75 more parties. This effect is large relative to an average of 1.89 parties in districts that used multi-member plurality rules. The DID_M estimate of the immediate impact of the incomplete list system on the effective number of competing parties is positive and statistically significant. This effect of the incomplete list system on the number of parties reflects how it was more permissive than multi-member plurality rules, which only reward the dominant party and thus lower incentives for smaller parties to participate and mobilize voters.

Table 4.

Changes in Patterns of Party Competition.

	(1)	(2)	(3)	(4)	(5)
			Competitiveness (Lower Values = More Competitive)
	ENP	Splinter Group	[1st versus 2nd]	[1st Vote Share]	[Minimum Gain]
Incomplete list	0.759**	0.289*	−0.240^†	−0.174**	−0.368**
	(0.206)	(0.093)	(0.119)	(0.056)	(0.074)
Wild cluster bootstrap p-value	0.001	0.004	0.105	0.038	$<$ 0.001
DID _M 95% CI	[0.002, 0.842]	[−0.033, 0.531]	[−0.666, −0.111]	[−0.340, −0.052]	[−0.678, −0.194]
DID _l 95% CI	[−0.390, 1.388]	[−0.134, 0.256]	[−0.908,-0.021]	[−0.491,0.009]	[−0.967,-0.039]
Mean of control group	1.89	0.33	0.36	0.65	0.36
Observations	134	134	134	134	134
R-squared	0.151	0.449	0.156	0.194	0.319
Number of provinces	15	15	15	15	15

Notes: † Significant at 90% level, * Significant at 95% level, ** Significant at 99% level. Robust standard errors clustered at provincial level in parentheses. All columns report wild cluster bootstrap p-value and 95% confidence interval of DID_M and DID_l estimates of immediate effect of the incomplete list.

Another interpretation of this finding is that the incomplete list system increased the number of parties and improved the representation of voter preferences—motivating voters to turn out. One could argue, for example, that working-class voters would be more likely to vote when the party system offers a left-wing option. However, Lupu and Stokes (2009) have shown that neither a class-based nor urban-rural cleavage had emerged in the party system before 1946.¹⁸ As congressman José Founrouge explained during the discussion of the 1912 electoral reform, except for the Socialist Party, political parties in Argentina did not represent economic interests nor religious views; instead, they were based on personal “sympathies and affection” or were “opposition parties”—meaning that they were formed to acquire power or dispute the power of an incumbent.¹⁹

Party Splinters

The measure of ENP in Column (1) includes all parties that competed in an election. Yet sometimes these parties were splinter factions of a “parent party.” Not all splinters were equal. In some cases, splinters formed because of conflicts between members of the same party. For example, in Santiago del Estero, the Radical Party was an archipelago of elites who shared an overarching partisan identity. The party repeatedly split into factions and then re-grouped as a response to personal conflicts, shifting loyalties towards national politicians, and electoral opportunism (López, 2022). In other cases, splinters were adaptations to electoral rules for short-term gain. For instance, in 1909, the two conservative groups in Corrientes, Liberales and Autonomistas, coalesced into a single party to win the governorship. In 1912, when Corrientes had to elect four legislative seats with the incomplete list system (so voters could only cast three votes), the incumbent Liberal-Autonomista party presented two different lists of candidates and managed to obtain all the contested seats (Solís Carnicer, 2001). The congressional files on the election acknowledged the splinter of the incumbent party, which the opposition protested, but argued that this practice was not banned by electoral law.²⁰

Strategic splinters were an anticipated consequence of the incomplete list system. The national legislators who debated the reform bill extensively discussed the issue. During the congressional debates, congressman Julio A. Costa, who opposed the electoral reform, anticipated strategic party splinters and argued that they would defeat the purpose of the reform—to grant representation to minorities.²¹ Congressman Manuel Peña, who supported the electoral reform, defended strategic splinters, arguing that they could impede tiny minorities (with less than a third of the votes) from receiving a disproportionate share of seats.²²

To see how the incomplete list fragmented the party system via splinters, Column 2 of Table 4 uses a binary indicator of splinters in a provincial election as the outcome variable. The results show that the incomplete list led, on average, to a 28.9 percentage point increase in the probability of splintering—a large effect relative to a baseline probability of 33% in the control units. The DID_M estimate of the immediate effect is statistically significant at the 10% level.²³ Interestingly, the effect of the incomplete list on party splinters accounts for approximately half of the effect on the ENP (Column 1). If the vote shares of each splinter group are collapsed into their parent party, the estimated effect of the incomplete list on the ENP declines from 0.76 (p = .002) to 0.39 (p = .018).

Electoral Competitiveness

If the additional parties mobilized more voters, one should expect that the incomplete list fueled electoral competition, and this is precisely what the data show. The last three columns of Table 4 show that the incomplete list system reduced the difference between the most voted party and the runner-up by 24 percentage points (Column 3); the share of votes of the most popular party by 17.4 percentage points (Column 4); and the minimum gain in vote share that would afford a party at least one additional legislative seat by 36.8 percentage points (Column 5). DID_M estimates show that the effect of the incomplete list system on all measures of competitiveness was statistically significant at the 5% level.

Heterogeneity by Previous Competitiveness

Cox et al. (2016) propose another prediction of mobilization-based mechanisms: a transition towards a more proportional system should increase turnout more when the competitiveness of elections is low under plurality rules.²⁴ The data confirm this prediction. Appendix E shows that a transition into the incomplete list in a competitive district where the dominant party received 50% of the votes under plurality rules decreased turnout, on average, by one percentage point—and this effect is statistically insignificant (p = .676). In contrast, the incomplete list system increased turnout by 6.2 percentage points (p = .012), on average, in uncompetitive districts where the dominant party received 80% of the votes with plurality rules. The average effect of the incomplete list on turnout in Table 3 is positive because elections with plurality rules were typically uncompetitive.

This exploration of mechanisms suggests that, by increasing the extent to which voter mobilization translated into legislative seats, the incomplete list allowed the entry of new parties and allowed party factions to form independent splinter groups. The overall result was a more competitive party system with more parties mobilizing voters.

Illustrative Example: Santiago del Estero

Before concluding this article, it is worth illustrating its main findings in the light of a concrete empirical case. Santiago del Estero had fewer than six legislative seats and alternated between multi-member plurality and the incomplete list system until 1920. The patterns of political competition in this province exemplify how parties reacted strategically to electoral rules and how party systems can change quite quickly, from one election to another, as electoral rules oscillate (see, e.g., López, 2022).

In 1916, Santiago del Estero had to elect three legislative seats, so elections were held under the incomplete list system—two seats for the majority and one for the minority. The election featured the subnational ruling party Unión Democrática (UD) and the opposition party Unión Cívica Radical (UCR). The opposition party won two of the three contested seats by a tiny margin—only 180 votes. Turnout in this election was 56%.

Two years later, in 1918, two seats were contested, so the electoral system was one of multi-member plurality. Anticipating fraud by the incumbent party, the opposition party, UCR, abstained from competing and demanded a federal intervention in the province. The result was a landslide victory of the ruling UD with 83% of the vote against minor parties. Turnout in this noncompetitive election was just 19 percent—and the election was eventually declared void. Even though the allegations of fraud played a part in the UCR’s decision to abstain from competing, it is likely that decision would have been different had the electoral system been the incomplete list—that way, the number of seats the ruling party could have obtained via fraud would be limited. The fraudulent election was repeated in 1919 and turnout was 45.6%, representing a 10 percentage point reduction relative to the previous election.

A year later, in 1920, the provincial political context was more favorable for the UCR. José A. Cabanillas, the governor and leader of UD, had died in 1919, and the federal government intervened in the province shortly after. The newly elected governor in 1920, the UCR candidate Manuel Cáceres, quickly gained control over the province’s political machine. The UCR was set for a landslide victory in the legislative election. Yet four seats were contested in 1920, so the province had to use the incomplete list system—with one seat reserved for the minority. This time, not only did the UCR not abstain like in the previous election, but two UCR splinter groups competed: the mainstream UCR linked to the governor received 52% of the votes and three seats, and the splinter faction UCR Lista Negra received 26% of the votes and the seat reserved for the minority. UD received 18% of the votes and no seats. Turnout in this election was 49 percent—a 3.4 percentage point increase from the prior year.

This study leverages the fact that many provinces, like Santiago del Estero, alternated between electoral systems across electoral cycles. The DID_M estimates used provinces that did not switch electoral systems in those same electoral cycles as control units, to infer what would have happened with turnout had the electoral system not changed. The general patterns mirror those of Santiago del Estero: turnout increased when districts transitioned into the incomplete list system and decreased when the electoral system reverted to multi-member plurality rules.

Conclusion

Studying the asymmetric roll-out of the 1912 electoral reform across provinces in Argentina, this article examines how parties adapted to exogenous changes in electoral rules across election cycles. The article estimated that an increase in the proportionality of the electoral system led to a four percentage point increase in turnout. Proportionality also increased the ENP, facilitated the rise of splinter groups, and made elections more competitive. The effect of proportionality on turnout was particularly pronounced in districts where elections were uncompetitive under plurality rules. These findings confirm the general pattern in the existing quasi-experimental literature (see, e.g., Fauvelle-Aymar & Lewis-Beck, 2008; Eggers, 2015; Cox et al., 2016; Paulsen, 2022).

This is the first quasi-experimental article to estimate the effect of proportionality on turnout in a Latin American case. While this finding is based on a single case study and is therefore insufficient to invalidate any general claims, it does suggest the need to revise a common belief, based on correlational findings, that electoral systems do not affect turnout in Latin America (e.g., Fornos et al., 2004; Perez-Liñán, 2001). Moreover, confirming previous findings (e.g., Fiva & Hix, 2021; Lago, 2019), a test for immediate effects of changes in the electoral system revealed that parties are quick to adapt to new electoral rules, with effects becoming noticeable in the first election under the new electoral rules (cf. Gallego et al., 2012; Taagepera, 1998).

This article’s unusual empirical setting provides advantages to estimate the effect of more proportional electoral rules (the incomplete list vs. multi-member plurality) on voter turnout. The gains in internal validity, of course, come at the cost of external validity. This article’s case is atypical. However, three factors suggest that the estimated effect of proportionality on turnout in this case might underestimate the impact elsewhere. First, existing research usually compares single-member districts with large-magnitude multi-member districts with PR, while this article focuses on a more subtle proportionalizing reform (from multi-member plurality to limited voting). Second, if it does take time for voters to learn how to use electoral systems (e.g., Gallego et al., 2012), then the oscillating context of this paper would erode part of the effect of proportionality on turnout. Third, voting was compulsory in Argentina after 1912, and research has shown that compulsory voting leads to higher turnout (e.g., Cox & Gonzalez, 2022; Fornos et al., 2004). Though compulsory voting was far from perfectly enforced, it might have limited, to an extent, the degree to which turnout could fall when elections used less proportional rules.

While one can speculate about the degree to which the results of this article can extend to other contexts, answering this question ultimately requires additional research. On the one hand, the positive estimates of the effect of proportionality on turnout in this article are similar to those of previous quasi-experimental studies (e.g., Eggers, 2015; Paulsen, 2022). On the other hand, the empirical results in the literature on the effect of proportionality on turnout are not directly comparable. Not only does each paper focus on different types and degrees of proportionality, but each paper also compares proportional systems against different baselines (single-member districts, two-round systems, etc.). The accumulation of similar findings might allow, in the future, a comprehensive meta-analysis that relies exclusively on quasi-experimental estimates and takes into account that the effect of proportionality on turnout depends on the type of proportionality and the baseline electoral system used in the comparison. This paper contributes to this promising collective enterprise.

This article has focused on the effects of the incomplete list system on voter turnout (and supplementarily, exploring mechanisms on patterns of political competition). Previous research has examined the origins of PR (e.g., Boix, 1999; Calvo, 2009; Leeman & Mares, 2014; Rokkan, 1970) and single-member districts (e.g., Ahmed, 2013). The incomplete list system was another reform that conservative elites pursued in the early stages of democratization, and its causes have thus far been insufficiently studied. A quantitative analysis of the origins of the limited vote is a promising topic for further investigation.

Supplemental Material

Supplemental Material - Does Proportionality Increase Turnout? A Study of Adaptation to Oscillating Electoral Systems

Supplemental Material for Does Proportionality Increase Turnout? A Study of Adaptation to Oscillating Electoral Systems by Valentin Figueroa in Comparative Political Studies

Footnotes

Acknowledgments

I am grateful to David Altman, Gary Cox, Adrián Lucardi, Marcos Salgado, Julieta Suárez-Cao, Guadalupe Tuñón, Francisco Urdinez, the editors, and three anonymous reviewers for helpful feedback, to Evelyn Kim for copy editing the paper, and to Bernardo Perez for excellent research assistance.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Valentin Figueroa

Data Availability Statement

The manuscript includes a footnote that says: “Replication materials and code can be found at .”

Supplemental Material

Supplemental material for this article is available online.

Notes

Author Biography

Valentín Figueroa is an assistant professor of political science at the Instituto de Ciencia Política, Pontificia Universidad Católica de Chile.

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