31,370 research outputs found
Boltzmann-type models with uncertain binary interactions
In this paper we study binary interaction schemes with uncertain parameters
for a general class of Boltzmann-type equations with applications in classical
gas and aggregation dynamics. We consider deterministic (i.e., a priori
averaged) and stochastic kinetic models, corresponding to different ways of
understanding the role of uncertainty in the system dynamics, and compare some
thermodynamic quantities of interest, such as the mean and the energy, which
characterise the asymptotic trends. Furthermore, via suitable scaling
techniques we derive the corresponding deterministic and stochastic
Fokker-Planck equations in order to gain more detailed insights into the
respective asymptotic distributions. We also provide numerical evidences of the
trends estimated theoretically by resorting to recently introduced structure
preserving uncertainty quantification methods
Scientific Polarization
Contemporary societies are often "polarized", in the sense that sub-groups
within these societies hold stably opposing beliefs, even when there is a fact
of the matter. Extant models of polarization do not capture the idea that some
beliefs are true and others false. Here we present a model, based on the
network epistemology framework of Bala and Goyal ["Learning from neighbors",
\textit{Rev. Econ. Stud.} \textbf{65}(3), 784-811 (1998)], in which
polarization emerges even though agents gather evidence about their beliefs,
and true belief yields a pay-off advantage. The key mechanism that generates
polarization involves treating evidence generated by other agents as uncertain
when their beliefs are relatively different from one's own.Comment: 22 pages, 5 figures, author final versio
Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions
In this article, we study the nonlinear Fokker-Planck (FP) equation that
arises as a mean-field (macroscopic) approximation of bounded confidence
opinion dynamics, where opinions are influenced by environmental noises and
opinions of radicals (stubborn individuals). The distribution of radical
opinions serves as an infinite-dimensional exogenous input to the FP equation,
visibly influencing the steady opinion profile. We establish mathematical
properties of the FP equation. In particular, we (i) show the well-posedness of
the dynamic equation, (ii) provide existence result accompanied by a
quantitative global estimate for the corresponding stationary solution, and
(iii) establish an explicit lower bound on the noise level that guarantees
exponential convergence of the dynamics to stationary state. Combining the
results in (ii) and (iii) readily yields the input-output stability of the
system for sufficiently large noises. Next, using Fourier analysis, the
structure of opinion clusters under the uniform initial distribution is
examined. Specifically, two numerical schemes for identification of
order-disorder transition and characterization of initial clustering behavior
are provided. The results of analysis are validated through several numerical
simulations of the continuum-agent model (partial differential equation) and
the corresponding discrete-agent model (interacting stochastic differential
equations) for a particular distribution of radicals
Understanding opinions. A cognitive and formal account
The study of opinions, their formation and change, is one of the defining
topics addressed by social psychology, but in recent years other disciplines,
as computer science and complexity, have addressed this challenge. Despite the
flourishing of different models and theories in both fields, several key
questions still remain unanswered. The aim of this paper is to challenge the
current theories on opinion by putting forward a cognitively grounded model
where opinions are described as specific mental representations whose main
properties are put forward. A comparison with reputation will be also
presented
Scientific Advice to Public Policy-Making
A feature of policy-making today is its dependence on scientific advice to deliver public policies that are robust, credible, and effective. This paper discusses how policy-making profits from scientific advice in areas where science and technology are significant. Particular attention is given to issues holding a high level of uncertainty, either because of inherent variability, because science is incomplete or controversial, or because data are inadequate to support a definitive answer. First, we analyse the social context that characterises the relationship between science and policy-making, with a focus on the decrease of public confidence in politicians and scientists. Second, we compare three different sets of guidelines on the collection and use of expertise in policy-making (issued by the UK, Canada and the European Commission, respectively) and identify two different approaches to scientific advice in policy-making. Third, based on a set of cross-national and multi-disciplinary case studies, we look at how the relationship between science and policy-making works in practice and propose a set of recommendations towards the establishment of a more robust and effective policy-making process.Scientific advice, Policy-making, Expertise
Modelling opinion dynamics under the impact of influencer and media strategies
Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of âinfluencersâ are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel framework for opinion dynamics that can accommodate various versions of opinion dynamics as well as account for different roles, namely that of individuals, media and influencers, who change their own opinion positions on different time scales. Numerical simulations of instances of this framework show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. The framework allows for mean-field approximations by partial differential equations, which reproduce those dynamics and allow for efficient large-scale simulations when the number of individuals is large. Based on the mean-field approximations, we can study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, our framework allows us to demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to a more flexible modelling approach in opinion dynamics and a better understanding of the different roles and strategies in the increasingly complex information ecosystem
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