Bayesian models of uncertainty in Ellsberg problems

Waterstone, Harry (2024): Bayesian models of uncertainty in Ellsberg problems. Dissertation, LMU München: Graduate School of Systemic Neurosciences (GSN)

Abstract

Decision theory, a framework for modelling human decision making in uncertain situations, plays an important role in cognitive science. It enables researchers to mathematically represent the different options open to a decision-making agent, as well as the preferences an agent has, and use these in a calculation to measure and predict the way agents decide. Decision theoretic models are built in experiments in behavioural cognitive science as well as in neuroscience, and are used to structure the experimental manipulations that generate the data of interest, whether that data is in the form of decision responses, or also scanning data indicating neural activation. A huge volume of research in formal decision theory focuses on fallacies and paradoxes. A fallacy is a situation where a decision rule or process looks at first glance to be reasonable, but leads to sub-optimal results, and a paradox is a situation where following a formal rule, in some situations, leads to contradiction. Both of these situations are interesting and fruitful areas for research as they illuminate the edges and limitations of formal models: the way we ad- just the formal model to account for these issues has important consequences for the way we do science. In this dissertation, I use the tools of philosophical conceptual analysis and Bayesian network modelling to analyse two paradoxes of interest. In my paper 1, I present a new way to mathematically model a situation known as the Ellsberg paradox, using a Bayesian network model. My paper 2 presents a conceptual classification of different categories of uncertainty that reveal another paradox. And my paper 3 combines the insights from the first two papers, extending the Bayesian network model to account for multiple preferences regarding the presentation of uncertainty.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Ellsberg, ambiguity, preferences, uncertainty, Bayesian modelling
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 570 Life sciences
• Faculties: Graduate School of Systemic Neurosciences (GSN)
• Language: English
• Date of oral examination: 5. July 2024
• 1. Referee: Hartmann, Stephan
• Signature of the printed copy: 0001/UMC 32082