Table A1: Model outcomes

|Training set accuracy|92.44%|
|---|---|
|Validation set accuracy|91.92%|
|Test set accuracy (on previously unseen data)|92.83%|
|Accuracy|0.928388|
|Precision|0.896705|
|Recall|0.959647|
|F1 score|0.927109|

literature, we train 300 dimensional vectors. We used a standard 10-word window size, in between a shorter window size (which tends to capture syntactic/functional relations between words) and a longer window size (which tends to capture topical relations between words). To improve accuracy, the classification model was also comprised of a Long Short-Term Memory layer in addition to the fully connected neural network layers and the initial embedding layer (Hochreiter and Schmidhuber 1997).

Applying this model to our data, we used the bottom 500 words of the case judgements, since the outcomes were found to be present towards the bottom of the judgements. As a training dataset, we applied the model to cases for which we could determine the outcome (in favor or against the defendant) directly from the case outcome variable of the metadata. There were 49,706, 6,214, and 6,213 cases in the training, testing, and validation sets, respectively. The results of the model are presented in table A1.

# **Using word embeddings to determine textual slant**

To determine each judge’s textual gender slant (i.e., the degree to which each judge exhibits gender bias in their written judgements), we make use of word embeddings, which model the text present in the judgements in the form of low dimensional Euclidean space vectors (Pennington, Socher, and Manning 2014). In other words, word embeddings are low dimensional vectors which can accommodate large vocabularies and corpora without increasing dimensionality. The representation resulting from them captures relations between the words. In order to catch semantic similarity amongst words, the positions are assigned to word vectors in the Euclidean space, such that the words that appear frequently in the same context have representations close to each other in the space, while words that appear rarely together have representations that are far apart.

To train our word embeddings, we used the GloVe algorithm, described above. The embeddings we trained were then used for identification of cultural dimensions in language (Kozlowski, Taddy, and Evans 2019). That is, we identified a gender dimension by taking the difference between the average normalized vector across a set of male words and the average normalized vector across a set of female words, as such: where _Nmale_ is the number of words used to identify the male dimension. In order to determine the similarity within these dimensions, we used cosine similarity as a measure, defined as follows: where _~x_ and _~y_ are non-zero vectors, _✓_ is the associated angle, and _k · k_ is the 2-norm. Therefore, we can see that words with male (female) _~_ connotations _~_ are going to be positively (negatively) correlated with the gender dimension defined by _male − female_ .

These dimensions were then used to construct the gender slant measures. For the first, we aimed to capture the strength of the association between gender and stereotypical attitudes, which identify men more closely with careers and women with family. Specifically, _~ ~_ we used the cosine similarity between the vector representingdimension, defined bythe gender _career_ dimension, _~ − family~_ defined. For our second measure, we aimed to capture stereotypical attitudesby _male − female_ , and the vector representing the _~_ career-family _~_ that associate _~_ men with “good” and women with “bad” words. For this measure, instead of _career − family_ , we used _good − bad_<sup>_~_</sup> .

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