Electoral rules and voter bias against female candidates in Brazilian congressional elections

ABSTRACT This paper examines whether and how electoral rules moderate the effect of voter bias on candidate choice. Voter bias against female candidates follows a pattern known as aversive sexism, which denotes that voters discriminate when the choice structure does not make the bias clear to others and to themselves. As a result, voters are less likely to vote for women when they can substitute ideologically close female candidates with male co-partisans. The paper uses survey data and a ballot experiment in Brazil to investigate why, contrary to conventional wisdom on the topic, voters are more likely to elect women running in plurality races for the Senate than in proportional races for the Chamber of Deputies. The results shed light on how institutions can produce voting patterns that harm the electoral prospects of female candidates.


Introduction
According to comparative research on women's representation, two features of electoral systems are the most effective in promoting the presence of women in parliaments around the world: proportional rule and gender quotas. In proportional systems, parties have incentives to present more diverse lists of candidates to maximize their vote shares and, as a consequence, their proportion of seats in the parliament (Darcy, Welch, and Clark 1994;Lijphart 1999;Norris 2006). Similarly, quota rules define different sets of institutional constraints for parties to include women and other marginalized groups in their party-lists, which in turn tends to increase the presence of those groups in legislative bodies (Dahlerup and Freidenvall 2005;Hughes 2011;Schwindt-Bayer 2009).
In Brazil, the adoption of quotas under proportional representation did not result in the expected increase in female presence in the lower house.
While female candidacies for the Chamber of Deputies (lower house) have increased from 6% to 32% over the last 7 congressional elections , the percentage of women elected for office has increased only from 7 to 15 throughout the same period. Meanwhile, the plurality system for the Senate displayed a smaller increase from 7% to 18% in female candidacies over the same period, while presenting a similar increase from 7% to 15% in the number of women elected. All in all, women are less successful when they run for the legislature with proportional rule and gender quotas than when they run for its plurality counterpart.
The literature on women and politics shows that institutional factors are at the core of the explanation for this puzzle (Sacchet and Speck 2012;Wylie 2018). While plurality rule for the Senate selects fewer female candidates to run, those candidates tend to have more campaign resources and visibility to compete. In the absence of that selection process for the highly personalized open-list proportional races for the Chamber, larger gender disparities in campaign resources produce a gender gap in vote shares. The evidence in Brazil is consistent with the broader literature that shows that open-list proportional systems with large electoral districts harm the electoral prospects of female candidates (Iversen and Rosenbluth 2010;Kirkland and Coppock 2018;Shugart, Valdini, and Suominen 2005;Valdini 2012).
To contribute to this debate, this paper builds from the perspective according to which that electoral rules can not only harm the election of women by affecting the nomination process and the distribution of campaign resources, but also by moderating the effect of voter bias on candidate choice (Valdini 2013). I argue that gender bias in elections follows a pattern known as aversive sexism (an extension of the concept of aversive racism from Dovidio and Gaertner (2004)). Aversive sexism denotes that individuals will not discriminate when the choice structure makes their biases evident to others and to themselves. Hence, the structure of the electoral race affects the extent to which votes are based on gender bias. In races with a few candidates competing for the same seat, the differentiation among the choices signals that when voters do not choose women who are ideologically close to them, they are engaging in discrimination. In races with many candidates, it is harder to attribute gender bias to decisions, since for every female candidate there is likely an ideologically similar man who voters can choose without signaling discriminatory intent.

Electoral rules and aversive sexism
Negative views about women in politics vary cross-nationally, but are usually explicitly endorsed by a small proportion of individuals (Morgan and Buice 2013;Norris and Inglehart 2001). Generally, those explicitly negative opinions tend to be seen as uncivil and as going against the basic principles of equality and democracy. However, as Dovidio and Gaertner (2004, 4) point out, "because of a range of normal cognitive, motivational, and sociocultural processes that promote intergroup biases," individuals tend to hold negative feelings towards individuals and groups at an unconscious level. Despite openly endorsing egalitarianism, some individuals are often prone to the influence of negative predispositions towards female authority that do not reach their awareness (Mo 2015;Monin and Miller 2001). 1 Even though negative attitudes towards women can explain patterns of cognition and behavior, previous studies on voting do not observe gender bias or even find a pro-woman bias. Across different contexts, experimental studies using hypothetical candidates and settings observe either no bias or higher proportions of votes for female candidates in comparison to male candidates (Aguilar, Cunow, and Desposato 2015;Clayton et al. 2020;Schwarz and Coppock 2020). However, while the literature suggests that prejudice can be eliminated or even reversed depending on how contexts and judgment tasks interact with stereotypes Biernat and Kobrynowicz (1997), most experimental studies on voter bias rarely consider the conditional nature of prejudice when interpreting observed levels of support for hypothetical candidates in hypothetical settings. Hence, the use of hypothetical stimuli in such studies may present limitations in mundane (Clayton et al. 2020;McDonald 2020). while using real candidates provides subjects with more realistic scenarios, it also makes it more difficult to isolate the effect of the sex of the candidate, since voters can rely on previous information. use an innovative design featuring real candidates in the context of the European Parliament elections and find a pro-woman bias that grows as subjects have more discretion to choose specific candidates rather than lists. However, while the candidates are real, they come from a list of elected members of the parliament, which are different from the general poll of candidates and make the study setting unique with respect to important features. 2 Bol et al. (2016) use the same data to show that subjects are more likely to pick co-national candidates in the study. While insightful, these findings suggest that gender considerations are combined with subjects' prior knowledge about real candidates, which is the main concern that hypothetical experiments attempt to avoid.
In this sense, using specific subsets of real candidates or hypothetical ones often produces settings that lack mundane realism. This limitation can be particularly problematic in the study of prejudice, since subjects may try to conceal the biases that the research is trying to uncover. From a theoretical standpoint, the crucial premise in this type of study should be that voter bias depends precisely on the setting, which certain choice structures making them more to rely on those biases. This pattern of behavior constitutes the mechanism proposed by the theory of aversive racism (Dovidio and Gaertner 2004). The idea of aversive sexism is an extension of the same perspective, since it applies the same psychological mechanism to gender (Mo 2015, 363). Individuals who engage in aversive sexism consciously endorse egalitarian views with respect to gender and do not discriminate against women in situations where the choice structure is strong enough to make discrimination evident to others and to themselves. Hence, the psychological mechanism of aversive sexism refers to the operation of an unconscious bias that individuals deny having and want to avoid manifesting not just to other individuals, but most fundamentally to themselves. Instead, they discriminate when the bases for social judgment are ambiguous, so that the bias underlying their behavior is unclear to others and to themselves. One key element in this theory is that, while voters hold ideological predispositions that they consider when evaluating candidates, they also have baseline gender preferences (Sanbonmatsu 2002). However, while voting based on ideology is seen as a legitimate expression of preferences, choosing candidates based on their gender is not. 3 Therefore, the extent to which voters' biases affects their voting behavior depends on whether gender attitudes overlap other politically relevant predispositions.
When voters must choose from a small number of candidates, each from a different party or ideological background, there is a probability that one of the parties will enter a female candidate in the race. In that case, voters from that party will likely find the female candidate to be the ideologically closest to their preferences. For certain voters, this situation presents a conflict between ideological views and gender bias. Voting against the female candidate who is ideologically close in this case not only sacrifices ideological proximity, but may also signal gender bias. When there are several seats available within the same district, parties have incentives to enter as many candidates as there are seats available, increasing not only the overall number of candidates in the race, but also the number of co-partisan candidates competing against each other. In that situation, there is a higher chance that voters will be able to find a male candidate that is as ideologically close or nearly as close to his/her preferences as the closest female candidate. As a result, biased voters can avoid casting a vote for a woman that they would otherwise be forced to pick if the structure of the race were different. 4 The main observable implication of the aversive sexism perspective is that, while voters see themselves with no ideologically viable alternative other than voting for a woman in a single-member district (SMD) race, they can replace that female candidate with a man in an open-list proportional (PR) race, where the male co-partisan likely offers a justifiable choice. 5 Hypothesis 1 (H1): Voters will be less likely to choose female candidates when there are male substitutes running for the same seat.
The second observable implication of the theory refers to which individuals are the most likely to engage in the behavior described above. Studies investigating the heterogeneous effects of ambiguous choice structures find that aversive prejudice is performed by individuals scoring lower values in batteries of explicit prejudice (Dovidio, Kawakami, and Gaertner 2000;Hing, Li, and Zanna 2002). Explicitly prejudiced individuals discriminate regardless of the choice structure, as long as their negative attitudes towards women in politics are as strong as or stronger than their other political predispositions. Given that aversive sexism is driven primarily by implicit biases that individuals are not aware of, the substitution of male-co-partisans for women is expected to occur among those who do not explicitly endorse sexist views.
Hypothesis 2 (H2): Substitution is more likely to be observed among voters who do not explicitly endorse sexist views in comparison to open sexists.
Notably, individuals who do not openly endorse sexist views could be "true non-sexists" instead of "aversive sexists." However, if that is the case, one would not observe the substitution behavior to vary based on explicit sexism. Hence, even though a third observable implication of the theory is that aversive sexism is more likely to be performed by individuals with high implicit bias and low explicit bias, the extent to which this is true only makes the test of Hypothesis 2 more conservative. In other words, if openly egalitarian individuals are primarily "true non-sexists" rather than "aversive sexists," then Hypothesis 2 would simply not be supported by data. Nonetheless, this scenario is unlikely to occur for two main reasons. First, studies show that the correlation between implicit and explicit attitudes is moderate at best, which denotes that a significant part of the low-explicit prejudice group in comprised of implicitly prejudiced individuals (Nosek 2005). Moreover, Setzler (2019) shows that measurement bias in standard sexism questions tends to be more common among individuals who are strong advocates of gender equality. Second, the claim that explicit sexism accurately reflects underlying levels of sexism (undermining the test of Hypothesis 2) defeats the purpose of conceptually separating implicit from explicit biases.
All in all, although measuring implicit bias would enhance descriptive accuracy, it would not invalidate the observable implications discussed above.
Another plausible mechanism to explain Hypothesis 2 is suggested in Dolan (2014). Since individuals who reject sexist views likely have weaker and less salient gender attitudes than other views, they will be more likely to choose based on the latter attitudes in a more restricted choice structure. They will rely on both orientations when the choice structure allows them to do so, that is, when male co-partisans are available in the less restricted choice structure. On the other hand, individuals who openly endorse sexism likely have gender attitudes that are as strong or stronger than their ideological views. Therefore, they are more likely to avoid voting for women under any choice structure. Since this explanation leads to the same observable implication as Hypothesis 2, one key observable implication that differentiates the two perspectives is the extent to individuals are willing to avoid the substitution behavior when it clearly conveys their gender bias. The sexist tradeoff perspective implies that individuals strategically weight different sets of attitudes and make different choices depending on the choice structure, without concerns about social desirability. Alternatively, the aversive sexism perspective suggests that social desirability is at the core of the substitution behavior. If those concerns are raised to individuals, they will likely change their behavior to avoid the attribution of sexist intent.
Hypothesis 3 (H3): Voters who do not explicitly endorse sexist views will be more likely to avoid the substation behavior if concerns of social desirability are raised before voting.

The case of the Brazilian legislative elections
Two specific features of the Brazilian case challenge the literature on women's representation. First, running counter to patterns observed in empirical research (Darcy, Welch, and Clark 1994;Lijphart 1999;Norris 2006), women are less successful in the proportional races for the Chamber of Deputies than in the plurality races for the Senate. The comparison between the two houses provides an interesting case because the races for both legislatures take place simultaneously and within the same electoral districts (the 27 Brazilian states). The Chamber of Deputies (lower house) uses an open-list d'Hondt proportional representation system, while the Senate (upper house) uses an SMD system. In this way, votes are cast for individual candidates rather than lists for each of the legislative positions, but under very different rules. 6 While the Senate uses plurality races in which a few candidates from different parties run for the seat, the Chamber elections are open-list PR races in which voters pick one out of several candidates from all parties. 7 The second challenging feature of the Brazilian case is the failure of the quota rule for the Chamber approved by the country's parliament in 1997, which also contradicts observed trends in comparative research (Dahlerup and Freidenvall 2005;Hughes 2011;Schwindt-Bayer 2009). In 1997, the Brazilian parliament approved Bill 9.504 (Article 10 (3)), which stated that parties should reserve a minimum of 30% of the candidacies in their list to each sex. However, parties justified failures to meet the requirement by arguing that an insufficient number of women claimed the reserved spots in the lists. In face of the failure of the quota law and pressured by women's groups, the country approved an amendment in 2009, changing the text to state that parties had to fill 30% of their lists with candidates of each sex and would not be allowed to transfer unclaimed spots to men. 8 Despite this change in the quota rule in 2009, the proportion of seats won by female candidates for the Chamber did not increase in the following elections.
The scholarship shows that institutional factors (features of the party and candidate dynamics related to electoral rules) are key determinants of the performance of women in these two types of systems (Fortin-Rittberger and Rittberger 2015; Wylie 2018). Due to its high level of personalization, the success of candidates running for the Chamber is strongly affected by the campaign resources they have (Samuels 2001). Candidates with more campaign resources in a fragmented environment are better able reach voters with grassroots campaigning and to increase their visibility. Under those circumstances, the extent to which female candidates are under-financed relative to men explains the gender gap in electoral success (Sacchet and Speck 2012;Wylie 2018). Moreover, to meet the 30% quota rule, parties also nominate non-viable female candidates (or laranjas), that is, candidates who do not effectively have resources and seek to compete for votes (Wylie, dos Santos, and Marcelino 2019). These disadvantages tend to be minimized for the Senate because under-financed candidates tend to not get nominated in plurality systems.
Nonetheless, there still seems to be a gender gap in electoral success for the Chamber after controlling for factors such as campaign resources, demographic and professional background, and incumbency status (Janusz 2018;Sacchet and Speck 2012). This gap might still be due to unobservable factors at the candidate-level. However, those are not yet accounted for by extant theories at that level of analysis. In this sense, this paper attempts to provide an explanation that is complementary to the scholarship that focuses on institutional factors by pursuing the answer at the other end of the process, that is, by looking at voters.

Evidence from survey data
The analyses in this section use the 2010 Brazilian Election Study, a post-electoral survey conducted after the second round of the presidential elections as part of the Comparative Study of Electoral Systems (CSES) project. 9 The study is based on face-to-face interviews with a nationally representative sample of 2,000 individuals eligible to vote. The survey includes questions about the vote choice for all races (Presidency, Senate, Chamber of Deputies, State Government, State Chamber) and questions on attitudes towards women in politics. 10 The survey relies on conventional items to measure explicit sexism. The questionnaire asked three items on endorsement for negative views about women in politics with statements using a 5-point agree/disagree scale. The statements asked the extent to which respondents agreed that "men are better suited for a political career than women" (17% agree), that "men tend to govern better when in office than women" (15% agree), and that "women still don't have the experience needed to govern well" (18% agree). The analyses use factor scores based on the three items (all factor loadings are higher than .80). For the experiment in the next section, although measuring implicit bias would help distinguish "true non-sexists" from "aversive sexists," data collection of those measures outside of an experimental lab for a nationwide sample in developing countries remains a challenge for research in the area. Nonetheless, given that implicit and explicit biases are not perfectly correlated, it is unlikely that the group of individuals who explicitly rejects sexism is composed exclusively by "true non-sexists." Therefore, measuring implicit sexism directly is not necessary to test the hypotheses from the aversive sexism perspective.
The survey includes closed-ended questions about the vote choice in all plurality races (Senate, State Government, and Presidency) and open-ended questions for proportional races (Chamber of Deputies and State Chamber). I recoded answers as equal to one for votes for female candidates and zero for votes for male candidates, while mentions of non-existent or non-applicable candidates were coded as missing values. 11 One concern about these questions is non-response, since voters may forget who they voted for shortly after the election. One the one hand, a total of 39% of respondents said that they had 9 Data and documentation are available through the project's website (www.cses.org). 10 Replication files (Stata files) for all analyses in the paper are available in the author's Data Archive on Dataverse (https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/HWMYYH).

11
In the 2010 elections, two senatorial candidates were elected per state. Since only 4 out of 2,000 respondents reported voting for two women, I recoded any vote for a woman as equal to one. forgotten or did not give valid answers to the question about the Senate, while 53% was the non-response rate for the Chamber vote. One the other hand, nonresponse was random with respect to respondents' levels of sexism, and therefore the results from the analyses are not due to selection. 12 The analyses consist of probit models for whether respondents voted for a woman for the Senate and the Chamber. 13 The main independent variable in the models is respondents' explicit sexism. The left side of Figure 1 displays the predicted probabilities of voting for a woman in each model (for Senate and Chamber) while the control variables are held at the grand mean. The right-side shows the heterogeneous treatment effects, that is, the difference in the probability of voting for a woman between the Senate and the Chamber for different levels of explicit sexism. 14 Respondents have a 0.26 of probability of voting for a woman for the Senate, a number that is higher than the proportion of women running (0.13). For the Chamber, while there were about 19% of women available for the seats corresponding to those respondents in 2010, the estimated probability of a respondent casting a vote for a woman is lower than 0.10. The decrease from 0.26 to 0.10 between the Senate and the Chamber is statistically significant at 0.05, which supports Hypothesis 1. Moreover, the results on the right-side of Figure 1 support Hypothesis 2, since there is a larger The models consider only respondents who gave valid answers to both questions (vote for Senate and vote for Chamber). Using all respondents who gave valid answers in each does not change the main results (see online appendix). 14 The models use post-stratification weights and control for information, party identification, ideology, religious affiliation, Bolsa Família recipient status, urban residency, employment, education, age, sex, race, economic evaluations, and state (district) fixed-effects. See online appendix for results. decrease in votes for women among respondents who score the lowest values in explicit sexism. The difference between effects among the lowest and highest levels of explicit sexism is statistically significant at 0.05.
Although the results provide support for Hypotheses 1 and 2, they do not capture the specific elements of the choice structure that the theory hypothesizes about. 15 While the comparison allows one to attribute the observed differences to the design of the electoral rules, it is still unclear whether it is in fact the introduction of male co-partisans in proportional races that allows voters to get away with discriminatory behavior when they vote for the Chamber.

Evidence from a ballot experiment
This section presents results from a ballot experiment conducted in Brazil during December of 2014. 16 The experiment manipulates the hypothesized choice set features that are expected to allow voters to substitute male co-partisans for ideologically close female candidates. Subjects were recruited using Facebook advertisements displayed to Brazilian users. The ads invited users to participate in a public opinion study in exchange for entering a lottery for a tablet. Subjects who clicked on the ad were sent to a Qualtrics survey page in which they read the survey information and were asked to provide consent for participating in the study. A total of 590 subjects provided complete responses. 17 The sample includes subjects from 25 out of the 27 Brazilian states. About 56% of respondents were women, and the average age was 43. The sample also over represents the southern and southeastern regions.
After agreeing to participate in the study, subjects answered background questions and proceeded to the main section of the study. The first stage of the study consisted of establishing substitutability among candidates, that is, setting the ideological domain of choice in which candidates would be similar or distinct. Since party attachments and ideological labels are weak in Brazil (Ames, Baker, and Rennó 2009;Ames and Smith 2010), the design relies on salient issues in the country in order to establish co-partisanship (substitutability) among candidates. The two items asked subjects whether they favored or opposed the death penalty for murder and the privatization of the Brazilian oil company Petrobras. These two specific issues were selected because national polls indicated opinions about them were the most evenly distributed in the public. 18 The combinations of answers to 15 Even though the models do not take into account gender differences in resources and quality among candidacies, that variation occurs at the state level, which is controlled for by the inclusion of fixed-effects. 16 The study was deemed exempt by the Vanderbilt University Institutional Review Board (IRB#141836). 17 The average response completion time was approximately 13 min. Subjects who took less than 5 min (the average time to read and fill the consent form and enter their information for the raffle of the tablet) to complete the study were excluded. 18 See: http://g1.globo.com/politica/eleicoes/2014/noticia/2014/09/maioria-e-contra-legalizar-maconha-ab orto-e-casamento-gay-diz-ibope.html. these questions produced four ideological profiles (favor/favor; favor/oppose, oppose/favor; oppose/oppose), which were then used as ballot information in order to generate the differences and similarities among candidates. After those questions, subjects cast their votes in the hypothetical race. The ballots showed information about the candidates and their opinions in the two policy stances.
The study included a 2-by-2 factorial design. Subjects were asked to vote in a race among hypothetical candidates. They were asked to read carefully about the candidates and to take their time to make the best choice. As part of the first manipulation condition, the ballot included names and last names of four candidates, alongside their ages, occupations, and opinions on the two policy areas mentioned above. Each of the four candidates corresponded to a unique ideological profile (favor/favor; favor/oppose; oppose/ favor; oppose/oppose), and one of the four was a woman (based on a female first name). 19 This ballot represents the choice structure of a plurality race, in which a few different candidates compete for the same seat. The candidates' first and last names, ages and occupations were randomly assigned, as well as the ballot position of each ideological profile and corresponding candidate. 20 The second type of ballot that half of the sample was randomly assigned to included 12 candidates, 3 of which were women (same proportion as the first condition). The four ideological profiles were the same as in the first condition, and a total of 3 candidates were assigned to each. Additionally, the ballot was set for female candidates to never share the same profile. Therefore, each of the three women in the ballot competed not only against male candidates from different profiles, but also against 2 ideologically identical male co-partisans. This ballot approximates the multi-member district race in a personalized proportional system.
The second manipulation in the factorial design uses a question order manipulation to examine the effect of asking sexism items before and after the vote primes concerns of social desirability. The measure of explicit sexism used in the analyses that follow comes from two 7-point agree-disagree items stating that "women still don't have the experience needed to govern well" (identical to the one from the survey data) and that "men make better leaders than women" (identical to the item commonly used in comparative surveys). Since only two items are used, the measure is a simple average between the two items. The sample is then divided between subjects who were unprimed (received the sexism items after the ballot) 19 The first/last names, occupations, and ages came from a list of the most common ones among candidates for the Chamber of Deputies in 2010. See online appendix for sample ballots. 20 Brazil uses electronic ballots in which the voter does not see the options available. While the ballot used in the experiment does not resemble that specific task, it seeks to emulate the task of evaluating and choosing a candidate.#8232; and primed (received the sexism items before the ballot). The expectation is that the tests of Hypotheses 1 and 2 should resemble the survey results among unprimed subjects. On the other hand, primed subjects, and particularly those who score low on explicit sexism, should change their behavior to disconfirm attributions of sexist intent, which corroborates Hypotheses 3. Although measuring implicit bias would help distinguish "true non-sexists" from "aversive sexists," data collection of those measures outside of an experimental lab for a nationwide sample in developing countries remains a challenge for research in the area. Nonetheless, given that implicit and explicit biases are not perfectly correlated, it is unlikely that the group of individuals who explicitly rejects sexism is composed exclusively by "true non-sexists." The results presented in Figure 2 are based on probit models of the probability of voting for a female candidate among unprimed subjects. 21 The left side figure shows the predicted probabilities of a subject voting for a woman under the two experimental conditions. The main variation of interest is whether the likelihood of a vote for a female candidate is higher under the 4-candidate condition than under the 12-candidate condition. The rightside graph shows the heterogeneous treatment effects, that is, the change in the probability of voting for a female candidate depending on the level of explicit sexism. The expectation is that subjects with low explicit sexism will be more likely to vote for women in the 4-candidate condition than under the 12-candidate condition, while explicit sexists should not be affected by the manipulation: The pattern of results on the left side of Figure 2 show that the predicted probability of vote for a woman is higher in the 4-candidate condition (0.26) than in the 12-candidate ballot (0.23). However, the estimates are not statistically different from each other, indicating that there is no support for Hypothesis 1. The comparison across levels of sexism supports Hypothesis 2. The negative effect of increasing the number of male co-partisans is stronger among subjects who score lower values on sexism than among subjects who explicitly endorse sexist views. The difference in the effects is statistically significant at 0.05. With respect to Hypothesis 2, the results follow the patterns from Figure 1 using survey data.
The aversive sexism perspective suggests that individuals who explicitly reject sexism engage in the substitution behavior because the choice structure relaxes their concerns about social desirability. One observable implication of this perspective is that, if those concerns are raised prior to the task, individuals who explicitly reject sexism should attempt to disprove 21 About 33% of subjects voted for candidates disagreeing with their issue positions (5% on both, 28% on at least one). The less educated, those reporting lower understanding of the task, and those in the 12candidate condition were more likely to do so. Given that those votes express confusion rather than a sacrifice of issue proximity, those subjects are included in the analyses because removing them would result in excluding aversive sexists who are also confused.
attributions of sexist intent. To test that, Figure 3 shows the extent of substitution of male by female candidates in the ballot experiment for respondents who received the sexism items prior to the voting task. 22 The inclusion of the battery before the ballot is expected to increase the salience of gender considerations and make all subjects aware that it could be a factor in their decisions (Mendelberg 2008). Therefore, if subjects are being strategic without concerns about social desirability, contrary to the aversive sexism perspective, the results should resemble the patterns found so far. Figure 3 provides support for Hypotheses 3. The results suggest that primed subjects who do not openly endorse sexist views change their behavior to avoid the attribution of sexist intent. The overall probability of vote for a female candidate follows the opposite pattern from Figure 2, by increasing from 0.21 to 0.26. The pattern is only suggestive since the estimates are not statistically different. More notably, the right-side graph shows the expected pattern for low-sexists. When primed to think about sexism before voting, those subjects change their behavior and become more likely to cast votes for female candidates when the choice structure removes the trade-off between sexism and ideology. The interaction between the treatment and levels of explicit sexism is statistically significant and follows the opposite pattern from unprimed subjects. 23 Also consistent with the aversive sexism perspective, explicit sexists do not seem to be guided by social desirability concerns, since they become less likely to vote for a woman in the 12-candidate condition. Although the treatment is not statistically significant among explicit sexists (given the low number of observations in those cells), those subjects should see the 12-candidate ballot as an opportunity to avoid the trade-off between ideology and gender attitudes eventually presented in the 4-candidate ballot.

Alternative explanations
Another perspective argues that voter bias affects choices under complex electoral environments (Aguilar, Cunow, and Desposato 2015;McDermott 1997). Large numbers of ideologically overlapping candidates produce complex choice sets in which learning and using information is difficult. Consequently, voters become more likely to rely on candidate gender as a cue. While the design discussed above does not include a condition where the number of alternatives is the only manipulated feature, Aguilar, Cunow, and Desposato (2015) do not observe voter bias to increase when subjects are presented with more candidates in a study with Brazilian subjects. Moreover, a 22 For full model estimates, see online appendix. 23 Polling primed and unprimed subjects in the same model yields statistically different results between the two question order conditions. See appendix for results.
post-manipulation question in the ballot experiment discussed in the previous section asked whether subjects felt that they understood the information about the candidates (on a 7-point agree-disagree scale). The treatment (ballot with 12 candidates) has a negative and statistically significant effect (at 0.05) on the extent to which subjects reported having understood the choice. Additionally, the level of understanding of the choice has a positive relationship with the probability of voting for a woman (statistically significant of 0.05), which indicates that subjects who had more difficulty in the task were more likely to display gender bias. 24 However, the inclusion of this post-manipulation variable in the main model does not change the patterns shown in the previous sections. 25 Also, another explanation for the patterns observed in the previous section is "affinity voting" (Golder et al. 2017;Sanbonmatsu 2002). This perspective states that women are more likely to vote for women, especially under circumstances where partisanship and ideology do not overlap gender affinity. Consequently, the reduced effect of sexism observed in the 12-candidate ballot could be due to female subjects, including those who score high values on sexism, becoming more likely to vote for women. Given this possibility, the patterns observed in Figures 2 and 3 could not be explained by aversive sexism, but instead by "affinity voting." However, this is not the case for the survey and experimental results. There is evidence of affinity voting in the survey results, but controlling for sex does not change the patterns shown for sexism in Figure 1. In the The question was asked immediately after the vote choice, which makes the results only suggestive of a relationship between the two variables. Asking such questions before the treatment could prime subjects and inflate the effect of cognitive overload. 25 See online appendix for results. experiment, even though women are generally more likely to vote for a female candidate, they do not become more likely to do so in the 12-candidate ballot. Also, controlling for an interaction between the treatment and subjects' sex does not change the patterns of results for sexism. 26 Finally, since open endorsement for sexism is an observed rather than manipulated moderator, one threat to the validity of the findings could be that unaccounted factors correlated to the moderator are not taken into account (Kam and Trussler 2017). To rule out that possibility, additional models using questions on opinions about other discriminated groups do not produce the moderating effect found when using the measure of sexism. 27 Therefore, there is no evidence that other out-group orientations are the true underlying moderators of the effects presented above.

Conclusion
This paper proposes that electoral rules moderate the effect of gender bias on voting behavior. Based on the notion of aversive sexism, I argue that voters discriminate against female candidates when the structure of the race does not force them to choose between their ideology and gender bias. In other words, voters are less likely to choose women when they can replace ideologically close female candidates with similar male co-partisans. Hence, in a SMD election in which parties enter one candidate to run for the seat, the differentiation between candidates makes it clear that, when voters do not pick the ideologically close woman, they are engaging in discriminatory behavior. On the other hand, in multi-member districts in which parties enter multiple candidates to compete for the same seats, voters can substitute male co-partisans for similar female candidates without signaling sexism.
As evidence of the theory, I focus on the puzzle of why proportional rule and gender quotasa combination of institutional features known to foster female parliamentary representation cross-nationallyhave failed to raise the number of seats occupied by women in the Brazilian Chamber of Deputies. I use postelectoral survey data from the 2010 elections in Brazil to show that individuals who do not openly express bias towards women in politics are the ones more likely to cast votes for women for the Senate (a SMD system with no quotas) while not doing so for the Chamber. I then use a ballot experiment to isolate the causal effect of increasing the number of male co-partisans on the likelihood of voting for female candidates. I show that, while votes for female candidates do not become significantly less common with of co-partisan competition, there is gender bias among the subset of subjects who do not openly endorse sexist views. Moreover, a question order design shows that subjects with lower explicit sexism are highly responsive to gender stimuli and change their behavior as a function of those considerations. While the experiment does not provide externally valid evidence about the extent of prejudice among voters, it presents a hypothetical setting that suggests which choice features can do so in the real world.
Finally, another implication of the theory is that women are less likely to win when parties enter multiple candidates in the race. Curiously, evidence shows that PR systems display higher levels of female representation due to factors related to higher co-partisan competition, such as higher district magnitude (Darcy, Welch, and Clark 1994;Kenworthy and Malami 1999). At first sight, this pattern contradicts the expectations of the aversive sexism perspective. However, other studies show that women's representation is tied more directly to whether electoral systems create incentives for candidates to cultivate personal votes (Thames and Williams 2010;Valdini 2013). When parties have more control over access and position of candidates in their lists and ballots, they become more able to balance the party list. This literature sheds light on a crucial difference between types of proportional systems. Closed-list systems tend to elect more women than open-list systems by allowing parties to have more control over the ballot (Iversen and Rosenbluth 2010;Kirkland and Coppock 2018;Shugart, Valdini, and Suominen 2005;Valdini 2012). Hence, an important implication of the aversive sexism theory is that increasing co-partisan competition does not have a positive effect on the election of women in personalized systems. This implication is consistent with the patterns observed between the two national legislatures in Brazil. Therefore, while Brazil does constitute an extreme case with respect to its large electoral districts and highly personalized races, the case fits a broader pattern identified in the crossnational literature.

Disclosure statement
No potential conflict of interest was reported by the author(s).