Limitations in bounded-rational probability updating
Abstract
Modern life is fraught with complicateddilemmas, for example, decisions of personal relevance (such as whether to commit to a mortgagefor the purchase of a home or not), decisions with societal impact (e.g., which party to vote for in anelection), and decisions by military, political, or financial agents (for example, what kind of aidshould a beleaguered friendly nation receive). Increasingly, the complexity of such decisions can bestaggering. At the same time, in our societies, information accessibility, availability, and quality havenever been greater. There are some dangers (notably relating to mis-information), but, with somecare, individuals even in the most remote locations (geographically and metaphorically) in oursocieties have an abundance of information at their disposal to guide their decisions. So, can thechallenge from complex decision dilemmas be mitigated from information overload, The established framework for understanding rational decision making is Bayesianprobability theory, a set of rules for inference under uncertain circumstances, including in relationto updating beliefs as new information becomes available. Bayesian theory benefits from powerfulnormative and adaptive justifications. Unfortunately, for any bounded-rational agent, employing(full) Bayesian theory is not possible. The problem is that Bayesian theory requires that we are ableto answer any combination of questions concurrently, which quickly becomes intractable in anyrealistic situation. This intractability has been at the heart of one of the most influential debates inbehavioral science, has been associated with three Nobel prizes (for Simon, Kahneman, and Thaler),and has led to some of the most influential ideas in psychology (such as heuristics and biases).If full Bayesian inference is not possible, what are options for bounded-rational inference?We have been at the forefront of an innovative approach in decision making, utilizing quantumtheory, the probability rules from quantum mechanics, without any of the physics. In quantumtheory, questions are divided into sets, such that within each set the situation is entirely classical,but across sets non-classical effects arise, such as interference effects. Thus, quantum theory can bethought of as a locally Bayesian theory. We think that many empirical findings considered to be(Bayesian) fallacies can be explained using quantum theory. Crucially, quantum reasoning is(informationally) ‘cheaper’ than Bayesian reasoning. So, we think that under conditions ofinformation overload, quantum reasoning is more likely to be employed.Consider then a modern decision maker faced with a difficult decision. Her aides may beproviding increasing amounts of information to help her settle her course of action. However,information overload may force a transition from Bayesian to quantum reasoning. What are theimplications for probability updating with quantum rules? The foundation of this proposal is a novelresult we recently discovered concerning multiple pieces of information all pointing in the samedirection- when the relevant representations are Bayesian, then more information reinforces theconclusion consistent with any single piece of information. However, when the representations arequantum, because of interference effects, any piece of information may undermine others, leadingto a deceleration in probability updating and reduced confidence in the conclusion.The proposed project will mathematically substantiate expectations for probability updatingfrom multiple pieces of information, with Bayesian vs. quantum representations, offer anexperimental demonstration to evaluate corresponding predictions, and explore some additionaltechnical directions (notably concerning the origins of quantum representations in cognition).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 22, 2024
- Source ID
- FA86552317220
Entities
People
- Emmanuel M. Pothos
Organizations
- Air Force Office of Scientific Research
- City, University of London
- United States Air Force