nucleation

QUESTION-348: In groups that discuss a sequence of issues under a stable network of relative influence, measured independently of the members' self-weights, does each member's influence over outcomes come to order as the network's eigenvector centralities and concentrate above them, as the DeGroot–Friedkin model proves for its own dynamics?

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Properties4
StatusOpen
Tagssocial-science, network-science
Linedistributed-agency
Cited as “bears on” byTHEORY-916 — In the DeGroot–Friedkin model, where a group reaches DeGroot consensus on each issue and each member's self-weight on the next issue equals their control over the last, with fixed relative interpersonal weights that form a strongly connected network, self-weights converge from every non-autocratic start to one equilibrium ordered by the eigenvector centralities of those weights: power accumulates above a centrality threshold, is autocratic exactly when the network is a star and democratic exactly when it is doubly stochastic; and in the networks that are not strongly connected that the authors treat, members to whom some other member does not listen, even indirectly, end with none

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Why it is a question

THEORY-916 holds the DeGroot–Friedkin theorems of Jia, MirTabatabaei, Friedkin and Bullo: with DeGroot consensus on each issue, reflected appraisal between issues and fixed relative weights, power comes to order as eigenvector centrality and accumulates above a threshold. Those are theorems about the model. The authors say “an assessment of the validity of the model has just begun” (p. 386; NOTE-1135).

The one test in the record, Friedkin, Jia and Bullo’s laboratory study (THEORY-902), used anchored dynamics and a network that changed from issue to issue. It supported the individual step and did not reach the predicted end state. Under the Friedkin–Johnsen step the same appraisal rule goes to autocracy instead (THEORY-1161), so which single-issue step real groups follow matters to the answer.

What would answer it

A test in groups with a stable network of relative influence, measured independently of the members’ self-weights, showing that their influence over outcomes across a sequence of issues orders as the network’s eigenvector centralities and concentrates above them. The model is refuted as a description if power in such groups orders otherwise. Simulations of the model cannot settle it.

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