Social biases are encoded in word embeddings. This presents a unique opportunity to study society historically and at scale, and a unique danger when embeddings are used in downstream applications. Here, we investigate the extent to which publicly-available word embeddings accurately reflect beliefs about certain kinds of people as measured via traditional survey methods. We find that biases found in word embeddings do, on average, closely mirror survey data across seventeen dimensions of social meaning. However, we also find that biases in embeddings are much more re-flective of survey data for some dimensions of meaning (e.g. gender) than others (e.g. race), and that we can be highly confident that embedding-based measures reflect survey data only for the most salient biases. In April of 2015, protests erupted over the murder of Freddie Gray, Jr. Questions about what to call those protesting quickly became the focus of a national debate. In an interview on CNN with Erin Burnett, 1 Baltimore City Councilman Carl Stokes admonished then-President Barack Obama and then-Mayor Stephanie Rawlings-Blake for using the word thugs to refer to the protesters. Burnett challenged Stokes' admonition, claiming the protesters were indeed thugs because They know it's wrong to steal and burn. Stokes responded by stating the protesters were ... children who have been set aside [and] marginalized. The argument between Burnett and Stokes is over the way we label people, the meanings of those labels, and the impacts these meanings can have. Councilman Stokes wants to avoid using the label thug because of its established, negative 1 http://nymag.com/intelligencer/2015/04/carl-stokes-to-cnn-thug-is-racially-charged.html | | | | || | | | || | ||| | | | | | | |||| ||| ||| | |||||| | |||||| | | | | | ||| | | |||| | | | | | | | | ||||| | | || ||||||||||||||| | | | ||| | | | | || | || | | ||| ||||| |||| | ||| | | | | | ||||| | | | | | | | | | | | | || | | | || | | || || | | || || | | | | | | |||||||||||||| | | || | | | || | | | || | | | || ||||| || |||| | || ||| ||| | || | || || | | | | | | ||||||| | thug child judge secretary Potency (weakstrong) Evaluation (badgood) Gender (manwoman) Black (not blackblack) Belief D i m en s i on Figure 1: Beliefs (x-axis) about four identities (sepa-rate plots) along four dimensions of social meaning (y-axis). connotation towards black Americans (Dow, 2016). The survey data collected for this paper, a sample of which is shown in Figure 1, provides further evidence of this association between thugs and black Americans. Respondents to our survey, on average, expected thugs to be bad, and that approximately 42.4% of thugs would be black. Of the 57 identities we studied, the only identity perceived to be more black was criminal, at 47.3%. The beliefs we have about people who hold particular identities (McCall and Simmons, 1978) are important, because they often determine the behaviors we take towards people who are labeled with those identities (Ridgeway and Smith-Lovin, 1999). 2 For example, as Councilman Stokes knows, 2 Different kinds of beliefs about identities have different names. For example, contextualized beliefs are called impressions (Heise, 1987), and aggregations of beliefs across multiple dimensions of meaning are called stereotypes (Fiske et al., 2002). The beliefs we study here are typically called sentiments or associations . However, given the distinct meaning of these terms in NLP, we use the general term belief in this paper. This aligns roughly with the generic use of the terms bias and stereotype in related NLP literature. we do not behave the same way towards children as we do towards thugs. This is because, as reflected in Figure 1, people generally believe that children are weak and good, whereas thugs are bad and powerful. This leads us to want to do things like help children, versus wanting to attack thugs (Heise, 2007). However, measuring beliefs is difficult. Traditionally, we have relied on surveys to collect these measurements. But there are tens of thousands of identities (Joseph et al., 2016; MacKinnon and Heise, 2010), and beliefs about them can form along many different dimensions of sociocultural meaning (e.g. gender, race, and others displayed in Figure 1). Measuring beliefs about many identities, on many dimensions, using traditional surveys can therefore be difficult. Further, measuring the evolution of beliefs is often impossible with surveys, because survey data is extremely sparse historically (Garg et al., 2018). Finally, measuring how these beliefs change with additional contextual information (e.g. beliefs about specific teachers, rather than teachers in general) is notoriously difficult with survey data (Heise, 2007). Recognizing these difficulties, scholars have begun to develop NLP tools to measure beliefs about identities historically, at scale, and in context (Joseph et al., 2017; Hoyle et al., 2019; Fast et al., 2016; Garg et al., 2018; Field et al., 2019). Most recent methods derive these measures by manipulating word embeddings. Studying beliefs enmeshed in word embeddings is also critical because embeddings are widely used in downstream NLP models, which are themselves beginning to label people, for example, as job-worthy or not (De-Arteaga et al., 2019). Measuring beliefs about people using embeddings therefore serves the dual purpose of understanding human biases and of ensuring such biases are not propelled further along by algorithms. However, work remains to understand when embedding-based measures of beliefs about identities accurately reflect more traditional survey measures, and why some beliefs may be reflected more accurately than others. The present work combines new and existing survey data with an extensive set of embedding-based measurement strategies to explore this at both the dimension level and the belief level. At the dimension level, for example, we ask, how well do embeddings capture beliefs about gender, relative to race? And if differences exist, why? Such issues have arisen in existing work, for example, where Garg et al. (2018) see correlations of .65 between embedding-based and survey-based measures of beliefs about gender, but only .15 for ethnicity-based beliefs. At the beliefs-level, we ask, for example, how much more accurately do we capture beliefs about the Potency (strength) of thugs, relative to beliefs about the Potency of children? Accuracy at this level is critical for linking historical trends in social behavior to societal-level beliefs about particular identities. We show that what we measure is more important than how we measure it in determining the correlation between embedding-based and survey-based measures of beliefs about people. At the dimension level, the beliefs we measure most accurately are also the most important for how we label others . At the belief level, assuming we can identify a good measurement model, embedding-based measures are significantly more accurate for more extreme, and more agreed upon, beliefs. All code and data necessary to replicate the analyses in this article can be found at https://github. Our work is grounded in literature on measuring beliefs about identities in social psychology in general and, more specifically, via word embeddings. We address these two literatures separately here. A common approach for measuring beliefs about specific identities is to assume a dimensional representation that is, to assume a set of distinct dimensions of social meaning can be used to characterize how we think and feel about someone that holds a particular identity. From this dimensional perspective, two primary questions arise. First, what are the dimensions along which beliefs form? Social psychologists have identified three classes of important dimensions: traits, affective meanings, and semantic associations. Traits represent visiblealthough also socioculturally definedcharacteristics like age, gender, and race (Freeman and Ambady, 2011). Affective dimensions of social meaning represent how we feel about a given person and/or identity (Todorov et al., 2015; Fiske et al., 2002; Heise, 2007). Here, we use the three affective dimensions proposed by Heise (2007) and that are popular in sociology (Rogers et al., 2013) Evaluation (good-ness/badness), Potency (strength/weakness), and Activity (active/passive). Finally, social psychologists often characterize beliefs about identities in terms of semantic associations to particular concepts (Freeman and Ambady, 2011) or institutions (MacKinnon and Heise, 2010). For example, people link the identities brother and sister together because they are both associated with the family institution. In the present work, we collect beliefs for seventeen different dimensions of social meaning, incorporating age, race, gender, evaluation, potency, activity, and six institutional associations. Second, given a theorized dimension of meaning, how should we measure society-wide beliefs about where particular identities lie on that dimension? Here, we adopt perhaps the most common approach, which uses semantic differential scales on surveys (Osgood et al., 1975). The semantic differential technique asks respondents to place an identity on a sliding scale with two opposing concepts (e.g. weak and strong, see the example in Figure 2A). Finally, it is worth noting that here, like in most social psychology research, we assume that responses from survey participants generalize to American culture writ large. This assumption is built on the well-established culture-as-consensus paradigm in psychological anthropology (Karabat-sos and Batchelder, 2003; Batchelder and Romney, 1988), and empirical work showing that people tend to agree on the vast majority of their beliefs about people (Heise, 2007). Nonetheless, many counterexamples exist (Berger et al., 1992; Smith-Lovin and Douglas, 1992). We leave questions about how to address these issues to future work. Embedding-based approaches to measuring beliefs typically follow a three step process of cor-pus/embedding selection, dimension selection, and word position measurement. Corpus/Embedding Selection Several recent works have argued that the corpus used can impact measures of beliefs about people derived from word embeddings (Lauscher and Glavas, 2019; Mirzaev et al., 2019; Sweeney and Najafian, 2019). For example, Brunet et al. (2019) show how to reduce gender bias in embeddings by removing particular documents from a corpus. However, several others have shown that in their analyses, the corpus used does not significantly impact results (Spirling and Rodriguez, 2019; Garg et al., 2018; Kozlowski et al., 2019; Caliskan et al., 2017). Differences in the embedding model used have also been observed to impact measurements (Chaloner and Mal-donado, 2019). Again, though, robustness checks from other studies suggest a limited effect beyond the somewhat general hyperparameters of window size and the number of dimensions estimated (Garg et al., 2018; Kozlowski et al., 2019). Dimension Selection To measure beliefs, one first must select a dimension along which the belief is assumed to be held. Much of the literature has focused on dimensions related to gender or race. Others, however, have seen value in moving beyond these dimensions (Agarwal et al., 2019; Sweeney and Najafian, 2019). Most relevant is the work of Kozlowski et al. (2019), who study the association of 59 concepts across 20 different dimensions of sociocultural meaning, and that of An et al. (2018), who induce 732 different dimensions using WordNet to study contextual effects of linguistic meaning. While neither work focuses heavily on identities, these efforts compliment our goal of studying a broad range of dimensions of social meaning. Scholars then identify a direction within the embedding that represents this dimension. To do so, an approach similar to the semantic differential idea is used. Terms are selected to represent the two ends of the dimension. For example, to identify the gender direction, words at one end might be he and him, and words at the other end, she and her. Scholarship varies on how these dimension-inducing word sets are selected. For example, several scholars have used demographically gendered and/or racialized names (Bolukbasi et al., 2016; Caliskan et al., 2017), while others have relied on careful extraction of concepts from dictionaries and thesauri (Kozlowski et al., 2019). Kozlowski et al. (2019) find that having more words at each end generally provides better measurements, and others have found a need to use frequently occurring terms (Ethayarajh et al., 2019; Brunet et al., 2019). Beyond these observations, however, scholars have generally found stable results as long as reasonable word sets are selected. Word Position Measurement Finally, the position of each identity along this direction must be identified. Doing so entails two major decisions. First, how should one quantify the direction, given the dimension-inducing words? For example, Bolukbasi et al. (2016) identify the direction by taking the first dimension of a PCA on the full set of direction words. Second, how should one define the position of points along this line? For example, several works use the cosine similarity between the identified bias direction and the embedding of each identity. Scholars have also recently proposed supervised methods for word position measurement (Sweeney and Najafian, 2019; Agarwal et al., 2019). Such approaches are important, but assume the existence of some training data, which may or may not be available in certain measurement contexts. We therefore do not explore these methods further in the present work. In sum, using embeddings to measure beliefs requires a series of decisions, the impacts of which are still debated. Below, we provide the most comprehensive study to date on the importance of these decisions on measurement quality. We collect two new survey datasets for this paper. The first measures beliefs about the 57 identities 3 in Table 1 on seventeen dimensions of social meaning described below. The second measures the ways in which a set of survey respondents label people with these identities in hypothetical social situations. We used a cluster-based approach to select the 57 identities we study. We study nine sets of six identities, where each set has been shown in prior work to be related in some way. Five of the sets are characterized by a salient association to a specific institution described by MacKinnon and Heise (2010). Three sets are characterized by salient trait similarities and differences on gender, age or race/ethnicity. And one set of identities is included where all identities have strong negative Evaluations. Finally, we include three random identities as a mechanism for comparison in other work not described here. For further details on the selection criteria, survey populations, and results, see the Appendix. We collected survey data on beliefs about identities from 247 respondents on Amazon's Mechanical Turk. Each survey respondent provided re-3 Because not all embedding models account for bigrams, we removed police officer from all analyses in this paper. However, for future purposes, we include it in our description of the data here. sponses for four different, randomly selected identities. Each identity was given to a total of 15 different respondents. For each identity, we asked a set of seven questions, some of which had multiple subparts. Following prior work, beliefs for affective dimensions were solicited using a slider-based Likert scale. For the Evaluative dimension, the opposing ends of the Likert scale were labeled bad, awful and good, nice. For the Potency dimension, powerless, little and powerful, big, and for the Activity dimension, slow, quiet, inac-tive and fast, noisy, active. See Heise (2010) for more details on the development of these questions. The fourth and fifth question used Likert scales to measure beliefs about age and gender, with ends representing young and old and Always male and Always female, respectively. The sixth question asked Of all [some identity, e.g., bullies], what percentage of them do you think are... and then provided one slider each for the following ethnic/racial categories drawn from the planned 2020 Census: White, Hispanic or Latino, Asian, Middle Eastern, and Black. The seventh question, modeled after the association-based measures from Hill et al. (2015), asked To what extent does thinking about [some identity, e.g., bullies] lead you to think about... and then provided a slider for the following institutional settings: family, politics, (criminal) justice, medicine, business, education, and religion. Each slider had qualitative labels ranging from Not at all, to Somewhat, to Immediate response. Dimension Identities Politics conservative, Democrat, liberal, Republican, politician, senator Family brother, sister, daughter, son, father, mother Law judge, criminal, lawyer, witness, cop, police officer Medicine doctor, physician, surgeon, nurse, patient, dentist Business executive, consultant, secretary, intern, banker, boss Gender woman, guy, girl, boy, man, lady Age teenager, kid, child, toddler, adult, minor Race & Ethnicity black, white, Hispanic, Asian, Arab, American NegativeEvalua-tion thug, idiot, jerk, goon, punk, bully Random principal, scientist, coach Table 1: The 57 identities we collect data on. We collect responses from 402 participants to a pair of identity labeling tasks. 4 Note that these respondents are different than those who provided the belief measurements . Each participant answered a set of 40 hypothetical identity labeling questions. Questions could be either an IsA or a SeenWith question. An example of an IsA question is given in Figure 1B). SeenWith questions were formatted in the same way, except the question text instead says Who would you say is most likely to be seen with a [mother]? Questions varied on both the identity provided in the text and the identities serving as potential answers. From the 57 identities we study, we create survey questions roughly 5 as follows: for a given identity, we generate 14 random sets of the 56 other identities; each set contains four identities. We then generate one IsA and one SeenWith question for each of these sets, where these four identities constitute the possible answers to the question, and the given identity is used in the question text. This process is then repeated ten times for each identity. This process generates ten questions for each of the 3,192 identity pairs for each type of question. 4 These identity labeling questions are similar to, but distinct from, those used in our prior work focused on the impact of semantic associations and semantic similarity on identity labeling decisions (Joseph and Carley, 2016). 5 Due to a bug in Qualtrics, a small percentage of questions were not asked or asked more than once. See Appendix for details Variable Description i A social identity (e.g. doctor, author) d A dimension of meaning (e.g. gender) r A survey respondent S d,i,r A matrix of survey responses to semantic differential measures on a given dimension d for identity i by respondent r . To further substantiate our claims, we ensure our main results hold using three other datasets on beliefs about identities: beliefs about gender for 287 occupational identities from Bolukbasi et al. (2016), beliefs about 195 national and occupational identities on the Big Five Personality Traits from Agarwal et al. (2019), and beliefs about 654 identities on the Evaluation, Potency, and Activity dimensions by Smith-Lovin and Robinson (2015). Our primary research question is, how accurately can we recover beliefs measured using surveys with word-embedding based measures? We study this first at the dimension level , i.e., how accurately do embedding-based measures reflect survey data across a set of identities on a given dimension of social meaning? We then study accuracy at the belief level , i.e., how accurately do embedding-based measures reflect survey data for specific identities on specific dimensions? Our approach is straightforward, but is best explained by introducing some additional notation, provided in Table 2. 4.1 Dimension-level analysis At the dimension level, we consider first how different factors relating to the measurement itself impact accuracy. We then study why measurements are more accurate for some dimensions than others. We do so by connecting the degree of accuracy for a given dimension to how important that dimension is in how survey respondents select identities for others in our identity labeling task. As discussed above, the accuracy of embedding-based measurements may vary across properties of the dimension being measured, as well as the way in which the embedding-based measurement is constructed. We first study the relative effects of a) the dimension ( d ), b) the embedding model ( E ), c) the dimension-inducing wordset ( dw ), and d) the word position measurement model ( wp ) on the accuracy of embedding-based measurements. As is standard in the literature, we use the Pearson correlation between the mean survey response and the output of the embedding-based measure as our definition of accuracy. That is, for a given dimension d , survey dataset S , embedding-based measure m E,dw,wp , and set of identities of size I , we compute the accuracy of the embedding-based measure as the Pearson correlation between { S d,i 0 ,  , S d,i 1 ,  , ..., S d,i I ,  } and { m E,dw,wp ( i 0 ) , m E,dw,wp ( i 0 ) , ..., m E,dw,wp ( i I ) } . We then run a linear regression to understand how accuracy varies across the factors considered. Our analysis involves all dimensions of social meaning studied in the four survey datasets described above. For embedding models, E , we consider twelve different publicly available cor-pus/embedding combinations from prior work. To construct dimension-inducing wordsets, dw , we using one of three approaches. The first is to use the same terms as were placed on the semantic differential scale on the survey (e.g. powerless, powerful, little, big for Potency, as in Figure 2a). In certain cases, we also include a survey-augmented condition that extends this wordset using a thesaurus, after discussion amongst authors. Third, where applicable, we use direction-inducing wordsets from prior work . Finally, we consider several of the major established approaches in the literature for word position measurement wp . We use the approaches from Kozlowski et al. (2019), Swinger et al. (2019), Ethayarajh et al. (2019), Bolukbasi et al. (2016), and Garg et al. (2018). As we will show, controlling for E , dw and wp , there are large differences in accuracy across dimensions. To better understand these differences across dimension, we compute two measurements. First, Kozlowski et al. (2019) show that the variance of the survey data on a dimension, that is, Var( S d,i 0 ,  , S d,i 1 ,  , ..., S d,i n ,  ) , is strongly correlated with the accuracy of embedding-based measures. However, they also note that high explained variance... reveals little about how these valences are deployed in social life (pg. 930). Here, we therefore compute a second measure that connects variance of the survey data on a given dimension to a significant social outcome, how strongly people rely on that dimension when labeling other people. To do so, we first construct a 57 x 17 matrix X of scaled-and-centered mean survey responses for each identity on each dimension in our survey data, i.e. X i 0 ,d 0 = S d 0 ,i 0 ,  . We then construct an observation with a binary outcome that pairs the identity in the question with each possible answer. The outcome is 1 if the answer was selected, and 0 otherwise. For example, in Figure 2B), the pairings created would be mother, adult, mother, sister, mother, son, and mother, lady. If the respondent answered lady, then the outcomes would be 0, 0, 0, and 1, respectively. The 40.3% of questions where respondents answered all are equally un-likely were ignored. In total, we obtained 9,597 responses where the respondent did not answer All are equally (un)likely, split roughly evenly between SeenWith and IsA questions. We then train a logistic regression model for IsA and SeenWith questions separately, each with seventeen parameters. For a given observation, the parameters represent the absolute difference between each dimension, e.g. the first parameter is | X i q ,d 0  X i a ,d 0 | , where i q is mother in Figure 2B), i a is, e.g., adult, and d 0 is, e.g., gender. In the Appendix, we provide full results for these regressions. Intuitively, larger negative coefficients for a given dimension indicate that the further away two identities are on that dimension, the less likely the respondent is to select them as a pair. For example, we find that Evaluation has a strong negative correlation for IsA questions, indicating that respondents typically do not expect two identities to be assigned to the same person if one identity is perceived to be for good people and the other for bad people. Positive coefficients imply assortativ-ity on the dimension. For example, for SeenWith questions, Potency has a positive coefficient, implying that we expect powerful identities to be seen with less powerful counterparts. The magnitude of these coefficients represent the importance given to that dimension by survey respondents. We use the maximum of the two coefficients across SeenWith and IsA questions as a measure of this importance. We are also interested in accuracy for specific beliefs. For example, how accurately do embedding-based measures reflect survey data on beliefs about the typical age of a boy? As an outcome for this belief-level analysis, we use a ranking task similar to prior work (Spirling and Rodriguez, 2019; Kozlowski et al., 2019). We describe this outcome by continuing with the example of beliefs about the age of boys. We first compute the set of identities N , for which S age,boy,   se ( S age,boy,  ) > S age,i,  + se ( S age,i,  ) , where se is the standard error function. That is, N represents all identities we are reasonably confident respondents believed to be younger than boy s. We then determine the subset of N , N c , where boy is also ranked above those identities in the embedding measure. We do the same for identities survey respondents said were older than boy s, adding these to N , and to N c if they are correctly ranked in the embedding measure. Finally, we use N c N to study accuracy at the belief level. We are interested both in overall levels of accuracy for belief-level measurements, as well as the factors that explain variation in accuracy. We consider four factors that might explain this variation (continuing with the age/boy example): sd ( S age,boy,  ) , the distance of S age,boy,  to the median over all identities on that dimension, the logged frequency of the identity in a large corpora, 6 and the number of synsets for the identity in WordNet. To study the impact of these different factors, we use a generalized additive model with a binomial link function where N c N is the outcome and points are weighted by N . Finally, as opposed to considering results across all possible E , dw , and wp , we first select those settings that maximize the Pearson correlation for each dimension. Across all conditions and survey datasets, the Pearson correlation between the embedding and survey measures is 0.32 [.31,.33]. However, considerable variation exists. Figure 3 presents results of a regression that attempts to explain the sources of this variance (x-axis) and the effects of each source (y-axis). Separate colors represent results from the four different survey datasets analyzed. In general, results are largely consistent across the different datasets, and thus we will not emphasize differences across datasets below. Figure 3 shows that the embedding model used can decrease correlation by as much as .35. As others have found, this effect decreases when one focuses only on 300-dimensional embeddings. It is worth noting, however, that no embedding model is universally best. For example, nine of the twelve embedding models studied are responsible for producing the highest observed correlation for at least one dimension. Selection of the dimension-inducing words, dw , also has a limited effect. The one exception is when survey-matched words are used for the Gender dimension, where correlations drop by, on average, around 0.5 relative to the he/she baseline. The fact that using the same words as the semantic differential scale is a terrible choice, but for only one of the seventeen dimensions studied, reflects the fact that selection of dw , like elements of other forms of quantitative social science, remains a mix of art and science (Sterling and Taveter, 2009). In contrast, even the most scientifically appealing approaches to word position measurement (Ethayarajh et al., 2019) provide marginal gains. The only consistent observation we draw is that approaches that normalize measurements across dimensions related to the same overarching concept (e.g. that normalize racialized beliefs across all perceived dimensions of race) perform slightly better. Results thus reflect that the details of measurement are less important than what is being measured. Reflecting this same fact, the strongest impacts on correlation between the survey and embedding-based measures come from which dimension is being studied. Some of these results reflect the salience of these dimensions in social life. Associations to institutions, which are most accurately measured on average, are a primary tool we use to sort people into groups (MacKinnon and Heise, 2010). And stronger correlations between the embedding and survey-based measures for Evaluation and Potency, relative to Activity, reflects the increased importance in affective perceptions of these two dimensions (Rogers et al., 2013). However, scholars largely agree that trait-based beliefs on gender and race serve as default characteristics (Ridgeway and Smith-Lovin, 1999) along which we almost automatically categorize others (Todorov et al., 2015). Given their shared salience, why is gender the only trait that can be accurately measured? Figure 4A) shows, as first identified by Kozlowski et al. (2019), that much of this is due to the variance of the survey data along that dimension; the correlation between variance and the coefficients in Figure 3 is 0.91. However, as discussed above, Kozlowski et al. (2019) study more general concepts on more general dimensions, and note that they have no easy way to connect their                  R = 0.91 ActivityAge AsianBlack Business Education Evaluation Family Gender Justice Latino Medicine Middle Eastern Politics Potency Religion White                  R = 0.86 Activity Age Asian Black Business Education Evaluation Family Gender Justice Latino Medicine Middle Eastern Politics Potency Religion White Coefficient in Figure 3 Maximum Importance in IsA or SeenWith Labeling Questions 0.02 0.04 0.06 0.02 0.04 0.06 0.00 0.05 0.10 0.15 0.20  0.8  0.6  0.4  0.2 0.0 Variance B A Figure 4: In both A) and B), the y-axis gives the coeffi-cient value for the regression presented in Figure 3. In A), the x-axis represents the variance in survey means along the dimension. In contrast, here, Figure 4B) shows a significant positive correlation between variance in the survey data along a dimension (and hence measurement accuracy) and that dimensions' importance in explaining patterns of labeling in our identity labeling task. Embedding-based measures of beliefs about identities, we therefore show, are most likely to reflect traditional survey measures particularly when those beliefs are salient for identity labeling. Critically, then, results for biases in word embeddings are tied not only to the salience of dimensions in general social life, but also to the identities selected for measurement. Selecting only heavily racialized and non-gendered identities, for example, might well reverse the positions of racialized dimensions and gender in Figure 4. This makes it all the more critical to identify theoretically-driven concepts salience in labeling, and variance in measurement that move beyond measures of specific identities on specific dimensions to help us understand what is measurable and what is not, particularly when survey data is not available. As with the dimension-level results, we find that embedding-based measures are generally accurate predictors of survey-based measures for specific beliefs. On average, 74.9% of the beliefs collected for this paper are correctly ranked, as are 82.1%, 72.0%, and 71.4% of the beliefs from Bolukbasi et al. (2016), Smith-Lovin and Robinson (2015), and Agarwal et al. (2019), respectively. One caveat to keep in mind, however, is that we focus only on the single best embedding measurement approach for each source/dimension combination. Regardless, as with the dimension-level results, there is considerable variance at the belief level. Some of this variance (approximately 32%, see the Appendix for full regression results ) can be explained by the factors we consider. The strongest explanation we find to explain ranking accuracy, reflected in the left-hand plot in Figure 5, is the distance of the survey-based belief measure from the median on its dimension. At the extremes, ranking accuracy is almost perfect. Because extreme observations are also most likely to be low variancefor example, consider that beliefs at the most extreme values of a scale must have zero variancea more general claim can be made: word embedding-based measures accurately capture our most extreme and agree-upon beliefs about people, but show significant unexplained (at least by us) variance for more neutral and/or less-agreed upon beliefs. This variance is on display in the right-hand plot in Figure 5, which gives results for the blackness dimension. The embedding-based measure captures with perfect accuracy racialized perceptions of the identities thug and criminal, but not, e.g., liberal, which is similar along the other explanatory factors we consider here. As far as we are aware, it remains an open question as to why this is the case. In this paper, we asked, can we trust measures of beliefs about people derived from word embeddings? We find the answer to be yes, at least on average. Depending on one's perspective, this could be good or bad. From a cultural studies/social psychological perspective, this positive correlation further validates efforts to use word embeddings to study perceptions of people historically, at scale, and in context. On the other hand, from the bias perspective, this suggests that a vast array of social biases are encoded in embeddings. However, we also find that some beliefs specifically, extreme beliefs on salient dimensions  are easier to measure than others. More generally, across four datasets, we find that what we measure is more important than how we measure it. Again, two different perspectives on this are needed. With respect to the study of culture and human stereotypes, we may be safest in studying only the most extreme results from embedding models, as has been done by, e.g., Spirling and Rodriguez (2019). From the bias perspective, given the rash of recent work on debiasing word embeddings, our results suggest that much more attention needs to be paid to how we are evaluating these approaches. Currently, upstream evaluations of debiasing are centered almost exclusively on occupational identities on gender, where some of the most salient social biases we know of exist ( Ridgeway, 2011). Others have argued that removing these salient beliefs may not remove gender information from embeddings (Gonen and Goldberg, 2019). But Gonen and Goldberg's 2019 argument relies on a technical deficiency of existing approaches. We can make a similar critique by simply changing what is being measured. For example, the correlation between gender beliefs and the gender direction in the Hard-Debiased embeddings of Bolukbasi et al. (2016) is 0.05 (p = .84) using identities in their data, and 0.4 (p < .05) using the identities in our data. Similarly, removing gender bias does not remove bias on other dimensions. For example, while Sweeney and Najafian (2019) show that the NumberBatch embeddings harbor the least gender bias, we find that they are the only embedding to show consistently high correlations with age, leading to the potential for ageism downstream. More generally, stereotypes exist along a network of beliefs (Freeman and Ambady, 2011) reflecting unwarranted correlations between many dimensions (Ridgeway, 2011); we must therefore be careful not to expect that removing meaning along one dimension will expel social biases from our models. K.J. was supported by NSF IIS-1939579. This research was supported in part a SUNY Germination Space Grant. We thank Lynn Smith-Lovin, Lisa Friedland, Tobias Schroeder, and Yuhao Du for comments on earlier versions of this work.
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