Blue First and Foremost: Female Descriptive Representation, Rape, and the Justice Gap

The degree to which female political actors influence policy is hotly debated in political science. However, relatively little research considers how women’s representation in the police influences policing outcomes. We argue that increasing women’s representation should be associated with increases in rape report rates but should not be associated with changes in rape arrest rates. We expect public perceptions of female police to affect victims’ willingness to report and cooperate with the police, but the masculine, hierarchical, and complex nature of police investigations of rape will make it difficult for those increases in reporting to translate into increases in arrests for those crimes. We leverage unique police administrative data from 1987 to 2016 and find that although women’s representation is associated with increased rape report rates, there is no relationship with rape arrest rates, highlighting an important justice gap. Our article has implications not only for the study of female representation and representative bureaucracy but also provides insights into how descriptive representation may be limited by institutional culture, norms, practices, and procedures.

officers were female (Federal Bureau of Investigation 2018).
One of the core political science debates is the extent to which ascriptive characteristics like the gender of political actors affect policy outcomes (Keiser et al. 2002;Meier and Nicholson-Crotty 2006). 2 We build on this literature to examine the role of female police officers in the administration of state force and as representatives of women's interests. 3As bureaucratic agents with a relatively large degree of discretion in decision making, who also can act as agents of repression and use force (Soss and Weaver 2017), police officers are uniquely situated to have a radical impact on the lives of those they interact with; they also have the potential to represent members of their own identity groups (Keiser et al. 2002;Meier and Nicholson-Crotty 2006).However, there is mixed evidence regarding the impact of female police officers on police outcomes (Poteyeva and Sun 2009).Do female police officers behave differently than male police officers, especially regarding crimes that disproportionately affect women like rape?Are female officers associated with increased rape reports, and do police agencies with greater female representation see higher rates of rape arrests?
We argue that although women's increased representation may increase victims' willingness to report rape, it alone is not sufficient to increase rape arrests.We claim that increased numbers of female police officers ought to be associated with increased numbers of rape reports, because women's representation may increase the public's comfort with and trust of the police, especially regarding sexual and gender-based crimes (Flores-Macías and Zarkin 2021; Karim 2020; Meier and Nicholson-Crotty 2006;Riccucci, Van Ryzin, and Lavena 2014;Schuck, Baldo, and Powell 2021).Women's representation may increase female victims' willingness to report rape because they may perceive female police as more sympathetic, more trustworthy, and more likely to take their complaints and reports seriously (Kennedy and Homant 1983;Meier and Nicholson-Crotty 2006).However, the impact of female officers on the number of rape arrests may be limited because of institutional features that decrease their interest in and ability to represent women's interests in several ways.First, even if female officers did want to represent women's interests through the active investigation of rape reports, individual officers are limited by departmental culture, norms, training, and practices, as well as legal, political, and budgetary factors beyond their immediate control.Rape arrests are often the product of multiple actors' decisions, not just one police officer, and an individual officer's assignment may limit her opportunity to work on a rape case.Moreover, female officers may not identify with or want to represent women's interests within the police because of masculine police cultures and fears of tokenism (Belknap 2014;Chan, Devery, and Doran 2003;Johnson 2011;Marks 2008).In sum, we expect that despite increased rape report rates associated with a higher percentage of female police officers, there will not be a parallel upward shift in rape arrest rates.
Using periodic data on women's representation within approximately 9,500 unique law enforcement agencies between 1987 and 2016, this study links the Law Enforcement Management and Administrative Statistics (LEMAS) series across this time period, providing a unique opportunity to test the impact of women's representation across time and in different types of law enforcement agencies throughout the country.This sample improves on those in previous studies on the impact of women's representation in the police that have largely either used a subset of large agencies (even though 71% of police forces serve communities under 10,000 ;Hyland and Davis 2019) or data aggregated to the county level.
We find that women's representation in the police is associated with more rape reports but not more rape arrests.Improving women's representation may increase the likelihood that a rape victim reports the assault, but there is no corresponding significant increase in the likelihood of an arrest.This justice gap is important and troubling, indicating that the strategy of "just add women and stir" is insufficient to improve the investigation of sexbased crimes (e.g., Celis et al. 2008;Karim et al. 2018).Yet, increasing women's physical representation within institutions, such as the police, remains a common focus of popular discourse, proposed reform programs, and literature on policing.These findings point to the importance of detailed data on the police that are often unavailable or nonexistent; they also highlight the need for careful evidence-based analysis of the impact of diversity in police forces that considers the institutional and social dynamics of police behavior.In other words, descriptive representation in the police may be mediated by police culture, institutional and organizational structure, and procedures used for some policing outcomes: with regard to rape arrests, female police officers may be "blue" first and women second.The question of whether the police provide adequate and equal services to all is a vital question not only for women but also for every American.crimes, especially ones that disproportionately affect women, such as domestic violence or sexual assault.
Women in political positions and public office are often perceived and evaluated differently by the public than their male counterparts.Research on female legislative candidates finds that gender stereotypes harm evaluations and perceptions of those candidates, that women must be more qualified than men to win races, and that they must outperform men once they are in office to retain their position (Anzia and Berry 2011;Bauer 2019;2020;Pearson and McGhee 2013).Although there are certainly stereotypes that can harm female political candidates and politicians, some research finds that gender diversity within institutions positively affects public perceptions of those institutions.Institutional gender diversity may increase perceptions of legitimacy, fairness, trustworthiness, and support of the institution within the broader bureaucracy and of police bureaucracy, in particular (Flores-Macías and Zarkin 2021; Gade and Wilkins 2012;Riccucci, Van Ryzin, and Jackson 2018;Riccucci, Van Ryzin, and Lavena 2014;Schuck, Baldo, and Powell 2021;Theobald and Haider-Markel 2009).Comparative policing research in other contexts supports this perspective: citizens in Liberia, Brazil, and Mexico perceive that increasing female police representation makes the police more trustworthy, more respectful of civil liberties, and less corrupt (Còrdova and Kras 2020;Flores-Macías and Zarkin 2021;Karim 2020).Although there may be differences in how women's representation affects attitudes in the United States and internationally because of varying levels of government legitimacy, capacity, and public interactions with the police, findings that increases in women's representation improve perceptions of the police are relatively consistent across countries, including in the United States (Barnes, Beaulieu, and Saxton 2018;Riccucci, Van Ryzin, and Lavena 2014;Schuck, Baldo, and Powell 2021).The positive effect of women's representation on perceptions of legitimacy appears to be primarily driven by perceptions among men that female police are outsiders within police and political networks, and thus are less likely to abuse their authority, and by perceptions among women that female police have higher risk aversion and as a result are unlikely to be corrupt (Barnes, Beaulieu, and Saxton 2018).
These changing perceptions of police induced by women's representation may translate into altered behaviors by the public, including an increased willingness to cooperate.Riccucci, Van Ryzin, and Li (2015) found that women are more willing to cooperate with the government when they encounter female bureaucrats, including taking on more costly behaviors.Similarly, research on racial representation in the bureaucracy finds that parents of students with a same-race teacher are more likely to trust that teacher and invest in co-productive behavior (Holt and Gershenson 2019).Other findings suggest that Black police officers increase perceptions of the police's legitimacy among Black Americans (Cochran and Warren 2012;Riccucci, Van Ryzin, and Jackson 2018).Improved perceptions of police legitimacy, trustworthiness, effectiveness, and fairness are not only important for the health of democracy but may also increase the public's willingness to coproduce and cooperate with the police, including reporting crimes of all types.
Although increasing women's representation in the police may improve perceptions of the police and increase reporting among both women and men, women may be particularly likely to show an increased willingness to engage with the police, especially regarding sexual violence.Theories of representative bureaucracy emphasize that female bureaucrats may only improve outcomes for women if the issue is considered a salient "women's issue" (Keiser et al. 2002).Sexual assault and rape have been politically identified as such because the overwhelming number of victims are women, and the perpetrators are men (Black et al. 2011;Keiser et al. 2002;Meier and Nicholson-Crotty 2006).Given social stigmas and taboos surrounding sexual assault, its designation as a "women's issue," and shared experiences of women within rape cultures, female victims of sexual assault may believe that female police will be more sympathetic and understanding to their plight and so may feel more comfortable reporting to a female police officer, especially if the perpetrator was male (Keiser et al. 2002;Kennedy and Homant 1983).One female police officer explained that victims prefer to interact with female officers: "If they are the victim and they've had a sexual assault…they would rather talk to me" (Rabe-Hemp 2017, 130).Indeed, there is some evidence that changing sex demographics in police forces may alter reporting rates of gender-based violence specifically or violent crime more generally (Meier and Nicholson-Crotty 2006;Miller and Segal 2019;Schuck 2018).For example, Schuck (2018) found that increases in women's representation in the police were associated with increased reporting of rape and that this relationship is moderated by agency structure, including the presence of a union, the provision of resources for victims, and the presence of community policing.
Even though the positive impact of women's representation on perceptions of police legitimacy and trustworthiness may increase both men's and women's willingness to report other gendered and nongendered crimes, we focus here on rape, because its designation as a women's issue combined with social stigmas surrounding sexual assault may make female victims particularly likely to positively respond to women's representation in the police.Yet, in the following analysis, we also probe the impact of female police officers on other types of crimes.It is important to note that a victim may not be aware of how many women work in their local police department when they are deciding whether to report.Instead, this mechanism may be more likely to operate when a female officer is the responding officer or when a victim has already decided to go to the police and their report is taken by a female officer whom she believes may ensure that the report is completed.
Hypothesis 1: Increases in women's representation in police forces should be associated with increases in rape reporting rates.Some argue that female police officers may be more effective, more likely to prioritize, and more proactive in investigations of rape.Although there is some evidence that female officers behave differently from male officers, 4 it is inconsistent (Brandl, Stroshine, and Frank 2001;Huber and Gunderson 2022;Poteyeva and Sun 2009).Many of the theories underlying these studies assume that female police will actively represent women's interests, 5 including those interests of victims of sexual violence.Keiser et al. (2002) outlined the following criteria for determining whether an issue area is gendered and therefore relevant for female bureaucrats: when that issue benefits (or, in this case, harms) women as a class, when the gender of a bureaucrat changes the client-bureaucrat interaction, and when the issue has been defined as a women's issue through a political process.Rape, thus, could be considered a women's issue because women are more likely to be exposed to the negative consequences of sexual violence and to be victims of sexual violence (Keiser et al. 2002).
However, it is important to note that not all women may identify with or be concerned with "women's issues."Female police officers may distance themselves from civilian women, given that careers in the police tend to attract more masculine men and women (Clinkinbeard, Solomon, and Rief 2020).Therefore, although female officers may seek to improve police responses to rape because of a desire to actively represent women's interests, this assumption may not hold within the police, a possibility that we explore more later.For example, even though female police officers are more likely to provide support to those involved in domestic violence situations (Stalans and Finn 2000;Sun 2007), male and female officers hold similar beliefs about sexual assault and domestic violence victims -and female officers may be even more likely to question the credibility of rape victims (Wentz and Archbold 2012).Similarly, although some studies find that female officers behave differently from each other in spheres other than gendered crimes, female officers are less likely to do the following: exhibit controlling behavior (Rabe-Hemp 2008), use weapons or injure suspects (Hoffman and Hickey 2005), initiate traffic stops (Shoub, Stauffer, and Song 2021), and use force (Ba et al. 2021).Yet other studies found that female and male police officers behaved similarly, or when differences were found, they were substantively small (Brandl, Stroshine, and Frank 2001;Hoffman and Hickey 2005;Poteyeva and Sun 2009;Rabe-Hemp 2008).Thus, it is unclear whether women's representation in the police changes arrest outcomes or whether female officers are more proactive regarding arrests for rape, in particular.
Although increasing sexual assault arrests may appear to be an ideal way for female bureaucrats to promote policy outcomes that are favorable to women-given that female police officers are street-level bureaucrats with high levels of discretion and that this crime is salient as a women's issue-the structure, culture, hierarchies, and practices of police forces may limit or dissuade women from actively representing women's issues (Keiser et al. 2002;Meier 1993).There are several reasons to doubt whether female police officers are able to or choose to have a meaningful impact on policing outcomes.We explore some of these reasons here and note that some (or all) of them may contribute to null effects of gender diversity on a variety of police outcomes.
First, female police officers face immense pressure to integrate into a masculine institutional culture shaped by masculine practices.Police culture privileges behaviors and characteristics commonly associated with masculinity, such as aggression, courage, and competitiveness, while devaluing tasks and characteristics associated with femininity, such as police work related to sexual violence (Brown 2007).A masculine police culture increases the likelihood that male (and female) officers will hold negative stereotypes toward women (Lockwood and Prohaska 2015).Police officers' behavior is directly shaped both by their own beliefs and departmental norms and practices (Johnson 2011).Adherence to traditional gender roles and the privileging of masculinity decreases the perceived seriousness of crimes against women, particularly sexual violence between partners, because the domination of men over women and the presence of violence in relationships are normalized (Lockwood and Prohaska 2015).Police departments with highly masculinized cultures are less likely to allocate the necessary resources and training to ensure the proper handling of gender-based crimes (Belknap 2014;Feder 1997;Heidensohn 1992;Loftus 2010;Martin 1982).Outside of gender-based crimes, female police representation is associated with a decrease in lethal force, but this is attributable to shifts in departmental culture in response to female officers, rather than the presence of these officers alone (Carmichael and Kent 2015).In addition, individuals-both male and femalewho hold more masculine views are more likely to be interested in policing careers, reinforcing the masculine culture of police (Clinkinbeard, Solomon, and Rief 2020).Thus, female police officers may themselves hold masculine and traditional gendered views and may have little to no desire to represent women's interests.
Second, female officers may feel a need to "prove" themselves and their loyalty to the police by not embracing their femininity and women's interests (Marks 2008).For example, one female police officer explained that her success in the police required her to deemphasize her femininity: "I am successful because I don't play up the 'female' part.I'm just one of the guys….We're not treated any differently.We're not babied because that's one thing I hate.I don't want to be babied because I am a girl.You know, I just get in there and do what I need to do, just like any of the guys would" (emphasis added; Rabe-Hemp 2017, 97).Because female officers are often "tokens" and otherwise have little institutional or cultural support, they are unlikely to radically alter police behavior or to act in a radically different way from their colleagues.Instead, they tend to embrace the dominant occupational identity of the department, feeling pressure to "keep your head down" or turn a blind eye to be accepted by their (male) colleagues (Chan, Devery, and Doran 2003).This pattern has been demonstrated with racial representation too: Wilkins and Williams (2008) found that the presence of Black officers increased racial profiling.Similarly, Nicholson-Crotty, Nicholson-Crotty, and Fernandez (2017) found that Black police officers do not decrease police-involved homicides until a critical mass of 35% Black officers is reached, because as a minority group in the police department, Black officers feel pressured to conform to organizational culture.
Finally, even if a female officer wanted to represent women's interests and improve the police response to rape reports, she may have a limited effect on whether a rape report results in an arrest.This is because arrests are often the product of the decisions of multiple police officers, police leaders (like sergeants and other supervisors), and prosecutors, rather than the outcome of individual actions (Morabito, Williams, and Pattavina 2019).As a result, even if a female officer were to want to use her discretion to actively pursue a rape case, the structure and process of pursuing arrests and the many people who may also influence the decision to approve an arrest may dilute her individual impact (Keiser et al. 2002).In other words, whereas female officers may have an observable impact with regard to policing outcomes determined by more individual discretion-such as traffic stops (e.g., Shoub, Stauffer, and Song 2021) or arrests while on patrol and involving the use of force (e.g., Ba et al. 2021)-they may be limited in their impact on outcomes that require coordination and cooperation among multiple offices and officials, such as rape arrests: any individual-level differences may not aggregate to the often group-level outcome of arrests.Rank-and-file officers are also limited in their ability to alter the behavior of other police officers.Moreover, female and male officers may not be evenly assigned to tasks and patrols, and thus, female officers may not be present for both the initial report taking and the decision to make an arrest.
In addition, officers' discretion in sexual assault cases depends on their department's mission, leadership, resources, and support (Andrews and Johnston Miller 2013).Police forces tend to be hierarchical; this may limit a female officer's ability to represent women's interests because hierarchical organizations tend to depersonalize relationships with outside groups and emphasize adherence with the in-group institutional identity (Keiser et al. 2002).Moreover, police often minimize victims' experiences by creating distinctions between "worthy" and "unworthy" victims based on the type of perpetrator-a stranger versus an acquaintance or partner-and the victims' life circumstances, appearance, criminal history, or socioeconomic status (Charman and Williams 2021).Police may use their discretion (and may feel institutional pressure) to pursue only those cases where the victim is perceived as "deserving" of justice or where the case is likely to lead to a result and conviction; they may "write off" or "get rid of" cases and, at times, actively pressure victims to drop complaints that are deemed "too messy" or involve an "undeserving" victim.This tendency for police officers to prefer or only pursue rape reports that are deemed "deserving" is exacerbated when departmental leaders or budgets do not prioritize rape and sexual assault crimes, forcing police officers to be highly selective in which cases they pursue (Charman and Williams 2021).Finally, a female police officer's interest in actively pursuing rape arrests may be dependent on the salience of rape within the community as a women's interest or issue.Women's bureaucratic representation only improves outcomes for women if the policy outcome is salient as a women's issue (Keiser et al. 2002).Even though rape and sexual assault are often considered crimes that are highly relevant to women nationally, some communities and some police agencies may not view rape as an important issue in their community.Thus, if rape is neither a salient issue in the community or within the department, female officers may not feel a need or interest to actively pursue rape arrests.
Thus, although there is the potential for female police officers to actively represent women's interests, which may increase the arrest rate for rape, they may face constraints on their interests, behavior, and priorities.As a result, they may be encouraged to view their relationships with other police officers as superseding their relationship or connection with other women, or they may simply be unable to alter policing outcomes with regard to rape arrests because of the complex, hierarchical nature of rape arrests and policing.
Hypothesis 2: Increases in women's representation in police forces should not be associated with changes in rape arrest rates.

Data and Methods
Although previous studies present suggestive evidence of a relationship between female representation and police outcomes, these findings have several limitations.First, many of these studies either used data from nonrepresentative samples of police agencies, from only one police force or one state, or from only police agencies in major cities (Meier and Nicholson-Crotty 2006;Saltzstein 1989).Most police departments in the United States serve small areas: in 2016, only 3% of police departments served communities of more than 100,000 people; as mentioned, 71% served communities with less than 10,000 residents (Hyland and Davis 2019).Thus, relying on data from large, urban areas may bias the results by overrepresenting police departments with higher rates of sexual assault and greater demographic diversity.Moreover, some studies used county-level data (e.g., Meier and Nicholson-Crotty 2006;Miller and Segal 2019), which is not ideal given that individual agencies make arrests.These limited data present a significant obstacle for researchers seeking to study how characteristics of the police affect a variety of policing outcomes.
To overcome these obstacles, we used the Law Enforcement Management and Administrative Statistics (LEMAS) series, data collected periodically by the federal government from approximately 3,000 law enforcement agencies in each survey year.These agencies are a nationally representative sample, which necessarily changes each survey year, 6 of the approximately 12,000 law enforcement agencies nationwide (see the Supplementary Material for details).LEMAS data have been used in criminology (e.g., Schuck 2014;2018, Shjarback andTodak 2019) though less often in political science (though, see Huber and Gunderson 2022).To our knowledge, we are the first to link the LEMAS data from the 1980s to the present, merging the data by unique agency identifiers and connecting it to crime records for all years in the series, despite the difficulties in doing so.Thus, this article provides the first test of the effect of female representation on policing outcomes using all available LEMAS data (1987, 1990, 1993, 1997, 2000, 2003, 2007, 2013, and 2016), comprising approximately 23,000 observations and more than 10,000 unique agencies.Because agencies may be included in some sample years and not others, our analysis cannot make within-agency comparisons over time and instead emphasizes broad observational patterns across agencies. 7Importantly, these results reflect aggregate patterns across agencies, rather than decisions made by individual police officers.Thus, we cannot make conclusions about the behavior of individual female and male officers but only whether women's representation within agencies alters policing outcomes of the police force.However, as a robustness check, we also examine individual-level data on arrest rates using data from Ba et al. (2021).
Our independent variable is the percentage of each agency's sworn, full-time workforce that is female.Sworn employees carry firearms, have arrest powers, and possess badges.This variable therefore defines the percentage of female police officers, and not clerks or other positions without arrest powers.Figure 1 shows the variable's distribution over time.The data exhibit significant variation, though the average percentage of female officers is relatively consistent and does not increase significantly over time.This reflects the stagnant growth in women's representation at the national level over the past 50 years.
To estimate the relationship between the percent of female police officers and the rape arrest and report rate, we estimate an ordinary least squares model using Equation 1: Our main coefficient of interest is β 1 , the percent of sworn officers that are female.Y i,t refers to two dependent variables, the first of which is the rate 8 of rape reports in agency i in year t.This variable is the rate of reported rapes per 100,000 jurisdiction population, because some jurisdictions are significantly larger than others, and thus the raw number has significant skew.The second dependent variable is the rape arrest rate in agency i in year t.This variable represents the rate of rape arrests per 100,000 population in the jurisdiction.Both variables come from the Uniform Crime Reporting Program at the Federal Bureau of Investigation, which has known problems, including incomplete reporting from agencies (Maltz 2006).We therefore include only those agencies that reported annual arrest and crime data to the FBI.
X i,t is a matrix of control variables that may influence the efficiency of the police department, rape reports and arrests, and women's representation. 9We control for the number of agency employees because well-staffed departments are more likely to receive complaints, arrest more perpetrators, and have female officers.We control for the percent of fulltime sworn officers who are Black to measure the demographic diversity of the police force and as a proxy for the diversity within the community more broadly. 10We also include a binary indicator for whether the agency is a county sheriff's office because of the unique electoral pressures that sheriffs face (Farris and Holman 2015) that may lead these agencies to act differently with regard to rape reports and arrests and to make different hiring decisions.Approximately one-quarter of the agencies in the data are county sheriff's offices.Additionally, in the specification with the arrest rate dependent variable, we control for the agency rape March 2024 | Vol. 22/No. 1 33 report rate.In some models we additionally control for agency budget to measure resources that may contribute to an increase in investigations of rape reports and whether the agency has a community policing component in its mission statement because women are more likely to join these departments. 11These latter two variables are only available for certain years, so we include them in only some specifications.
Finally, δ t represents year-fixed effects for each year of the LEMAS data (see the Supplementary Material for alternate fixed effects). 12We do not include agency-fixed effects 13 because more than half the sample are agencies surveyed only once.We are limited by the availability of agency-and city-level covariates so we only have a few control variables.Ideally, we would include a measure of institutional culture and specialized training or units on rape, but inconsistent or absent data from LEMAS make that impossible.Future studies should explore these factors to directly test the impact of institutional culture, training, and resources.
Table 1 shows the summary statistics for variables used in the analyses.Of note is the maximum value of the percent of female officers: 28 agency-years record the percent of female officers as 100%.Most of these agencies have only one or two employees who happen to be women.We include them in the main analysis, although the results do not change if we exclude them.On average, agencies comprise about 8% women (about 18 women per agency) and make about 9 arrests for rape per 100,000 jurisdiction population-although they receive about 29 reports of rape for that same population size: this is a significant difference between the number of rapes reported and the number that result in legal action for the victims.Table 2 estimates Equation 1. Columns 1 and 2 estimate only the relationship between the percent of female police officers and the rape report rate and rape arrest rate, respectively; Columns 3 and 4 add a series of control variables across the years 1987-2016; and columns 5 and 6 add controls that limit the analysis to post-1997.We estimate columns 3 and 4, and 5 and 6 separately, because we are concerned that those missing control variables that limit our sample size could skew the representativeness of our sample; we are cautious about drawing firm conclusions on the basis of including those covariates only.
In Columns 1 and 2, the percent of female officers is positively and significantly correlated with both the rape arrest rate and the rape report rate.Once we add control variables, however, some of those magnitudes change.For instance, column 4 indicates a negative correlation between female officers and rape arrest rates, although this does not reach statistical significance with the inclusion of additional control variables in column 6.This finding suggests both the importance of controlling for these confounding factors and the potentially counterintuitive effect of female officers on rape arrests.Column 4 shows a negative correlation between female officers and rape arrest rates, but that significance disappears once we include a wider set of control variables in column 6.This null effect is consistent with our expectations of a null effect of female police officers on rape arrest rates.Yet, columns 3 and 5 show that one potential impact of increasing female representation is indeed higher rates of rape reports.This suggests that rape victims may be more likely to report their assaults to female officers (e.g., Meier and Nicholson-Crotty 2006;Miller and Segal 2019;Schuck 2018), with no (or a negative) commensurate increase in the actual arrests for those crimes.This represents a significant and troubling justice gap for victims of rape.
Figure 2 illustrates the patterns from table 2 with a regression line showing the relationship between percent female officers and the rape arrest and report rates.There appears to be a slightly positive association between female officers and the rape report rate and a fairly flat though overall negative relationship between female officers and the rape arrest rate.This graph may point to a potential nonparametric relationship between female officers and rape arrest and report rates; that is, the association between female police and arrest and report rates may switch signs as the percent of female police grows.We explore this possibility in the Supplementary Material and find some evidence for this phenomenon.
The control variables in table 2 are largely significant and as we predicted: the number of employees (in column 3), the rape report rate, and sheriff's offices are associated with higher arrest rates.Interestingly, the percent of Black officers is associated with higher rates of both rape reports and arrests.This correlation could be an indication that multiple forms of diversity-based on both gender and race-and improved descriptive representation may increase reporting and arrest rates.There appears to be no significant effect of community policing on arrests, but there is some evidence that it increases the rape report rate.
To see whether the relationships in table 2 are unique to the crime of rape, we consider the effect of female police officers on the rate of reports and arrests for violent crime -murder, assault, robbery, and rape-as defined by the FBI.Table 3 uses these dependent variables and finds little evidence that female representation in the police is associated with increased arrest rates for violent crimes, consistent with our findings regarding rape.We also find inconsistent evidence that female police are associated with increases in report rates for violent crimes.Although the specification is significant in columns 1 and 3, once we add additional control variables, the coefficient is no longer significant (whereas it stays significant and positive in table 2).We attribute at least part of the significance of violent crime reporting and arrest rates in columns 1 and 3 to the fact that rapes are included in our calculation of violent crimes, following the typical FBI calculation of this variable. 14An additional specification with property crimes is in the Supplementary Material and is similarly insignificant once we add control variables.We take this as evidence that this positive relationship between female police officers and report rates is unique to the crime of  rape; that is, a justice gap exists among victims of gendered crimes that does not seem to exist among victims of other types of violent or property crimes.We estimate several robustness checks in the Supplementary Material, including a matched analysis; nonparametric (i.e., squared) measures of female representation; subsets by year and agency type; county-or state-or agency-fixed effects to account for heterogeneity in police agencies and police responses to rape across counties, states, and agencies; and clustered errors, all of which are fairly robust. 15Our main findings on the positive and significant association between female police and the rate of reported rapes remain, though we do find some evidence of a nonparametric effect as well.
We also replicate the results found by Ba et al. ( 2021) and subset their arrest data to sex crimes arrests only.Briefly, Ba et al. (2021) used data on daily patrol assignments from the Chicago Police Department (CPD) to compare how officers of different demographic profiles behave while on the job.One of their findings is that female officers make fewer arrests than their male counterparts.We use their data and code to replicate their results with one key difference: we limit arrests to only sex crimes to analyze how female officers behave with regard to arrests for these crimes. 16This replication and extension provide supplemental support for our main results.Our research uses aggregate data from police departments, whereas Ba et al. ( 2021) used individual-level data, and yet we find similar outcomes; female officers are not significantly associated with substantive increases in arrests for sex crimes.This suggestive evidence supports our main findings and highlights that those results are consistent across different contexts. 17 Taken together, the robustness checks provide additional evidence of our main findings and indeed point to a troubling justice gap: female police officers may increase the rape report rate with no commensurate increase in rape arrest rates.This provides suggestive evidence that increasing women's representation within police forces may improve the public's and particularly rape victims' perception of the police and may make victims more willing to report the crime.This supports previous findings that women's participation in police forces and other institutions improves perceptions of legitimacy and trust and increases cooperation by the public with institutional agents (Barnes, Beaulieu, and Saxton 2018;Flores-Macías and Zarkin 2021;Karim 2020;Riccucci, Van Ryzin, and Lavena 2014).However, female police alone may not be able to substantively affect the arrest rate.We do not take this as evidence that female police officers are not doing their job or that they have no impact on policing outcomes more generally, but rather that there may be larger institutional and organizational barriers to secure justice for rape victims.Individual officers are limited by departmental culture, norms, training, and practices, as well as legal, political, and budgetary factors beyond their immediate control.Moreover, female officers may face pressure to "fit in" as "one of the guys," may face discrimination and tokenism, and may simply not identify with or desire to represent women's interests within the police.Moreover, some scholars argue that to change police behavior, it is important to recruit men who respect women as equals and discuss gender stereotyping during police training (Belknap (2014).Additionally, even if female officers wished to actively pursue a rape case, the process of taking a case from initial report to arrest often involves other police officers, legal representatives, and political offices, which may dilute the effect of female officers.Similarly, female and male officers may be assigned to different duties and patrols, which may limit female officers' impact on arrest decisions.Although this analysis cannot directly uncover why female police officers are not associated with increased arrest rates due to the daunting, if not impossible, task of measuring the culture of police departments and the complex and varied process of arrests across departments, the results highlight that simply adding women to the police force does not immediately translate into improvements for victims of rape; the findings also underscore the need for more careful analysis not only of descriptive diversity within police forces but also of institutional cultures, training, professionalization, arrest procedures, and norms.

Discussion and Conclusion
We contribute to the essential debate of whether demographic representation affects outcomes in police bureaucracy by analyzing whether female police officers are associated with differences in rape reporting and arrest rates.Although female representation is significantly and positively associated with increases in rape reporting, it is not associated with positive changes in rape arrests.This highlights that the strategy of "just add women and stir" alone is not sufficient to alter police behavior (Belknap 2014;Carmichael and Kent 2015;Karim et al. 2018;Wentz and Archbold 2012).Moreover, this highlights a significant and troubling justice gap for victims of sexual assault.Even though increasing the gender (and racial and other characteristics) diversity of police departments means these departments better reflect the communities they police and, it is hoped, improves community-police relations and increases the public's willingness to report crimes, we find little evidence that this strategy alone is enough to change police behavior with regard to arrests for rape.This highlights that, despite police officers having the potential to use their discretion to represent their interests or beliefs, they are still limited by police culture, organizational structure, and processes.At least in this context, female police officers appear to be "blue" first-both in terms of belonging to a police culture and being constrained by police procedures, budgets, and policies-and women second.
Future studies should explicitly examine the root cause of the null effect of women's representation on arrests for rape.Several factors that may limit their impact are institutional cultures, the complex and multifaceted process of arrest decision making, issues of tokenism for women, professionalization pressures to fit in with colleagues and prioritize certain crimes, departmental norms and leadership, and the roles and experiences of female officers: future work should directly explore these possible limitations.
Many reform initiatives have assumed that increasing women's representation will improve responses to sexual violence, and in fact some research finds that increasing the number of female police officers does affect some policing outcomes (Ba et al. 2021;Shoub, Stauffer, and Song 2021).We hope that these findings will act as a catalyst for more research on the potential and limitations for demographic representation of women within the police.Previous work indicates that institutional cultures and leadership powerfully dictate the behavior of bureaucrats; thus, police culture should be carefully interrogated to examine how it affects arrest rates, justice, and representation.Additionally, these data are cross-sectional and only provide a snapshot of police force composition.Future studies should further probe the causal relationship between the positive relationship with reporting and the lack of a relationship with arrests for rape, Moreover, future work should explore other types of gendered diversity, including LGBTQþ representation, and how gender diversity may intersect with racial and ethnic diversity.Finally, this data cannot identify the roles or tasks to which male and female police officers were assigned, which may influence their impact both on report and arrest rates (Shoub, Stauffer, and Song 2021).Future work should tease out the causal forces behind this (lack of an) effect.
This investigation is essential to our understanding of policing and justice (Soss and Weaver 2017).In the aftermath of prominent incidents of police violence (George Floyd and Breonna Taylor, among countless others), it is vital to understand the determinants of police behavior.Police forces have neglected to investigate or devote resources to gender-based crimes and violence against women, despite their prevalence and deleterious effects for victims and communities more broadly.Although one in five women will be raped in their lifetime (Black et al. 2011), sexual violence is underreported, and the arrest rate for sexual assault cases is only 19% (Morabito, Williams, and Pattavina 2019).These crimes not only severely harm the victims but also undermine the legitimacy of the police and the government.With increasing pressure and attention paid to gendered crimes in the aftermath of the #MeToo Movement, it is key that scholarship and policymakers prioritize evidence-based policy solutions, rather than solutions based on stereotypes, and examine the impacts in multiple settings with detailed police administrative data and representative samples.Growing access to and availability of more fine-grained policing data (e.g., Ba et al. 2021;Cohen et al. 2019;Shoub, Stauffer, and Song 2021) will allow scholars to investigate these relationships in more detail.
One proposed solution to police bias and violence has been to hire more women and more Black police officers in the expectation that members of these groups will change police behavior.More research is needed to explore how the integration of female and Black officers affects outcomes at multiple levels from writing tickets and performing traffic stops to arrest patterns and police violence.The findings presented here contribute to scholarship that shows that simply adding women to an institution will not necessarily provide opportunities for women to substantively represent the interests of women (e.g., Celis et al. 2008).
However, despite recognition of the limitations of a "just add women and stir" approach among scholars of gender and politics, a focus on women's physical representation within institutions, such as the police, remains a common focus of popular discourse, proposed reform programs, and literature on policing.Thus, future scholarship should continue to investigate how the structures, processes, priorities, leadership, power dynamics, and culture of those institutions provide an opportunity for both men and women to improve services and policy outcomes for women.In the meantime, a troubling justice gap remains for victims of sexual violence, and police reforms are needed that emphasize evidence-based changes to prompt real procedure change.
Notes 1 Evidence of whether the #MeToo movement has had an impact on arrests is mixed.See Levy and Mattsson (2021) and the report by Owen Bowcott, "#MeToo and the Justice System: Complaints up, but Convictions down," The Guardian, October 15, 2019.https://www.theguardian.com/world/2019/oct/15/metoo-justice-system-complaints-up-convictionsdown. 2 Gender is the socially constructed roles, behaviors, and attributes considered appropriate for women and men, whereas sex refers to biological sex (Butler 2011).We use the word "women" to refer to members of the female sex.Because we cannot observe or measure each officer's gender identity, our discussion focuses on female representation, rather than a broader, and indeed necessary, exploration of gender.However, future analyses should explore other types of gendered representation within police forces.3 See existing work on female police officers, including Ba et al. (2021); Barnes, Beaulieu, and Saxton (2018); Karim (2020); Karim et al. (2018), Riccucci, Van Ryzin, and Lavena (2014); Schuck (2018);and Shoub, Stauffer, and Song (2021).4 For example, see Ba et al. (2021); Bazley, Lersch, and Mieczkowski (2007); Brandl, Stroshine, and Frank (2001); Karim et al. (2018); Miller and Segal (2019); Schuck (2018), Shoub et al. (2020); Shoub, Stauffer, and Song (2021);and Sun (2007).5 The definition of "women's interests" has been debated and is fluid but often includes childcare, maternity, sexuality, women's participation in the economy, and gender equality (Celis et al. 2014).6 LEMAS includes all agencies with more than 100 employees and samples smaller agencies from strata based on characteristics like number of full-time sworn officers and agency type.In this time period, 86-97.4% of requested agencies completed questionnaires, with typically lower response rates among sheriffs' departments than local or state departments.We do not think that female representation influenced response rates, but we explore differences by agency type in the Supplementary Material and find robust results.LEMAS changed its weighting strategy in 1997, and when we explored subsets of the data in the Supplementary Material, the results are robust.7 However, in the Supplementary Material, we explore within-agency effects for the subset of the sample for which there are multiple agency observations across years.Results are robust.

Figure 2
Figure 2Scatterplot of percent female officers and the rape report and arrest rates.Source: Data from LEMAS.

Table 1
Gender Composition and Crime Data ofUS Police Forces, 1987-2016

Table 2
The Effect of Female Police on Rape Report and ArrestRates, 1987Rates,  -2016

Table 3
The Effect of Female Police on Violent Crime (VC)Report and Arrest Rates, 1987-2016