Expertise and confidence explain how social influence evolves along intellective tasks

TL;DR

This work investigates how interpersonal influence evolves in small teams performing sequential intellective tasks, linking expertise and confidence to influence while uncovering underperformance biases. It blends empirical data with theory to propose three cognitive-dynamical hypotheses and several modeling approaches: a cognitively grounded DRP dynamical model, a convex linear estimator, and a deep neural-network predictor that uses message content, timing, and accuracy. Empirical results show higher expertise and confidence correlate with greater persuasiveness, and underperformers tend to misestimate others' expertise; Granger causality suggests a precedence from expertise to confidence and persuasiveness. The findings advance understanding of transactive memory and social learning in groups and offer multiple predictive tools for evolving influence networks in collaborative settings, balancing interpretability and predictive accuracy.

Abstract

Discovering the antecedents of individuals' influence in collaborative environments is an important, practical, and challenging problem. In this paper, we study interpersonal influence in small groups of individuals who collectively execute a sequence of intellective tasks. We observe that along an issue sequence with feedback, individuals with higher expertise and social confidence are accorded higher interpersonal influence. We also observe that low-performing individuals tend to underestimate their high-performing teammate's expertise. Based on these observations, we introduce three hypotheses and present empirical and theoretical support for their validity. We report empirical evidence on longstanding theories of transactive memory systems, social comparison, and confidence heuristics on the origins of social influence. We propose a cognitive dynamical model inspired by these theories to describe the process by which individuals adjust interpersonal influences over time. We demonstrate the model's accuracy in predicting individuals' influence and provide analytical results on its asymptotic behavior for the case with identically performing individuals. Lastly, we propose a novel approach using deep neural networks on a pre-trained text embedding model for predicting the influence of individuals. Using message contents, message times, and individual correctness collected during tasks, we are able to accurately predict individuals' self-reported influence over time. Extensive experiments verify the accuracy of the proposed models compared to baselines such as structural balance and reflected appraisal model. While the neural networks model is the most accurate, the dynamical model is the most interpretable for influence prediction.

Figures (8)

• Figure 1: Deep learning model architecture: A deep encoder model in a two-tower framework he2017neural for learning the three mappings of connectivity network, content of messages, and history of appraisals. The final layer computes the cosine similarity with the ground truth influence matrix and back-propagates the error using Stochastic Gradient Descent (SGD).
• Figure 2: Dynamics of the influence matrix in one team:$M$ shows a $4\times4$ influence matrix for this team. Every panel shows how much every subject reports others influenced them over time. in other words, it shows the amount of appraisal every person assigns to team members including themselves over time. After answering all questions, we observe that member 2 is the most accurate (cumulative correctness rate for member #1= 49%, member #2= 70%, member #3= 36%, and member #4= 58%). This figure illustrates the team's interpersonal appraisals reflect the accuracy of the team members, which was ascertained early on in the experiment.
• Figure 3: Granger causality result: This figure shows the proportion of statistically significant Granger causality of timeseries of confidence, persuasiveness and expertise in all teams. The $p$-values have been corrected using Benjamini-Hochberg (BH) procedure with False Discovery Rate of 5% has required $p\text{-value} < 0.03$ as statistical significance threshold.
• Figure 4: Cognitive model evaluation: The mean squared error (MSE) and the Kullback-Leibler (KL) divergence for different dynamical models over nine rounds of influence matrix estimation. Differentiation (D model) takes into account hypothesis \ref{['hp:hypothesis1']}. Differentiation, Reversion (DR model) is inspired by hypotheses \ref{['hp:hypothesis1']} and \ref{['hp:hypothesis2']}. Differentiation, Reversion, Perceived (DRP model) uses hypotheses \ref{['hp:hypothesis1']}, \ref{['hp:hypothesis2']}, and \ref{['hp:hypothesis3']}. For the models, we use the hyperparameter $\tau=0.4$. In this figure boxes show the interquartile range of the errors, the whiskers show minimum and maximum of the range of the distribution. In each box, the dot shows the average and the line shows the median of the portrayed distribution. Left: Single-round forecast error of various dynamical models for predicting the influence matrix one round ahead. The models estimate $\hat{M}^{(t+1)}$ using the expertise $\bar{y}^{(t)}$ and the reported influence matrix from the previous round $M^{(t)}$. Right: Multi-round forecast error of various dynamical models for predicting the influence matrix multiple rounds ahead. Outliers are not shown for better readability. The models estimate $\hat{M}^{(t+1)}$ using the expertise $\bar{y}^{(t)}$ and the initial ground truth $M^{(1)}$ influence matrix reported by individuals. For rounds $t+1\geq 2$, the dynamics use the predicted influence matrix from the previous round $\hat{M}^{(t)}$, instead of $M^{(t)}$. For rounds $t\geq 4$, the influence network remains relatively constant, so the cognitive dynamical model offers incremental improvements to the baseline models for single-round forecast. However, this model gives significant improvements in accuracy from baseline models for all rounds in multi-round prediction.
• Figure 5: Improvement in machine learning models by adding more features: Average of Mean Square Error (MSE) of estimated influence matrix from the ground truth in the test set of influence matrices. Titles show the list of features fed to the models. The error bar shows the standard deviation in 1000 bootstrap on test error. Both machine learning models improve when given more features from the logs.

Theorems & Definitions (5)

• Lemma 1: Dynamic models preserve row-stochasticity
• Lemma 2: Equilibrium and convergence of DRP model with uniform expertise
• Lemma 3
• Lemma 4
• Lemma 5