Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1709.07121

Discrete-Time Polar Opinion Dynamics with Susceptibility

Ji Liu·Mengbin Ye·Brian D. O. Anderson·Tamer Başar·Angelia Nedić
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper considers a discrete-time opinion dynamics model in which each individual's susceptibility to being influenced by others is dependent on her current opinion. We assume that the social network has time-varying topology and that the opinions are scalars on a continuous interval. We first propose a general opinion dynamics model based on the DeGroot model, with a general function to describe the functional dependence of each individual's susceptibility on her own opinion, and show that this general model is analogous to the Friedkin-Johnsen model, which assumes a constant susceptibility for each individual. We then consider two specific functions in which the individual's susceptibility depends on the \emph{polarity} of her opinion, and provide motivating social examples. First, we consider stubborn positives, who have reduced susceptibility if their opinions are at one end of the interval and increased susceptibility if their opinions are at the opposite end. A court jury is used as a motivating example. Second, we consider stubborn neutrals, who have reduced susceptibility when their opinions are in the middle of the spectrum, and our motivating examples are social networks discussing established social norms or institutionalized behavior. For each specific susceptibility model, we establish the initial and graph topology conditions in which consensus is reached, and develop necessary and sufficient conditions on the initial conditions for the final consensus value to be at either extreme of the opinion interval. Simulations are provided to show the effects of the susceptibility function when compared to the DeGroot model.

Explore related subjects

cs.SIcs.MAcs.SYeess.SYmath.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ji Liu, Mengbin Ye, Brian D. O. Anderson, Tamer Başar, Angelia Nedić. 2017-09-21. Discrete-Time Polar Opinion Dynamics with Susceptibility. https://doi.org/10.1109/cdc.2018.8619071

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Two Fault Lines: Latent Polarity Geometry in X Community Notes

Community Notes is X's crowdsourced fact-checking system. A note is published beneath the post it corrects only when raters who usually disagree both rate it helpful, a design called bridging. To apply that rule, the system learns who disagrees with whom from the ratings alone, placing every rater and note on one line, the polarity axis. Every scorer in the production pipeline uses a single axis. Refitting the base model these scorers share on the full public data (212.9M ratings, 2.33M notes, 1.07M raters), we find that one axis is too few. The space is at least two-dimensional. The first axis is left/right politics, while the second, which we interpret as trust in institutions, is largely independent of the first. A held-out test confirms that the second axis improves prediction of unseen ratings, while a third adds little. A second rater dimension learned from one set of topics predicts how raters judge COVID and Ukraine notes excluded from the fit, so it does not merely restate subject matter. Among heavily rated notes that barely divide raters politically, the published share falls from 71.5% to 11.7% as second-axis disagreement grows. A one-axis fit records these notes only as weakly polarised and less helpful; the information that raters at one end of the second axis support them is lost. Authors write notes matching their own position on both axes (r = 0.538 and 0.358), and a small minority of raters cast most ratings (Gini = 0.718). Fewer notes are published in the smallest language communities, but the shortfall is in ratings received, not in how the rule treats them. Keeping ratings per note constant, only Hindi stays below the global rate of 10.85%, and Greek moves from 7.76% to 11.68%. We argue for a bridging model with more than one axis of disagreement, and for recruiting raters in the languages the current design reaches least.

cs.SI↗
arXiv2026

Setting the clock: Evaluating temporal window parameters for coordinated behavior detection

Coordinated behavior is a central mechanism of online collective action. On social media platforms, it can support legitimate mobilization, but it can also be exploited in disinformation campaigns, astroturfing, and information operations. Detecting coordinated behavior on social media platforms typically relies on coordination networks, where users are linked when they perform similar actions within shared temporal windows. While the temporal window is central to how coordination is operationalized, it is often treated as an implementation detail rather than as a substantive modeling decision. This paper presents a first analysis of how two key temporal parameters, window length and stride, affect the detection of coordinated communities within information operation campaigns. We find that window length determines which coordination patterns are detectable, while window stride has negligible effect on precision and recall. Our analysis highlights selecting appropriate temporal window parameters as an open methodological challenge requiring careful treatment.

cs.SI↗
arXiv2026

Auditing bipartite motif interpretations: a worked example with conservation checks and open-path decomposition

Motif profiles of bipartite agent-object networks, such as tourist-site visits and customer-item transactions, are read as evidence about structural roles and about differences between networks, often without asking what the two degree sequences already fix. In a simple bipartite graph the induced k-fan count on one node type is a sum of degree combinations, so it has zero variance under a null that preserves both degree sequences. We apply this known result to a reconstructed tourism rating network of 17 tourists, 80 sites and 637 edges, the sole inferential worked example, and, as a provenance-limited illustration, to published motif-instance aggregates over 36 monthly luxury customer-item networks. The four fan classes are exact functions of the degree sequences: in the tourism network the raw fan counts and the size-3 two-fan ratio (84.7% fan-out) restate those sequences. The published luxury counts require at least 89,502 customer-item edges against 26,451 reported transactions, so their 99.8% fan-in is reported as a descriptive value only. Against a hard bipartite configuration null, the four-cycle count is degree-consistent (z about +1.0) and the open path is deficient (z about -5.8) by 2,243 instances, 2.4% of the null mean; the deficit survives every leave-one-tourist-out re-run (z -4.5 to -8.1). An exact identity splits it at the point estimate into 64.4% mixing and 35.6% four-cycle, but that split is not an attribution: the observed mixing term lies below all 500 null samples, the two components are almost collinear under the null (r = 0.968), and the mixing share ranges from 36.6% to 116.5% under leave-one-tourist-out deletion. The deficit is extreme relative to the sampled null, while its class-level interpretation is undetermined and unstable. We give a four-step pre-interpretation check and a reference implementation.

cs.SI↗