A new degree of freedom for opinion dynamics models: the arbitrariness of scales

Dino Carpentras; Alejandro Dinkelberg; Michael Quayle

Home/Archive/arXiv

arXiv · 2010.04788

A new degree of freedom for opinion dynamics models: the arbitrariness of scales

Dino Carpentras·Alejandro Dinkelberg·Michael Quayle

View original source ↗Read source document ↗Export metadata ↓

Abstract

Opinion dynamics models have been developed to study and predict the evolution of public opinion. Intensive research has been carried out on these models, especially exploring the different rules and topologies, which can be considered two degrees of freedom of these models. In this paper we introduce what can be considered a third degree of freedom. Since it is not possible to directly access someone's opinions without measuring them, we always need to choose a way to transform real world opinions (e.g. being anti-Trump) into numbers. However, the properties of this transformation are usually not discussed in opinion dynamics literature. For example, it would be fundamental to know if this transformation of opinions into numbers should be unique, or if several are possible; and in the latter case, how the choice of the scale would affect the model dynamics. In this article we explore this question by using the knowledge developed in psychometrics. This field has been studying how to transform psychological constructs (such as opinions) into numbers for more than 100 years. We start by introducing this phenomenon by looking at a simple example in opinion dynamics. Then we provide the necessary mathematical background and analyze three opinion dynamics models introduced by Hegselmann and Krause. Finally, we test the models using agent-based simulations both in the case of perfect scales (infinite precision) and in the case of real world scales. Both in the theoretical analysis and in the simulations, we show how the choice of the scale (even in the case of perfect accuracy and precision) can strongly change the model's dynamics. Indeed, by choosing a different scale it is possible to (1) find different numbers of final opinion clusters, (2) change the mean value of the final opinion distribution up to a change of $\pm 100 \%$ and (3) even transform one model into another.

Explore related subjects

physics.soc-ph math.DS

Keep this discovery

BibTeX RIS

Dino Carpentras, Alejandro Dinkelberg, Michael Quayle. 2020-10-09. A new degree of freedom for opinion dynamics models: the arbitrariness of scales. https://arxiv.org/abs/2010.04788

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

KEEP EXPLORING

Related papers

arXiv2026

Energy pathway variety and the progress of the energy transition in European countries

The integration of new energy forms into existing energy infrastructure has emerged as a critical challenge in the context of the pursuit of a sustainable energy transition. One of the main challenges is understanding how this integration takes place not only from the introduction, but also as energy follows existing paths or creates new ones through which it is transformed and used by different activities. Here we introduce techniques from network science to analyse this process for the case of 29 European countries between 1992 and 2021. We study how new energy forms increase or decrease the variety (heterogeneity) of paths through the system of each country by establishing new ones and replacing or phasing out existing ones. We find that the transition to systems based on renewable energy is characterised by an initial increase in the variety of paths while the heterogeneity of paths decreases at the end of the transition, when the proportion of non-renewables in the system tends to zero. We then demonstrate that greater heterogeneity (complexity) is associated with larger annual fluctuations in the proportion of non-renewable sources in the system, establishing a direct relationship between the progress of the transition and the complexity of the energy system in which it occurs. This contributes to the understanding of general properties of the dynamics of the energy transition and effects that accelerate or deter it.

physics.soc-ph↗

arXiv2026

Fundamental limits to identifying node and tie memory in temporal networks: marginal artefacts and spreading dynamics

Temporal-network models attribute memory in contact data to either node self-excitation (branching ratio n_node) or tie reinforcement (kappa), carrying major consequences for epidemic spreading. We prove that when event initiators are observed, the two mechanisms are orthogonal: the Fisher information is block-diagonal and neither trades off against the other. In undirected proximity data, where initiators are unobserved, marginalising over them couples the mechanisms into a structural confound that survives posterior smoothing. On empirical proximity, messaging, and email records, however, a cruder failure dominates: fitted node memory is pinned to the inter-event marginal law and remains virtually invariant across latent label posterior samples (coefficient of variation below 1%). An inter-event-order shuffle test and burstiness-memory diagnostics reveal that exponential-Hawkes node memory is recovered from none, while tie reinforcement remains identifiable throughout. This near-unidentifiability is intrinsic, not an artefact of the exponential kernel: refitting flexible scale-free (sum-of-exponentials) kernels on synthetic power-law self-exciting processes fails to distinguish genuine node memory from memoryless renewal controls, with identical collapses recurring on algorithmic networks (edit bots, cloud microservices) and cortical spiking. Downstream epidemic consequences are quantitative: simulations fitted to empirical contact records under-predict outbreak sizes by up to a factor of 2.5 and shift the epidemic threshold. We conclude that observational temporal networks face a two-fold identifiability boundary: contact directionality is essential to decouple tie reinforcement, whereas heavy-tailed node self-excitation is intrinsically unidentifiable from contact timings alone.

physics.soc-ph↗

arXiv2026

Assessing extreme flood impacts on urban rail transit: A passenger-oriented, resilience-informed framework

Urban rail transit systems (URTSs) are increasingly exposed to extreme floods following heavy precipitation, yet passenger travel impacts are often assessed through delay-based indicators that overlook infeasible journeys under large-scale disruptions. This study develops a passenger-oriented, resilience-informed framework for assessing flood impacts on URTS journeys from disruption onset to recovery completion. The framework presents a novel six-category classification of journey impacts, explicitly considering rerouting, alternative station use, and a delay threshold. It is demonstrated through hourly dynamic simulations of 15 London URTS lines under 30-year, 100-year, and 1,000-year flood risk scenarios. Results indicate that severe flood disruptions lead to substantial unsatisfied demand, driven primarily by unavailable routes rather than unacceptable delays. Compared with finer behaviour adjustments, rerouting dominates travel impacts. These findings highlight the significance of moving beyond delay-based assessment and provide valuable evidence on essential behavioural mechanisms for strategic-level stress testing intended to inform URTS flood resilience intervention planning.

physics.soc-ph↗