Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a riot. Most existing works focus on contagions where individuals’ states are represented by binary variables, and propagation takes place over a single isolated network. However, characterization of an individual’s standing on a given matter as a binary state might be overly simplistic as most of our opinions, feelings, and perceptions vary over more than two states. Also, most real-world contagions take place over multiple networks (e.g., Twitter and Facebook) or involve multiplex networks where individuals engage in different types of relationships (e.g., co-worker, family, etc.). To this end, this paper studies multi-stage complex contagions that take place over multi-layer or multiplex networks. Under a linear threshold based contagion model, we first give analytic results for the expected size of global cascades, i.e., cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. Then, analytic results are confirmed by an extensive numerical study. In addition, we demonstrate how the dynamics of complex contagions is affected by the structural properties of the networks. In particular, we reveal an interesting connection between the assortativity of a network and the impact of hyper-active nodes on the cascade size.
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A Vector Threshold Model for the Simultaneous Spread of Correlated Influence
Spread of influence is one of the most widely studied propagation processes in the literature on complex networks. Examples include the rise of collective action to join a riot and diffusion of beliefs, norms, and cultural fads, to name a few. Most existing works on modeling influence propagation consider a single content (e.g., an opinion, decision, product, political view, etc.) spreading over a network independent from everything else. However, most real-life examples involve multiple correlated contents spreading simultaneously and exhibiting positive (e.g., opinions on same-sex marriage and gun control) or negative (e.g., opinions on universal health care and tax-relief for the “rich”) correlation. To accommodate these cases, this paper proposes the vector threshold model, as an extension of the widely used Watts threshold model for complex contagions. Here, the state of a node is represented by a binary vector representing their opinion on a number of content items. Nodes switch their states based on the influence they receive from their neighbors in the network. The influence is represented by a vector containing the proportion of neighbors who support each content; both positively and negatively correlated contents can be captured in this formulation by using different rules for switching node states. Our main result is concerned with the expected size of global cascades, i.e., cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. We also derive conditions on network structure for global cascades to be possible. Analytic results are supported by a numerical study.
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- Award ID(s):
- 1813637
- NSF-PAR ID:
- 10196220
- Date Published:
- Journal Name:
- ICC 2019 - 2019 IEEE International Conference on Communications (ICC)
- Page Range / eLocation ID:
- 1 to 7
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Expert testimony varies in scientific quality and jurors have a difficult time evaluating evidence quality (McAuliff et al., 2009). In the current study, we apply Fuzzy Trace Theory principles, examining whether visual and gist aids help jurors calibrate to the strength of scientific evidence. Additionally we were interested in the role of jurors’ individual differences in scientific reasoning skills in their understanding of case evidence. Contrary to our preregistered hypotheses, there was no effect of evidence condition or gist aid on evidence understanding. However, individual differences between jurors’ numeracy skills predicted evidence understanding. Summary Poor-quality expert evidence is sometimes admitted into court (Smithburn, 2004). Jurors’ calibration to evidence strength varies widely and is not robustly understood. For instance, previous research has established jurors lack understanding of the role of control groups, confounds, and sample sizes in scientific research (McAuliff, Kovera, & Nunez, 2009; Mill, Gray, & Mandel, 1994). Still others have found that jurors can distinguish weak from strong evidence when the evidence is presented alone, yet not when simultaneously presented with case details (Smith, Bull, & Holliday, 2011). This research highlights the need to present evidence to jurors in a way they can understand. Fuzzy Trace Theory purports that people encode information in exact, verbatim representations and through “gist” representations, which represent summary of meaning (Reyna & Brainerd, 1995). It is possible that the presenting complex scientific evidence to people with verbatim content or appealing to the gist, or bottom-line meaning of the information may influence juror understanding of that evidence. Application of Fuzzy Trace Theory in the medical field has shown that gist representations are beneficial for helping laypeople better understand risk and benefits of medical treatment (Brust-Renck, Reyna, Wilhelms, & Lazar, 2016). Yet, little research has applied Fuzzy Trace Theory to information comprehension and application within the context of a jury (c.f. Reyna et. al., 2015). Additionally, it is likely that jurors’ individual characteristics, such as scientific reasoning abilities and cognitive tendencies, influence their ability to understand and apply complex scientific information (Coutinho, 2006). Methods The purpose of this study was to examine how jurors calibrate to the strength of scientific information, and whether individual difference variables and gist aids inspired by Fuzzy Trace Theory help jurors better understand complicated science of differing quality. 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We are building a full model with these various operationalizations to be presented at APLS, but focus only on one of the calibration DVs (i.e., objective understanding of the mtDNA evidence) in the current proposal. We conducted a general linear model with total score on the mtDNA understanding measure as the DV and quality of scientific evidence condition, decision aid condition, and the four individual difference measures (i.e., NFC, ATS, WNS, and SRS) as predictors. Contrary to our main hypotheses, neither evidence quality nor decision aid condition affected juror understanding. However, the individual difference variables did: we found significant main effects for Scientific Reasoning Skills, F(1, 427) = 16.03, p <.001, np2 = .04, Weller Numeracy Scale, F(1, 427) = 15.19, p <.001, np2 = .03, and Need for Cognition, F(1, 427) = 16.80, p <.001, np2 = .04, such that those who scored higher on these measures displayed better understanding of the scientific evidence. In addition there was a significant interaction of evidence quality condition and scores on the Weller’s Numeracy Scale, F(1, 427) = 4.10, p = .04, np2 = .01. Further results will be discussed. Discussion These data suggest jurors are not sensitive to differences in the quality of scientific mtDNA evidence, and also that our attempt at helping sensitize them with Fuzzy Trace Theory-inspired aids did not improve calibration. Individual scientific reasoning abilities and general cognition styles were better predictors of understanding this scientific information. These results suggest a need for further exploration of approaches to help jurors differentiate between high and low quality evidence. Note: The 3rd author was supported by an AP-LS AP Award for her role in this research. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills help jurors understand complex scientific evidence.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICC.2019.8761313
