Supplemental Materials and Methods



Supplemental Materials

Purity Homophily in Social Networks

by M. Dehghani et al., 2016, JEP: General



Supplemental Materials and Methods

Study 1

Method

Measuring Moral Rhetoric in Twitter. In traditional LSA, given a corpus of documents D and a vocabulary of content words V, each row in the source matrix represents a word w and each column represents a document d. The cells represent the frequency of the particular word in the relevant document. For our study we used the Wordspace paradigm, as implemented by Infomap (Schütze, 1998). In this paradigm each column of the source matrix represents a keyword rather than a document. These keywords were selected based on their informativity, measured using the following formula:

tf.idf (c) = tf (c)  (log (D + 1) - log (df (c)))

where tf (c) is the term frequency of the word used for column c and df (c) is the document frequency of c. As is the default for Infomap, we selected the top 2,000 words to function as keywords. The vocabulary (i.e., the rows) was populated with the top 20,000 words based on the same measure. In other words, the vocabulary list includes the 20,000 highest frequency words, after stopwords have been removed. Consequently, our source matrix for the semantic vector space consisted of 20,000 rows and 2,000 columns. The measure of word frequency used by Wordspace is based on the frequency in which w appears within the context of the keyword represented by a particular column c. Here we define context, as is frequently done in implementations of Wordspace, as a window of +/-15 words. That is, each cell in the matrix is a count of the number of times in the corpus that the word w occurs within 15 words of the keyword c. In both traditional LSA and Wordspace the word co-occurrence matrix is transformed by Singular Value Decomposition, resulting in three matrices U, ∑, and V*, of which we only used the matrix of left singular vectors found in U, after truncating it to 100 dimensions. Consequently, each word w was represented by a 100-dimensional vector.

Community Detection. The Clauset, Newman, and Moore (2004) algorithm starts in an unclustered state by assuming that all the nodes in the graph form singleton communities (i.e. assuming that each users has its own individual community). Then, it iteratively calculates likely improvements of modularity when two adjacent communities are merged. Modularity in this context is the strength of a community partition by taking into account the degree distribution of the nodes in the graph. Two communities are then merged if this likelihood is higher than a threshold. This process is repeated until there are no more communities left to be merged.

Analysis. Our main analysis relies on a supervised machine learning technique called Support Vector Machines (SVMs) regression, first introduced by Vapnik (2000). SVMs represent features, or data points, as points in space and tries to find a hyperplane that is maximally distant from nearest training data points of each of the categories. SVMs can be used for classification as well as regressions analysis. SVM regression uses ε–insensitive loss function which penalizes errors which are greater than threshold ε and ignores errors which are situated within a certain distance of the threshold ε known as the epsilon intensive band. It performs linear regression in the high-dimension feature space using ε-insensitive loss and tries to reduce model complexity by introducing (non-negative) slack variables.

Results

The monotonicity is shown by the Tukey HSD test (page 6; see Table 1a for descriptive statistics and Table 2a for Tukey HSD test results). Purity difference is the only one that increases at each point. To test linearity of the models, we compared fitting a U-shaped model to a linear model. The U-shaped model fitted purity least compared to the other concerns (purity: F = 538.56, harm: F = 3482.11, fairness: F = 15318.95, authority: F = 3533.21, loyalty: F = 2109.90)

Observed relationship between purity and distance not due to general differences between liberals and conservatives (Study 1):

a) Controlling for political differences: As discussed on page 9-10 of the paper, two main large communities exist in the network, representing liberals and conservatives within the US. In order to see if the reported effects of purity on distance is stable across political groups, we examined the relationship between distance and purity difference within these two communities. This analysis revealed that the positive linear relationship between distance and difference in purity loadings holds even within both clusters (page 12-13). This pattern indicates that the observed relationship cannot be explained by general political differences between liberals and conservatives.

b) Examining the underlying words behind the purity dimension: We examined the LSA vectors used in the analysis, and queried the 100 nearest neighbors of the purity dimension (which itself is a composite space of MFD word vectors). This analysis can be seen as similar to examining item loadings in a factor analysis. Of these top 100 words, only one was related to religion (“church”, number 29) and four were related to politics (“obamacare”, number 3; “obama”, number 11; “boehner”, number 34; “tedcruz”, number 73). Words like 'life' and 'concerned' are more frequent and closer to the aggregate vector of the concern. To continue the factor analysis comparison, we examined the 100 highest loading items (words) and found that our purity factor loads on only one religion item and four political items. This indicates that the reported effect cannot be due to religious or political words.

Study 2

A pilot study was ran to test the items used in Study 2. This pilot study also showed unique effects of purity difference on physical distance (only the bench question was used), but not on self-reported similarity or willingness to have conversations (for which we had no a priori hypothesis for). Study 2, preregistered on the Open Science Framework (), replicated and extended this physical distance finding.

Survey Instructions

Thank you for agreeing to participate in our study. First, we will ask you to make a series of judgments about potentially moral scenarios. Click the next button to proceed. Below you’ll be presented with a variety of situations and be asked to say whether certain behaviors in those situations would be morally wrong. Please use the following scale from 1 to 7, to indicate the degree to which you judge the behavior to be wrong (if at all).

1 Not at all wrong; has nothing to do with morality

2

3

4

5

6

7 Very wrong; an extremely immoral action

Harm Items

1. You see a man quickly canceling a blind date as soon as he sees the woman.

2. You see a woman clearly avoiding sitting next to an obese woman on the bus.

3. You see a girl saying that another girl is too ugly to be a varsity cheerleader.

4. You see a girl laughing at another student forgetting her lines at a school play.

Fairness Items

1. You see a student getting an A on a group project when he didn't do his part.

2. You see a manager taking half the doughnuts from a box, leaving little for others.

3. You see a girl asking for allowance even though her brother did her chores for her.

4. You see a boy skipping to the front of the line because his friend is an employee.

Ingroup Loyalty Items

1. You see the US Ambassador joking in Great Britain about the stupidity of Americans.

2. You see a former Secretary of State publicly giving up his citizenship to the US.

3. You see an American telling foreigners that the US is an evil force in the world.

4. You see a former US General saying publicly he would never buy any American product.

Authority Items

1. You see a boy spray-painting anarchy symbols on the side of the police station.

2. You see a student talking back to the principal in front of the classroom.

3. You see a group of teenagers joking loudly and goofing off during church services.

4. You see a girl ignoring her father's orders by taking the car after her curfew.

Purity Items

1. You see a man having sex with a frozen chicken before cooking it for dinner.

2. You see a woman burping and farting loudly while eating at a fast food truck.

3. You see two first cousins getting married to each other in an elaborate wedding.

4. You see a homosexual in a gay bar offering sex to anyone who buys him a drink.

Harm Different Feedback

Thank you for completing our questions about moral scenarios. In the future, we intend to place participants into discussion pairs based on their answer compatibility. Based on your responses, we have paired you with another participant who has also completed these questions. We would like feedback about how you would feel about talking with another participant who has the following compatibility with you: Your responses were highly similar for concerns of Fairness (89% similarity), Loyalty (96% similarity), Authority (93% similarity), and Purity (94% similarity). You differed, however, on your responses for concerns of Harm (24% similarity). Here is list of the items that you answered that reflected Harm concerns: 1. You see a man quickly canceling a blind date as soon as he sees the woman. 2. You see a woman clearly avoiding sitting next to an obese woman on the bus. 3. You see a girl saying that another girl is too ugly to be a varsity cheerleader. 4. You see a girl laughing at another student forgetting her lines at a school play.

Fairness Different Feedback

Thank you for completing our questions about moral scenarios. In the future, we intend to place participants into discussion pairs based on their answer compatibility. Based on your responses, we have paired you with another participant who has also completed these questions. We would like feedback about how you would feel about talking with another participant who has the following compatibility with you: Your responses were highly similar for concerns of Harm (89% similarity), Loyalty (96% similarity), Authority (93% similarity), and Purity (94% similarity). You differed, however, on your responses for concerns of Fairness (24% similarity). Here is list of the items that you answered that reflected Fairness concerns: 1. You see a student getting an A on a group project when he didn't do his part. 2. You see a manager taking half the doughnuts from a box, leaving little for others. 3. You see a girl asking for allowance even though her brother did her chores for her. 4. You see a boy skipping to the front of the line because his friend is an employee.

Loyalty Different Feedback

Thank you for completing our questions about moral scenarios. In the future, we intend to place participants into discussion pairs based on their answer compatibility. Based on your responses, we have paired you with another participant who has also completed these questions. We would like feedback about how you would feel about talking with another participant who has the following compatibility with you: Your responses were highly similar for concerns of Harm (89% similarity), Fairness (96% similarity), Authority (93% similarity), and Purity (94% similarity). You differed, however, on your responses for concerns of Loyalty (24% similarity). Here is list of the items that you answered that reflected Loyalty concerns: 1. You see the US Ambassador joking in Great Britain about the stupidity of Americans. 2. You see a former Secretary of State publicly giving up his citizenship to the US. 3. You see an American telling foreigners that the US is an evil force in the world. 4. You see a former US General saying publicly he would never buy any American product.

Authority Different Feedback

Thank you for completing our questions about moral scenarios. In the future, we intend to place participants into discussion pairs based on their answer compatibility. Based on your responses, we have paired you with another participant who has also completed these questions. We would like feedback about how you would feel about talking with another participant who has the following compatibility with you: Your responses were highly similar for concerns of Harm (89% similarity), Fairness (96% similarity), Loyalty (93% similarity), and Purity (94% similarity). You differed, however, on your responses for concerns of Authority (24% similarity). Here is list of the items that you answered that reflected Authority concerns: 1. You see a boy spray-painting anarchy symbols on the side of the police station. 2. You see a student talking back to the principal in front of the classroom. 3. You see a group of teenagers joking loudly and goofing off during church services. 4. You see a girl ignoring her father's orders by taking the car after her curfew.

Purity Different Feedback

Thank you for completing our questions about moral scenarios. In the future, we intend to place participants into discussion pairs based on their answer compatibility. Based on your responses, we have paired you with another participant who has also completed these questions. We would like feedback about how you would feel about talking with another participant who has the following compatibility with you: Your responses were highly similar for concerns of Harm (89% similarity), Fairness (96% similarity), Loyalty (93% similarity), and Authority (94% similarity). You differed, however, on your responses for concerns of Purity (24% similarity). Here is list of the items that you answered that reflected Purity concerns: 1. You see a man having sex with a frozen chicken before cooking it for dinner. 2. You see a woman burping and farting loudly while eating at a fast food truck. 3. You see two first cousins getting married to each other in an elaborate wedding. 4. You see a homosexual in a gay bar offering sex to anyone who buys him a drink.

Social Distancing Questions

1. If you were sitting on a bench with this person, how close to them would you be willing to sit?

as near as possible (1)

very near (2)

somewhat near (3)

somewhat far away (4)

very far away (5)

As far away as possible (6)

2. According to my first feelings (reactions), I would willingly admit a person with these values into the following classifications:

As close relatives by marriage (1)

As my close personal friends (2)

As neighbors on the same street (3)

As co-workers in the same occupation (4)

As citizens in my country (5)

As only visitors in my country (6)

Would exclude from my country (7)

Manipulation Check Item

1. Which of the following types of concerns did you differ from your partner on?

Harm Concerns (such as a girl saying that another girl is too ugly to be a varsity cheerleader) (1)

Fairness Concerns (such as a boy skipping to the front of the line because his friend is an employee) (2)

Loyalty Concerns (such as a former Secretary of State publicly giving up his citizenship to the US) (3)

Authority Concerns (such as a student talking back to the principal in front of the classroom) (4)

Purity Concerns (such as two first cousins getting married to each other in an elaborate wedding) (5)

Study 3

|Table 1a |

|Summary Statistics for Moral Differences Across Distance Levels |

| |Distance |

| |1 | |2 | |3 | |4 | |5 |

|Moral |M (SD) | |M (SD) | |M (SD) | |M (SD) | |M (SD) |

|Foundation |[99% CI] | |[99% CI] | |[99% CI] | |[99% CI] | |[99% CI] |

|Harm |0.0244 (0.024) | |0.0280 (0.026) | |0.0305 (0.026) | |0.0313 (0.025) | |0.0303 (0.024) |

| |[0.0240, 0.0247] | |[0.0280, 0.0281] | |[0.0304, 0.0305] | |[0.0313, 0.0314] | |[0.0301, 0.0305] |

|Fairness |0.0384 (0.000) | |0.0482 (0.000) | |0.0511 (0.000) | |0.0503 (0.000) | |0.0477 (0.000) |

| |[0.0379, 0.0388] | |[0.0481, 0.0482] | |[0.0510, 0.0511] | |[0.0504, 0.0502] | |[0.0474, 0.0480] |

|Loyalty |0.0303 (0.024) | |0.0329 (0.026) | |0.0333 (0.026) | |0.0321 (0.025) | |0.0302 (0.024) |

| |[0.0299, 0.0306] | |[0.0329, 0.0329] | |[0.0332, 0.0333] | |[0.0320, 0.0321] | |[0.0304, 0.0305] |

|Authority |0.0333 (0.026) | |0.0366 (0.028) | |0.0376 (0.029) | |0.0370 (0.029) | |0.0354 (0.027) |

| |[0.0329, 0.0337] | |[0.0366, 0.0367] | |[0.0376, 0.0376] | |[0.0369, 0.0370] | |[0.0352, 0.0356] |

|Purity |0.0278 (0.022) | |0.0323 (0.025) | |0.0371 (0.030) | |0.0445 (0.035) | |0.0468 (0.036) |

| |[0.0275, 0.0281] | |[0.0323, 0.0322] | |[0.0371, 0.0371] | |[0.0446, 0.0444] | |[0.0471, 0.0465] |

|Table 2a |

|Tukey’s HSD Comparisons of Moral Differences Between Distance Levels |

|Moral |

|Foundations |

|Model Test |MRMSEa†† | |MRMSEPurity - MRMSEa††† | |d | |t |Sig. |

| |(SD) [95% CI] | |[95% CI] | | | | | |

|Social Processes|0.4498 (0.0065) | |-0.0075 [-0.0057, -0.0092] | |-0.5941 | |-8.3962 | ................
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