NICOP - Anticipating decisions and Bells bound
Abstract
Research into the normative and descriptive foundations of decision making has been attractingintense scrutiny, partly because of the immense scope for practical application, including improvedprediction for decision making, normative prescription in situations of applied significance, and theidentification of the principles which could support artificial decision makers. A predominantapproach has been the classical/ Bayesian probability theory (CPT), but a number of widelypublicized discrepancies between behavior and CPT prediction have led to several alternativeapproaches. A key corresponding realization is that CPT does not provide the only formal frameworkfor decision making: an alternative possibility is the so-called Quantum probability theory (QPT), therules for how to assign probabilities to events from quantum mechanics, without any of the physics.There are many differences between CPT and QPT, which provide a nuanced picture for thecircumstances when CPT or QPT might be the more appropriate framework for understandinghuman decisions. For example, in CPT events are definitely true or false, but in QPT there are eventswhich can be neither. In CPT a set of questions can in principle all be resolved concurrently, so thatwe can talk about the probability of any combination of question outcomes (these joint probabilitiesalways have to exist). In QPT some questions are incompatible and this means that it is typicallyimpossible to resolve them concurrently. For incompatible questions, certainty for one introducesuncertainty for the other. Probabilistic inference in QPT is strongly contextual and perspectivedependent, while in CPT it is not (naturally) so.The application of QPT in decision theory is still relatively novel. There has been extensivework exploring what novel predictions can be made by QPT decision models, including in relation tothe key issue of normative prescription. The proposed research is in this vein: specifically, we explorethe extent to which decision makers can correlate with each other. The question of correlation is ofkey significance in many situations, both in relation to cooperation/ coordination and in adversarialcontexts, in relation to prediction and anticipation of hostile actions.A classical expectation is that two decision makers, Alice, Bob, can hope to coordinate, ifthey exchange some information, prior to going their separate ways. If at the time of the decisionmaking, Alice, Bob do not communicate directly with each other, then the degree of correlation fortheir answers must be constrained by a specific bound, Bell~s bound, after the physicist whopioneered these ingenious ideas. Bell~s bound still allows for high correlations in decision outcomes,which may be a result of e.g. Alice, Bob determined to coordinate as much as possible. QPT allows asubtler perspective: suppose Alice, Bob~s questions are contextual, so that the optimal answer forAlice~s questions depends on Bob~s questions and vice versa. Then, it is possible for Alice, Bob tosuper-correlate, that is, correlate to a degree not allowed classically. Super-correlation cannot beachieved just by coordination prior to separation. Alice, Bob need to have a sufficiently deepsituational understanding of each other~s circumstances, to anticipate not just the answers but alsothe questions.Overall, for the first time, using the technical tools developed in QPT to study supercorrelations,we propose to explore the possibility of super-correlations in human decision making. Apositive result will revolutionize our understanding of the extent to which two (or more) individualscan coordinate with each other and provide insight into the circumstances that make supercorrelationspossible.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2018
- Source ID
- N629091912000
Entities
People
- Emmanuel M. Pothos
Organizations
- Office of Naval Research
- United States Navy