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The paper designs a quantum model of decision-making (QMDM) that utilizes neuroscientific evidence. The new model provides both normative and positive implications to economics. First, it enhances the study of decision-making which is an extension of the expected utility theory (EUT) in mathematical economics. Second, we demonstrate how the quantum model mitigates drawbacks of the expected utility theory of today.

This paper provides a novel quantum model of decision-making (QMDM) for mathematical economics. The model approach is based on recent neuroeconomic evidence [

The remainder of the paper is structured as follows. Section 2 presents a literature review. In Section 3, we describe the QMDM. This model enables us to get a better understanding of the role of the decision-making process. Section 4 concludes the paper.

Until today, the dominant decision-making model in economics is the EUT. Von Neumann and Morgenstern [

Definition 1 A revealed preference relation is defined as

Definition 2 The utility function

The function

Despite its rigorous foundation and tremendous flexibility of the EUT, there are several caveats and unsolved issues. These limitations are illustrated by so-called decision-making paradoxes, for instance, the St. Petersburg paradox [

Even more problematic, the standard and alternative theories are unable to explain the dynamic inconsistency paradox by Kydland and Prescott [

where x and y are the choice alternatives,

A quantum model eases all problems significantly and the approach is backed by neuroeconomic evidence. The working of sophisticated quantum processes and networks was discovered already by Max Planck a century ago [

The advantage of a QMDM is simple. First, it could be interpreted as a generalization of the EUT. Second, it solves the decision-making paradoxes and it is in line with recent research in neuroeconomics. The QMDM provides two innovative issues: First, it demonstrates why people sometimes choose or prefer low utility options; Second, the model considers the impact of groups and thus the interaction mechanism during the decision- making process. Consequently, the QMDM does not only tackle the present decision-making paradoxes, it explains the individual reasoning within groups, such as the unexplained error-attenuation effect.

In this section, we demonstrate the mechanism of the QMDM. In particular, we illustrate a solution to the following problem: people often choose an option with lower utility because they are more attracted to the alternative, however, this fact cannot be modeled within the standard EUT. The QMDM nicely solves this issue.

Let us consider a group of agents. Each agent A is a decision-maker, whose decisions are influenced by other group members. Agents choose among several choices, called lotteries or prospects. Each prospect is a vector in a Hilbert space

where

This is a Hilbert space, or in economic terminology the decision space of the whole group. Usually, an agent A considers a set of prospect states, such as

in the space of mind^{1} Based on a concept of a prospect operator, I define the prospect probabilities to be the average of the prospect operator. A prospect operator is each prospect

with the property of

and on the other hand, the so-called attraction factor

These two elements have the property that the probability of a prospect

The utility factor ^{2} that can be normalized as

Respectively, the attraction factor satisfies the following property

^{1}The ordering procedure is discussed in [

^{2} where

According to recent neuroscientific research by Krajbich et al. [

In summary, the prospect probability in Equation (9) consists of two terms: the utility and the attraction term. A prospect is more attractive if it provides more certain gain or less uncertain loss. In the end, the decision- maker chooses the most preferable prospect with the highest probability. Such a prospect is called the optimal prospect

Let me demonstrate the working of the model with a simple example. Suppose prospect

Since the utility factor is calculated with

Proposition 1 Let prospect

Proof. Given that

and for

The proof for the indifference relationship follows respectively.

Thus, this model can disentangle the “economic utility” into an objective “utility factor” and a subjective “attraction factor”. However, the key difference of the QMDM is due to the attraction factor. This is definitely a novel element in the economic decision-making literature. Moreover, it allows computing the attraction factor with experimental data, such as

Even the proponents of the drift-diffusion model find similar evidence. For instance, Krajbich et al. [

All in all, the “Quantum Model of Decision-Making” (QMDM) demonstrates useful insights on the allocation and application of individual and group choices. I demonstrate that this model is an extension of the Expected Utility Theory (EUT) and thus the QMDM is just the generalization of the present workhorse model in economics. Consequently, the QMDM could be applied as a new framework in theoretical economics without changing the whole economic thinking. Moreover, the model enhances the modeling of choices while considering the present decision-making paradoxes and neuroscientific evidence. Even if, this model is not the final development in the ongoing debate, it is a tractable alternative and does not open the Pandora’s Box of rational choice theory in special and economic thinking in general.

I would like to thank two anonymous referees for helpful comments and my IB-research assistants for editing the paper. Moreover, I gratefully acknowledge financial support from the RRI-Reutlingen Research Institute.