A biased assimilation model on signed graphs

Abstract

This work introduces antagonistic interactions into the so-called biased assimilation model of opinion dynamics, a nonlinear model expressing the bias of the agents towards their own opinions. In this model, opinions exchanged in a signed network are multiplied by a state dependent term having the bias as exponent. For small values of the bias parameters, while for structurally balanced networks polarization always occurs, we show that for structurally unbalanced networks also a state of indecision (corresponding to the centroid of the opinion hypercube) is a local attractor. When instead the biases are all large, the opinions usually polarize. In particular, for large enough biases if all agents take the same initial stance (i.e., are all on the same side of the indecision state), then the opinions polarize all to the same extreme value for both structurally balanced network and structurally unbalanced network.

Signed Social Networks With Biased Assimilation

“…Accordingly, at every update, agent i weights both its neighbors' and its own opinions by a state-dependent factor, while in [9] the factor weighting each node's own opinion is constant. This modification does not affect the qualitative behavior of the model, see [29]. As in the analysis of [27], here we also take the values of the bias parameters identical for all nodes.…”

“…A preliminary version of this paper appears in the proceed-ings of CDC 2020 [29]. This conference paper deals with a slightly different version of the model (different individual bias coefficients) and mainly explores the asymptotic behavior we discuss in Section III.…”

Partisan Confidence Model for Group Polarization

“…Theorem 1. Given the PC dynamics (15), with the discounting function d i satisfying ( 16) as well as (17) for a non-increasing di : [0, 1] → [0, 1], let a connected subset B ⊆ V of agents have the bubble number γ B . Assume that inequality…”

“…where ( 32) is identical to (16), while (33) is the marginal case of (17). For any y ∈ [−1, 1] n , it should be clear that…”

“…A notable example is the Altafini model [13,14], in which the notion of antagonism among individuals is incorporated, leading to an influx of models that consider antagonistic relationships in opinion networks. Among these, some models have also included bounded confidence and biased assimilation, each of which can be viewed as a type of confirmation bias, as an individual's characteristics in the dynamics [15][16][17]. While antagonistic interactions/relationships can contribute to and justify the tendency toward more extreme beliefs in a divided population, such as that of the United States with respect to political ideology (see Fig.…”