More Options, but Less Willing to Cast a Valid Vote: Evidence From Electoral Reform in Chile

• Published date: 01 March 2025
• DOI: http://doi.org/10.1177/00104140241237480
• Author: Loreto Cox,Carmen Le Foulon
• Date: 01 March 2025

Article

Comparative Political Studies

2025, Vol. 58(3) 562–607

© The Author(s) 2024

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DOI: 10.1177/00104140241237480

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More Options, but Less

Willing to Cast a Valid

Vote: Evidence From

Electoral Reform in Chile

Loreto Cox

1

and Carmen Le Foulon

2



Abstract

How do large-magnitude proportional systems affect invalid voting? We

evaluate a Chilean electoral system reform that introduced proportionality.

Voting is voluntary, and legislative and presidential elections are held con-

currently. We compare the invalid votes between different types of elections

before and after the reform using various difference-in-differences strategies.

We f‌ind that invalid voting increased in legislative compared to presidential

elections (pre-trends were parallel). The increase in invalid voting is greater in

post-reform districts with higher magnitude and is not due to pre-reform

district characteristics. The results of heterogeneity analyses and a survey

experiment suggest the mechanism behind these f‌indings is the cognitive

burden associated with a longer ballot. This research highlights an under-

studied aspect of electoral systems: higher district magnitudes may be de-

mobilizing in terms of valid voting for citizens who are more vulnerable to

cognitive burden, even among those motivated enough to vote in the f‌irst-

order election.

1

Pontif‌icia Universidad Católica de Chile, Santiago, Chile

2

Universidad Adolfo Ib´

añez, Peñalol´

en, Chile

Corresponding Author:

Loreto Cox, Escuela de Gobierno, Pontif‌icia Universidad Católica de Chile, Avda, Vicuña

Mackenna 4860, Edif‌icio Mide, Piso 3 - Macul, Santiago 7820436, Chile.

Email: loretocox@uc.cl

Data Availability Statement included at the end of the article

Keywords

invalid voting, representation and electoral systems, elections, public opinion,

and voting behavior, quantitative methods, Latin American Politics

Electoral rules are one of the most relevant institutions shaping voter behavior,

and district magnitude, one of its central features. Extensive research studies

the consequences of proportionality (e.g., Benoit, 2007;Gallegher & Mitchell,

2005;Grofman & Lijphart, 2003;Persson et al., 2005;Profeta & Woodhouse,

2022;Samuels, 1999), yet the effects of district magnitude on invalid voting

1

have received little attention. Invalid voting in legislative elections can often

reach double digits,

2

and since these votes do not count in determining

electoral outcomes, they carry the same problems for representation as voter

abstention.

A rich and growing body of literature studies invalid voting (e.g. Cohen,

2018a,2018;Kouba & Lysek, 2019;Power & Garand, 2007;Singh, 2019;

Uggla, 2008). Cross-national studies have studied the association between

institutional factors and invalid voting on legislative elections, but they must

either rely on national average district magnitude, obscuring the within-

country variation (Power & Garand, 2007) or analyze different types of

elections. Other studies, within or cross-country use the number of effective

candidates or parties which are only in part attributable to the electoral rules

(Cohen, 2018a;McAllister & Makkai, 1993;Uggla, 2008), or analyze local,

not legislative, elections (Barnes & Rangel, 2018;Lundell & H ¨

ogstr¨

om, 2021;

Mart´

ınez i Coma & Werner, 2019).

The research on the effects of district magnitude on turnout also illuminates

that on its effects on invalid voting since both resort to similar underlying

mechanisms. As district magnitude increases, two mechanisms with opposing

effects come into play: While district magnitude may encourage electoral

participation by increasing the number of political alternatives (e.g. Powell,

1986;Radcliff & Davis, 2000), higher district magnitudesboost the complexity

of political systems –and thus, voters’cognitive burden–which may depress

turnout (Cancela & Geys, 2016;Herrnson et al., 2015;Lau & Redlawsk,

2006).

3

The effect of cognitive burden should be greater among electoral

systems with stronger incentives for candidates to cultivate a personal vote

(Carey & Shugart, 1995),this is, where candidates’attributesare more relevant

for the voters’decision. Hence,this problem is particularly acuteunder open-list

proportionalrepresentation, as Power and Roberts(1995) found in Brazil, but it

also applies, to some degree, to all preferential-list electoral systems where the

candidates’characteristics are relevant.

4

Partly due to these opposing effects (Taagepera et al., 2014) and partly due

to data limitations, the impact of district magnitude on turnout remains

Cox and Le Foulon 563

unsettled. Muraoka and Barceló (2019) employ a quasi-experimental design

from Japan municipal elections and f‌ind that district magnitude has a negative

impact on turnout, although it is a context where parties play only a marginal

role. Looking specif‌ically at invalid voting, Cohen (2018a) f‌inds that in

presidential races in Latin America, an increase in the available options

(measured as a change in the number of candidates between elections) de-

creases invalid voting, even while the number of options (measured as the

number of candidates in a given election) has the opposite effect. Thus, further

research is needed to understand whether those results apply to legislative

elections or in contexts where parties are relevant.

We follow an original approach to study the effect of district magnitude on

invalid voting. We take advantage of an electoral reform to legislative

elections in Chile that created new districts with a higher magnitude, with

increases in magnitude that vary across districts and also differ in Senate

versus House districts. Presidential and legislative elections are held con-

currently and lists are open. Voting is voluntary but once a voter arrives at the

polling station, she is handed a separate ballot for each election, without the

chance to reject one, and after passing through the secret chamber, she must

deposit each ballot in a separate box. A longstanding literature from American

politics has studied a similar phenomenon: voters who roll off, this is, who go

the polls but fail to complete lower-order ballots (e.g. Walker, 1966); in our

case, citizens are required to vote for all elections when already at the polls.

We thus use a difference-in-differences (DiD) approach to estimate the re-

form’s causal effect: we compare the share of invalid votes (null and blank)

between presidential elections and legislative elections (Senate and House),

before and after the reform. Pre-trends were fairly parallel. We also exploit

variation in the increase in magnitude by districts.

Our results indicate that invalid voting increased in legislative elections

compared to presidential elections after the electoral reform. The increase is

electorally relevant (on average, 3 points) and is associated with the new

district magnitude: the share of both null and blank votes in legislative versus

presidential elections is greater where the increase in magnitude was larger, for

both the House and the Senate. Moreover, if we compare the relative increase

in the magnitude of the House with respect to the Senate’s new districts, we

also f‌ind that larger differences in magnitude between both chambers are

associated with a greater difference in the share of nulls and blanks. Placebo

tests reveal that these results are absent for previous years. Together, this

evidence suggests that having districts with a greater number of seats reduces

the number of valid votes.

But why do districts with higher magnitudes increase the incidence of

invalid voting? We f‌ind heterogenous effects at the municipality level that are

consistent with an explanation that a longer ballot constitutes a cognitive

burden, as the effects are greater in poorer and less educated municipalities. To

564 Comparative Political Studies 58(3)