Control of opinion dynamics in multiple dimensions

The context of the research
The fundamental concept of opinion dynamics, that a collection of individuals interacts and updates their opinions over time, has been represented in an ever-growing varity of models. In a simple model individuals update their opinions in discrete time steps by taking a weighted average of the opinions of those around them, leadinf to a linear dynamical system. For such systems there exists clear condistions for when consensus can arise and methods to predict what opinion the group will reach. This simple model has been develpoed in a range of different directions, some include more realistic features such as online media or stubborn individuals , propose different conditions for interaction, apply alternative mathematical techniques, or make any number of other adaptations.
A major contribution is the models of Hegselmann and Krause, and Deffuant et al. which independently introduced bounded confidence: the idea that individuals only interact if thier opinions are already sufficeintly close. This condition creates nonlinearity and can lead to the formation of opinion clusters. This originally discrete time models has been adapted into continuous time models, then into stochastic models and finally into corrsponding PDE models describing the evolution of the opinion distribution in a large population. Under various parameter regimes these models can exhibit a range of interesting behaviours: in some scenarios opinions coalesce or become more moderate over time, in other cases multiple distinct opinions persist and in some cases no clear opinions emerge at all. With unprecendented access to the opinions of people across the world it is easy to see compareable situations in real life, with data from social media allowing the possibility of narrowing the gap between meathematical models and newly observable dynamics. The undeinable impact of online communication makes it increasingly important to develop our understnading of how individuals and groups opinions are formed and what can be done to avoid the spread of potentially dangerous disinformation.
Due to the complex nature of opinion dynamics, especially in modes with individulaised agents, undelaying social networks or nonlinear interactions, it is often necessary to explore the behaviour of the model through extensive simulation.
This project aims to improve the accuracy of opinion dynamics models by combining multidomensional opinions and dynamic network structure with existing models, and investigate the possibility of control in such systems.
The objectives are to exten opinion dynamics models into multiple dimensions exploring different ways in which nodes may interact based on their opinions on various topics. Incorporate dynamic network structure to mirror how individuals relationships may evolve over time in response to their (dis)agreement on various topics. Use network structure and sentiment analaysis from Twitter data to observe real multidimensional opinion formation and compare this to the behaviuors observed in models.
The novelty of the research methodology
Weighting the opinions of others natrually creates a network structure, and so the influence of social networks on opinion dynamics has been explored. However the conclusion of a dynamic network, in particular one in which the network structure is coupled with individuals opinions, is a novel development.
The potential impact, applications and benefits
If it is found that incorporating multiple opinions provides a more realistic model of opinion formation, an understanding of how such systems can be controlled could be useful in designing promotional campaigns, reducing the impace of misinformation or encoraging/ discouraging cooperation between different organisations.
This project falls into the mathematical sciences research area.
External Partener - Improbable - will provide expertise in developing data driven models, will provide technical support.

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.