Quantum Propensity in Economics

Abstract

This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations or market failures. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision-makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized, via an entropic force, to incorporate effects such as interference and entanglement that characterise human decision-making. Applications to some common problems and topics in economics and finance, including the use of quantum artificial intelligence, are discussed.

Keywords: quantum artificial intelligence; quantum cognition; quantum computing; quantum decision theory; quantum economics; quantum finance; quantum probability.

FIGURE 1

(A) A coin toss for a balanced coin can be expressed as a superposition of two states, heads and tails. (B) because the 2-norm of a probability is its square, we can also consider negative projections. (C) Applying the Hadamard transformation rotates S1 by 45 degrees clockwise which aligns with the H axis (S3).

FIGURE 2

The order effect for two questions labelled A and B. The state vector (grey line) is at an angle $\theta$ to the axes for A. The axes for B are rotated by an angle $\phi$ to those for A.

FIGURE 3

Quantum circuit for a decision B influenced by a context A.

FIGURE 4

The curves show propensity as a function of price, measured in millions of dollars. Both are centered at p = 1, but the panel on the right has a higher level of price flexibility. The arrows indicate the strength and direction of the associated entropic forces (discussed later).