Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - BPI (Bayesian Peer Influence: Group Beliefs, Polarisation and Segregation)

Teaser

The objective of this research is to provide a new framework to model and analyse dynamics of group beliefs, in order to study phenomena such as group polarisation, segregation and discrimination. To do so we were planning to introduce a simple heuristic that captures how...

Summary

The objective of this research is to provide a new framework to model and analyse dynamics of group beliefs, in order to study phenomena such as group polarisation, segregation and discrimination. To do so we were planning to introduce a simple heuristic that captures how individuals learn from others’ beliefs, and to explore its properties, and analyse the implications of belief dynamics for economic and political interactions. In line with this goal, the achievements of this project so far are as follows.

Work performed

\"(i) A working paper entitled \"\"Combining Forecasts in the Presence of Ambiguity over Correlation Structures\"\" (Revise and resubmit at the Journal of Economic Theory). This working paper proposes a general form of learning from others\' beliefs. It introduces a new methodology with which we are able to consider how individuals combine forecasts and beliefs in a detail-free, general manner, without making specific assumptions. In the paper we study decision making in the presence of such a learning model. At the extreme, this model introduces the BPI heuristic, according to which individuals completely neglect correlation across information resources. Away from this extreme case, we show how individuals account for some correlation across the information sources of others and how this only depends on the BPI heuristic and a simple parameter capturing the perception of correlation. We show that in the presence of large data, individuals may revert to the extreme case of completely neglecting correlation. In that sense we endogenise the BPI heuristic. We apply this research to CDO rating, and risky and cautious shifts in group behaviour.
(ii) A published paper entitled \"\"Information Diffusion in Networks with the Bayesian Peer Influence Heuristic\"\" (published in Games and Economic Behaviour, 2018). This paper uses the BPI heuristic to analyse the convergence properties of repeated communication in networks. We show under what environments groups can learn correctly and when the BPI leads to wrong learning.
(iii) A published paper entitled The Co-evolution of Segregation, Polarised Beliefs and Discrimination: The Case of Private vs. State Education, published in the American Economic Journal: Microeconomics, 2017. In a dynamic model, we characterize a necessary and sufficient condition on initial levels of segregation and beliefs under which full polarisation of beliefs and long-run labour market discrimination are sustainable when individuals update beliefs using the BPI.
(iv) A working paper entitled \"\"Media Power via the Correlation of News Content”, with Ines Moreno de Barreda ( revise and resubmit in the Journal of Public Economics). This paper focuses on how strategic players, for example political strategists or media owners who can coordinate several media outlets, can manipulate the beliefs of individuals that use the BPI. The main take away point from the paper is how regulation on social media and news ownership can limit this type of manipulation. This paper shows how political polarisation can result from politicians and strategists abusing the BPI learning process by voters.
(v) A working paper entitled “Persuasion with Correlation Neglect’’, with Ines Moreno de Barreda, (Revise and resubmit in the Journal of Political Economy) exploring the theoretical foundations for strategic manipulation of individuals who use the BPI heuristic. This paper while laying the grounds for the paper described in (iii), allows for a richer environment and explores under what conditions individuals who use the BPI can be manipulated by others who use a simple strategy of simply repeating messages.
(vi) A working paper entitled “Immigration into Prejudiced Societies: The effects of Segregation and Echo Chambers”. In this paper we show the effect of segregation according to ethnicity for example on updating with the BPI heuristic on beliefs about different groups. This paper is in a preliminary stage.
(vii) A working paper entitled “Common Value Auctions with Ambiguity over Correlation”, with Krittanai Laohakunakorn (Revise and resubmit in the Journal of Economic Theory.). This paper uses the general belief formation environment formulated in (i), around the BPI, to explore the behavioural economics of auctions. We show that when bidders have ambiguity over correlation structures the seller’s revenue decreases for the case of common value auctions.
(viii) A survey entitled “Echo Chambers and Their Effects on Economic\"

Final results

Our novel methodology is to use insights from information theory to model how individuals perceive correlation. We formulate the BPI heuristic and explore how to generalize this approach using tools from information theory. We use this in decision theory, in models of information design by strategic players, and in game theoretical models using equilibrium analysis.

This led us to novel and unconventional models of decision making:

1. The maximum likelihood approach to combining forecasts.
2. A new model to analyse degrees of correlation neglect.
3. A novel approach to modelling populism as a simple mispecified model of the world.