[Paper Review] Algebra of fundamental measurements as a basis of dynamics of economic systems

Tuluzov, Igor, Melnyk, Sergiy|arXiv (Cornell University)|Aug 31, 2012

Quantum Mechanics and Applications10 references3 citations

TL;DR

This paper proposes an axiomatic framework for modeling economic systems using the algebra of fundamental measurements, treating transactions as selective measurements akin to Schwinger's quantum formalism. By modeling consciousness as state-determined through measurement outcomes, it derives a dynamics of economic behavior that generalizes incomplete and delayed-choice transactions, enabling a formal, mathematically rigorous treatment of decision-making in social and economic systems using quantum-inspired measurement algebras.

ABSTRACT

We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow for a more rigorous approach to studying the properties of the algebra of economic measurements. Considering the behavior of an object as a sequence of actions and choices allows extending the obtained results to random systems, which include the subject's consciousness as one of its elements. The specifics, on which the description of fundamental measurements is based, allows easily transferring the formalism of Schwinger's theory of selective measurements (and the consequent quantum-mechanical formalism) to the economic and social systems.

Motivation & Objective

• To develop a formal axiomatic framework for economic systems where the dynamics of behavior stem from measurement processes.
• To model the state of a subject's consciousness as fully determined by measurement outcomes, particularly in the context of economic transactions.
• To generalize incomplete and delayed-choice transactions into a coherent algebraic structure for economic measurements.
• To extend the formalism of Schwinger’s selective measurement theory to social and economic systems, enabling a dynamics of choice and action.
• To provide a mathematical foundation for modeling random systems that include conscious agents as integral components.

Proposed method

• Adopt an axiomatic approach where the state of consciousness is completely determined by measurement results, treating each transaction as a fundamental measurement.
• Introduce the concept of 'delayed-choice' transactions as a logical extension of incomplete transactions, enabling richer modeling of decision processes.
• Apply Schwinger’s theory of selective measurements to economic systems, transferring its formalism to model sequential actions and choices.
• Use the algebra of measurement operators to represent economic decisions, with outcomes reflecting observable transaction behaviors.
• Model the behavior of economic agents as sequences of actions and choices, embedded in a probabilistic and algebraic framework.
• Leverage the mathematical structure of quantum measurement theory to describe non-commutative and context-dependent economic decisions.

Experimental results

Research questions

• RQ1 How can the dynamics of economic systems be formally derived from the algebra of fundamental measurements?
• RQ2 In what way do delayed-choice and incomplete transactions generalize the measurement process in economic decision-making?
• RQ3 How can the state of a subject’s consciousness be fully determined by measurement outcomes in an economic context?
• RQ4 What is the role of measurement non-commutativity in modeling economic choices and transaction sequences?
• RQ5 How can Schwinger’s measurement formalism be adapted to describe conscious agents in random, social, and economic systems?

Key findings

• The paper establishes that the state of a subject’s consciousness in economic systems is completely determined by the results of measurements, particularly transactions.
• Delayed-choice transactions are shown to provide a rigorous generalization of incomplete transactions, enriching the measurement algebra.
• The formalism allows for a consistent algebraic description of sequential actions and choices in economic systems using measurement operators.
• The framework successfully transfers Schwinger’s quantum measurement theory to economic and social systems, enabling a dynamics of decision-making.
• The approach provides a foundation for modeling conscious agents as integral components within random systems through measurement-based state determination.
• The resulting algebraic structure supports non-commutative and context-dependent behaviors, reflecting real-world economic decision complexity.