Preparing a (quantum) belief system

Abstract

In this paper we investigate the potential for persuasion linked to the quantum indeterminacy of beliefs. We first formulate the persuasion problem in the context of quantum-like beliefs. We provide an economic example of belief manipulation that illustrates the setting. We next establish a theoretical result showing that in the absence of constraints on measurements, any belief state can be obtained as the result of a suitable sequence of measurements. We finally discuss the practical significance of our result in the context of persuasion.Receiver's decision to act depends on her beliefs about the world. In [11] and related works the beliefs are given as a probability distribution over a set of states of the world. A central assumption is that uncertainty is formulated in the standard classical framework. As a consequence the updating of Receiver's beliefs follows Bayes' rule.However as amply documented the functioning of the mind is more complex and often people do not follow Bayes rule. Cognitive sciences propose alternatives to Bayesianism. One avenue of research within cognitive sciences appeals to the formalism of quantum mechanics. A main reason is that QM has properties that reminds of the paradoxical phenomena exhibited in human cognition. Quantum cognition has been successful in explaining a wide variety of behavioral phenomena such as disjunction

Targeting in quantum persuasion problem

“…This is generally not the case in the quantum context where opting for a sequence of measurements can significantly increase Sender's persuasion power. We already mentioned an important result obtained in [7]. Namely, if Sender is not constrained with respect to the number of measurements, then starting from any prior he can with near certainty have Receiver's belief transit into any targeted belief state.…”

“…An important feature of the quantum situation is that this relation is probabilistic: the state of the system only defines the probabilities for the different outcomes. We represent MD M as follows 7 A behavioral justification for this rule is provided in [8]. And in [3] Lüders rule is shown to be a direct generalization of Bayes rule.…”

“…Given an initial state (a prior) B and a final state (target) T , we search for an IS (including one MD or a sequence of MDs) which transforms B into T with the largest possible probability. We know from ( [7]) that with a large enough sequence of measurements, starting from any prior, the probability for that transition can be made arbitrary close to 1. In the next section we show that this probability can be made larger than 1/n with two measurements only.…”

“…In this paper we build further on a theoretical result [7] that establishes the power of unconstrained belief manipulation or persuasion in the context of non-classical (quan-tum) uncertainty. That result was a first step in the development of Quantum persuasion theory in the spirit of 'Bayesian Persuasion' by Kamenica and Gentskow [11], hereafter KG.…”

Comparison of The Possibilities of Application of Spectrum and Gaming Theories in Modelling Market Economy Negotiations

“…Therefore, the alternatives α₂ and β₁ are now chosen as more useful. In summary, the diagonal utility matrix means that perspectives are evaluated by projecting the results of an underlying object with known benefits [17][18][19][20][21][22]. In practice, the person will appreciate the perspective by designing on subjective frameworks that will not fit perfectly with the classical version and will give negative weights to undesirable outcomes [23][24][25].…”