Networked experiments and modeling for producing collective identity in a group of human subjects using an iterative abduction framework

Abstract

Group or collective identity is an individual’s cognitive, moral, and emotional connection with a broader community, category, practice, or institution. There are many different contexts in which collective identity operates, and a host of application domains where collective identity is important. Collective identity is studied across myriad academic disciplines. Consequently, there is interest in understanding the collective identity formation process. In laboratory and other settings, collective identity is fostered through priming a group of human subjects. However, there have been no works in developing agent-based models for simulating collective identity formation processes. Our focus is understanding a game that is designed to produce collective identity within a group. To study this process, we build an online game platform; perform and analyze controlled laboratory experiments involving teams; build, exercise, and evaluate network-based agent-based models; and form and evaluate hypotheses about collective identity. We conduct these steps in multiple abductive iterations of experiments and modeling to improve our understanding of collective identity as this looping process unfolds. Our work serves as an exemplar of using abductive looping in the social sciences. Findings on collective identity include the observation that increased team performance in the game, resulting in increased monetary earnings for all players, did not produce a measured increase in collective identity among them.

Appendices

A Supplemental related work

Related work topics that augment those in Sect. 3 are provided here. See Table 2 for a listing of all related work topics.

1.1 A.1 Individual anagram games: modeling

In  Tresselt (1968), problem solving and verbal cues are analyzed with an anagram game. Tresselt (1968) modifies the H. Kendler and S. Kendler (1962) mediational model of problem-solving behavior (introducing word length and letter position), to understand anagram problem solving. This is a theoretical model of individual anagram games.

1.2 A.2 Individual anagram games: experiments and modeling

These works combine experiments and modeling. In Feather (1969), it was found that subjects who were initially confident of passing an anagram game test tended to attribute success to ability and failure to bad luck. However, subjects who were initially not confident tended to attribute success to good luck and failure to lack of ability. Results are discussed in terms of Heiderian theory and a valence-difficulty model. In  Feather and Simon (1971a, b), two individuals played anagram games simultaneously but independently to test whether a person attributed her success (if she performed better) to skill versus good fortune, and failure to inferior skill or bad luck. Attributions were found to be dependent on expectations of players. Results are discussed in terms of models involving Heider’s principle of balance and his analysis of the causes of action, in terms of positivity biases in social perception, and as indicating effects of the social context of performance upon attribution and valence.

1.3 A.3 Modeling of CI

Lustick (2000), Rousseau and van der Veen (2005) use ABMs to study identity diffusion. An agent adopts (changes) her type of identity to that of a neighbor with a stronger (higher valued) type of identity. Hence, these are contagion processes and are implemented much like voter models (de Oliveira 1992; Pereira and Moreira 2005). Other works modeling collective identity (van Zomeren et al. 2008; Chen and Li 2009; Benjamin et al. 2016; Ackland and O’Neil 2011) are presented in Sect. 3.3.

1.4 A.4 Agent-based models of anagram games and formation of CI

The Charness et al. (2014) work in Sect. 3.6 has no modeling for the group anagram game. This motivated the online experiments and ABMs in Ren et al. (2018). This article is an expansion of Ren et al. (2018). In this work, we model the priming process of producing CI, which is the group anagram game. There are no ABMs (or models of any kind) of group anagram games, to our knowledge, other than ours.

1.5 A.5 Studies of phenomena related to CI

Many phenomena, such as in-group and out-group effects are related to CI. In Brewer and Silver (1978), Perdue et al. (1990), laboratory experiments with no interactions between subjects are performed. In  Brewer and Silver (1978), it was found that bias in favor of the in-group on a reward allocation task was unaffected by the arbitrariness of classification into groups. An effort was made to assure that subjects in the arbitrary condition would not perceive the out-group as dissimilar. They found that similarity-dissimilarity of the out-group did not affect allocation bias as long as the in-group was perceived as similar to the subject. Subjects were divided clearly into groups labeled “dark” and “light”. Subjects then were asked to indicate their ratings first of “the other members of my group” and then of “the members of the other group” on a series of six-point bipolar scales (friendly-unfriendly; trustworthy-untrustworthy; cooperative-competitive; intelligent-stupid; weak-strong; generous-stingy; likeable-unlikeable). In  Perdue et al. (1990), classical conditioning in-group and out-group descriptors (e.g., “us” and “them”) are used to establish evaluative responses to novel, unfamiliar targets. Nonsense syllables unobtrusively paired with in-group designating pronouns (e.g., “we”) were rated as more pleasant than syllables paired with out-group designators (e.g., “they”).

Paris et al. (1972) study how the anticipated interaction between groups determines the representations that groups have of each other. When students are categorized into groups, discrimination occurs such that the in-group is more favorably represented than the out-group before interaction takes place and also when no interaction is anticipated. Such discrimination is stronger when competitive interaction is anticipated in an important situation. In this condition, intergroup differences are also more easily projected on physical traits. Categorization is shown to be not only an independent variable but also a dependent variable in intergroup relations.

In  Kahn and Ryen (1972), Own Group Bias (OGB) was measured by differences in pre and postgame scores on the evaluative scales of the Semantic Differential (SD).

In  Shank et al. (2015), an experiment on Amazon Mechanical Turk was used to develop an agent-based simulation to understand how people’s motivations and behaviors within public goods dilemmas interact with the properties of the dilemma to lead to collective outcomes. They predict how the public good’s benefit and size, combined with controlling individual versus group properties, produce different levels of cooperation in public goods dilemmas.

In  Sethi and Somanathan (2006), a simple model of collective action is presented as a framework for empirical research into the issue of when collective action in the commons will be successful.

In  van Zomeren et al. (2008), an integrative social identity model of collective action (SIMCA) is developed that incorporates three socio-psychological perspectives on collective action. Instructions for coders were to answer different questions like “Does the measure of identification (used in this study) refer to a disadvantaged group or a social movement?”, “Is this group incidentally disadvantaged or structurally disadvantaged?”. Coders also rated the extent to which collective disadvantage was structural on a 5-point Likert-type scale ranging from 1 (not at all) to 5 (very much).

In  Salganik and Watts (2009), new insights into the role of individual behavior on collective outcomes are obtained using a multiple-worlds experimental design in a web-based experiment in which 2930 participants listened to, rated, and download 48 songs by up-and-coming bands.

In  Suri and Watts (2011), laboratory experiments with interactions between subjects are performed. Web-based experiments are conducted where 24 individuals played a local public goods game arranged on one of five network topologies that varied between disconnected cliques and a random regular graphs. It was found that although players did generally behave like conditional cooperators, they were as likely to decrease their contributions in response to low contributing neighbors as they were to increase their contributions in response to high contributing neighbors. They also found that positive effects of cooperation were contagious only to direct neighbors in the network.

In Capraro (2013), online experiments using Amazon Mechanical Turk were used to develop a predictive model of human cooperation able to organize a number of different experimental findings that are not explained by the standard model.

In  Rousseau and van der Veen (2005), an agent-based computer simulation of identity change explores how changes in the attributes of the individual and/or elements of the environment influence the dependent variable: the degree of shared identity in a population.

There is a host of other studies that investigate phenomena such as cooperation and a person’s affinity for a group that are closely related to CI. In Worchel et al. (1977), Charness et al. (2007) laboratory experiments with interactions between subjects are performed. They study concepts such as group attraction and salience, respectively, which are related to CI. In  Worchel et al. (1977), study groups worked cooperatively on two tasks and results were interpreted as showing that both previous interaction and success of combined effort are important variables in determining when intergroup cooperation will increase intergroup attraction. In  Charness et al. (2007), groups perform two stage games as priming tasks, the Battle of the Sexes and Prisoner’s Dilemma. Results show that the salience of the group affects behavior of members, as well as the behavior of people in another group, and that participants anticipate these effects.

1.6 A.6 Data-driven: combining experiments and data-driven modeling

This section reports on works that combine experiments with data-driven modeling. These works cover explore-exploit networked experiments with limited modeling (Mason and Watts 2012); individual models of single-choice (i.e., one-shot) evacuation decisions (Nguyen et al. 2017); ABM of emotion and information contagions spreading on a network and comparisons with a single event (Li et al. 2014); and ABM of solar panel adoption and comparisons with data in San Diego county (Zhang et al. 2016). See  Zhang and Vorobeychik (2019) for a review of innovation diffusion models. None of these works use ABMs to model networked experiments where individuals take a series of actions (that may be repeated) over time, to study CI, as we do.

In Luhmann and Rajaram (2015), small-scale laboratory experiments and an ABM were used to analyze the dynamics of collaborative inhibition. In Gates et al. (2017), the model in Luhmann and Rajaram (2015) was tested against human data collected in a large-scale experiment to find that participants demonstrate non-monotonicities not evident in the predictions. These unexpected results motivate more recent work in elucidating the algorithms underlying collaborative memory. In Paxton et al. (2018), using real-time online social experiments data, a statistical model is used to study interpersonal coordination in a “minimally interactive context” to explore how people become coupled in their perceptual and memory systems while performing a task together.

In contrast to the above works, where controlled experiments are used to produce data that are then used for modeling, there are many models based on observational data. We survey some of these works here.

In Korolov et al. (2016), the possibility of predicting a social protest (planned, or unplanned) based on social media messaging is studied. In Nguyen et al. (2016), to help increase the performance of retweet prediction, a flexible model under the framework of Random Forest classifier captures a number of behavior signals affecting user’s retweet decision. In Hu et al. (2014), a semantic model that can naturally represent various academic social networks, especially various complex semantic relationships among social actors, is presented. In Qin et al. (2017), the proposed method integrates topology and content of networks, and introduces a novel adaptive parameter for controlling the contribution of content with respect to the identified mismatch degree between the topological and content information. In Attema et al. (2015), data-driven multi-agent models predict Twitter trends. In van Maanen and van der Vecht (2013), a method that implements, validates, and improves an individual behavior model is proposed. The multi-agent model contains the social network structure, individual behavior parameters, and the scenario that are obtained from empirical data. In Lee and Oh (2013), emergence and propagation of reputations in social networks is modeled with a distributed algorithm. In Chierichetti et al. (2014), using several Twitter data sets, focusing in particular on the tweets sent during the soccer World Cup of 2010, a model of how users switch between producing information or sentiments and sharing others news or sentiments is developed. In Korolov et al. (2015), a theoretical analysis is developed for how social-chatter quantitatively relates to action via a superlinear scaling law.

Other works include using data from geotagged social media messages and data from mobile health applications (Tran and Lee 2016; Kurashima et al. 2018) In Tran and Lee (2016), to understand citizen reactions regarding Ebola, a large-scale data-driven analysis of geotagged social media messages is performed. In Kurashima et al. (2018), data from mobile health applications is used to develop a statistical model, called TIPAS (Time-varying, Interdependent, and Periodic Action Sequences). This approach is based on personalized, multivariate temporal point processes that model time-varying action propensities through a mixture of Gaussian intensities. Their model captures short-term and long-term periodic interdependencies between actions through Hawkes process-based self-excitations.

Clearly, much of the modeling of observational data is motivated by social media.

B Experimental data

This Appendix describes data from the game experiments of Sect. 4. In this section we present an analysis of the experimental data that illustrates how players interact in the anagram games. We focus on experimental data that are useful in modeling. We identify four main actions $a_i \in A$, $1 \le i \le 4$, in the set A of actions for a player during the game: (1) request letter from neighbor, (2) reply with letter to a request from a neighbor, (3) form and submit valid word, and (4) think (i.e., a no-op).

We define the following variables for the actions in the game:

• When $v_i$ sends a requests for a letter to $v_j$, a request sent occurs.

• When $v_j$ receives the letter request from $v_i$, a request received occurs.

• When $v_j$ replies with the letter requested from $v_i$, a reply sent occurs.

• When $v_i$ receives the letter reply from $v_j$, a reply received occurs.

• When $v_i$ uses its own letters to form a word, a word formed occurs.

Table 14 shows a summary of the section plots and the questions we answer with the analyses.

Table 14 Summary of the analyses in the Experimental Data Sect. B, and the questions we answer. Section B.1 presents histograms for the timestamps for letter requests. Section B.2 presents histograms for the timestamps for letter replies. Section B.3 presents histograms for the timestamps of the time duration between replies received and requests sent. Section B.4 presents histograms for the timestamps for words formed

1.1 B.1 Timestamp for letter request

The number of letters a player can request through a game depends on the number of its neighbors. Each neighbor can share up to three letters (the initial three letters), so if a player has $k=2$ neighbors, then six letters can be requested throughout the game. If a player has $k=8$ neighbors, then 24 letters can be requested. We want to analyze the behavior of players with reference to the letter request action and answer the following questions. When do players request letters during the game? How does the number of neighbors affects the behavior of a player to request a letter in the game?

Figure 22 shows a histogram with 10 bins of 30-s each of timestamps for request sent, for 47 experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. It indicates that more letters are being requested during the first half of the 300-second anagram game. To analyze whether the number of neighbors affects the letter request, Figure B.1 in Appendix B.1.1 from Cedeno (2019) shows histograms with 10 bins of 30-s each for request sent for experiments with $\hbox {k}= 2$, 3, 4, 5, 6, 8. The same trends exist for each value of k. However, if there are few neighbors ($\hbox {k}=2$) and consequently fewer available letters (3 letters per neighbor), there are fewer letter requests and letter replies near the end of the game.

Fig. 22

Probability density distribution for time of request sent over the 300-s anagram game. Each of the bins on the x-axis corresponds to 30-s intervals. It shows experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. Letter requests are made throughout the game, rather than solely at the outset

1.2 B.2 Timestamp for letter reply sent

The number of letters a player can reply with, in response to letter requests, through a game depends on the number of its neighbors. Each neighbor can share up to 3 letters, so if a player has $k=2$ neighbors, then 6 letters can be replied (when requested) at any time through the game, since the number of letters assigned initially is three. We want to analyze the behavior of players with reference to the letter reply action and answer the following questions. When do players reply letters during the game? How do the number of neighbors affects the behavior of a player to reply a letter in the game?

Figure 23 shows a histogram with 10 bins of 30 s each, for reply sent, for 47 experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. It indicates that letter requests are being replied to throughout the game, but more so at the earlier stages of the game. To analyze whether the number of neighbors affects the letter request, Figure B.2 in Appendix B.1.2 in Cedeno (2019) shows histograms with 10 bins of timestamp for reply sent for experiments with $k= 2, 3, 4, 5, 6, 8$. Similar trends are obtained when data are broken down by k. We find that letter reply are made throughout the game, rather than solely at the outset.

Fig. 23

Probability density distribution for time of reply sent over the 300-s anagram game. Each of the bins on the x-axis corresponds to 30-s intervals. It shows experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. Letter replies are made throughout the game, rather than solely at the outset

1.3 B.3 Time duration from sending a letter request to receiving the requested letter

When $v_i$ requests a letter of $v_j$, it has to wait for $v_j$ to respond. Once $v_j$ replies with the letter, then $v_i$ is allowed to use the received letter and form words to contribute to the team. This time duration between request sent and reply received reveals how long players take to reply to their neighbors’ requests. A player only has to request a letter (and receive it) on one occasion to use it as any number of times in forming words. Remember that these rules were designed to foster word construction, to increase earnings potential, and to foster team cohesion. We want to analyze the behavior of players with reference to the time duration between the timestamps of the letter reply action and the letter request action, to answer the following questions. How long does it take for players to reply to a letter request? How does the number of neighbors affect the difference between the timestamps of the letter reply action and the letter request action?

Figure 24 shows a histogram with 10 bins of 30-s each, for the time difference between reply received and request sent, for 47 experiments with $k=2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used estimate the probability density function. Players generally respond relatively quickly to their neighbors letter requests with replies typically made within 30 s of the request.

Fig. 24

Probability density distribution for time duration between requesting a letter and replying to the request, over the 300-s anagram game. Each of the bins on the x-axis corresponds to 30-s intervals. It shows experiments with $k=2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. Players generally respond relatively quickly to their neighbors letter requests, with replies typically made within 30 s of the request

To analyze whether this behavior is common while increasing the number of k neighbors in a game, Figure B.3 in Appendix B.1.3 in Cedeno (2019) shows histograms with 10 bins of 30-s each of timestamp change between reply received and request sent for experiments with $k= 2, 3, 4, 5, 6, 8$. The number of neighbors doesn’t affect this type of action, players generally respond relatively quickly to their neighbors letter requests with replies typically made within 30 s of the request.

1.4 B.4 Timestamp for word formed

At any time during a game, a player can form a word and submit it for validation to our web application. If a player possesses letters to form a valid word, then she forms and submits a word, the application validates it, and the word is added to the game screen. We want to analyze the behavior of players with reference to the action of word formed and answer the following questions. When do players submit words during the game? How does the number of neighbors and the number of available letters affects the number of words formed by a player?

Figure 25 shows a histogram with 10 bins of 30-s each for word formed, for 47 experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used estimate the probability density function. It suggests that words are being formed throughout the game, and even up through the end of the game. This justifies a 5-min anagram game duration. To analyze whether the number of neighbors affects the word formation, Figure B.4 in Appendix B.1.4 in Cedeno (2019) shows histograms with 10 bins of 30-s each for timestamp of word formed for experiments with $k= 2, 3, 4, 5, 6, 8$. Word submissions are made throughout the game, and the number of neighbors and available letters does not affect this behavior.

Fig. 25

Probability density distribution for time of forming words over the 300-s anagram game. Each of the bins on the x-axis corresponds to 30-s intervals. It shows experiments with $k= 2, 3, 4, 5, 6, 8$. A kernel-density estimation with Gaussian kernels is used to estimate the probability density function. Word submissions are made throughout the game, and the numbers of neighbors and available letters do not affect this type of action

C Modeling supplement

This Appendix contains several figures that support the modeling of Sect. 5. See Figs. 26 and 27.

Fig. 26

Within each subfigure we show KL-divergence values for Baseline Model M0 across the five parameters of x at 1-min intervals: lower values are better. Each plot contains data over a time window: a 0–1 min, b 1–2 min, c 2–3 min, d 3–4 min and e 4–5 min, of the 5-min anagram game. The data are for conditions $(n=10, k=2)$. These plots show that request-related predictions are better than reply-related predictions over all time intervals. The reply-related predictions are better in the second half of the 5-min anagram games, but Fig. 23 shows that in experiments, there are fewer replies in the second half of the games

Fig. 27

Within each subfigure we show KL-divergence values for the Baseline Model M0 (in green) and Model M1 (in red) across the five parameters of x: lower values are better. The modeling conditions are experiment with $k=2$. Each plot contains data over a time window: a 0–1 min, b 1–2 min, c 2–3 min, d 3–4 min and e 4–5 min, of the 5-min anagram game. While Model M0 has good predictions for minute 3 and minute 5 (with the exception of the words formed), Model M1 has better predictions for minute 3 and minute 5 for all five x variables (color figure online)