In Model 1, we train the decision tree without allowing the algorithm to access the individual's gender. This approach helps correct for potential algorithm biases associated with the detection of gender in the data, as well as the absence of nonbinary options to capture gender identity.

# **_Model 2: Decision Tree on Citizen Participation after Correcting for Bias in the Algorithm: No Gender Variable Nor Gender Proxies (Gender Deproxing)_**

In Model 2, we apply a deproxing strategy, which involves removing not only the gender variable but also any covariates that serve as proxies—those highly correlated with gender and thus likely to carry gender-related bias. In our analysis, employment status was identified as the most strongly correlated proxy for gender. As a result, we remove both the gender variable and employment status from the list of covariates.

# **_Model 3: Decision Tree on Citizen Participation after Correcting for Bias in the Algorithm: Women and Men-only_**

In this model, we analyze how algorithms predict participation separately for female and male samples, excluding any information about the opposite gender.

# **_Model 4: Decision Tree on Citizen Participation after Correcting for Bias in the Algorithm: Gender Switching_**

In Model 4, we simulate a gender-blind society by switching the gender of each individual— assigning males as females and vice versa.

# **_Model 5: Decision Tree on Citizen Participation after Simulating a Less/More Machista Society: Scaling Machismo_**

In Model 5, we use counterfactuals to explore how the success path to citizen participation would differ in alternative scenarios, representing both a less machista and a more machista Latin American society, as reflected in Latinobarómetro data. We construct two main counterfactuals: first, by scaling down individual observations of the composite gender score while preserving the original distribution, simulating a society with reduced levels of machismo.<sup>2</sup> Our primary counterfactual envisions a Latin American society with half the current machismo level, but we also examine scenarios with machismo levels ranging from 0.01 to 1, where 1 represents the current distribution of the score. Additionally, we consider a scenario where machismo is doubled. Since the composite gender score is normalized between 0 and 1, doubling the score truncates the distribution at 1, altering the original variable distribution.

# **_Model 6: Decision Tree on Citizen Participation after Simulating a Less Machista Society: Shifting Machismo Distribution_**

In Model 6, we apply a second counterfactual approach by shifting the gender bias score for each individual observation, deducting a fixed value of 0.25 from each score.<sup>3</sup> This method alters the distribution of the data, simulating a less machista society. The goal is to explore different ways

> 2 Maintaining the original distribution ensures the analysis remains realistic and reflective of the true essence of Latin American society, as represented by the current distribution of machismo. By shifting this distribution to the left, we aim to provide a more authentic depiction of how reduced levels of machismo could influence pathways to citizen participation.

> 3 The choice of a shift amount of 0.25 is informed by the observation that beyond this threshold, the gender score ceases to appear in the success path (refer to Figure 4, Panel B).

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