  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.
