Vladimir A. Lefebvre, "The Law of Self-Reflexion". Reflexive Processes and Control,
2002, Vol. 1, No.2, pp. 91-99.
The centuries-old philosophical idea that man has an image of the self containing
an image of the self (of the second order) obtains a new life in the mathematical
model of the subject possessing reflexion. One assumption underlying the model is
that the subject tends to generate patterns of behavior such that some kind of
similarity is established between the subject himself and his second order image of
the self. We demonstrate that this model allows a single explanation for three
diverse, experimentally observed phenomena: (a) the nonlinear relation between
magnitude estimation and categorization of identical stimuli (Parducci, Stevens,
Galanter), (b) the avoidance of the value of 0.5 in estimating stimuli equidistant
from two samples on a psychological scale (Poulton, Simmonds), and (c) the formal
correspondence between, on the one hand, frequency of choice for particular
alternatives and, on the other, reinforcement rate, found in some experiments with
animals and people (Herrnstein, Baum). The results obtained allow us to
hypothesize that the reflexive metaphor represents a general principle for
regulation of both human and animal behavior.
Vladimir A. Lefebvre and Jack Adams-Webber. "Functions of Fast Reflexion in
Bipolar Choice”. Reflexive Processes and Control. 2002, Vol. 1, No.1, pp. 29-40.
We demonstrate here how to theoretically deduce a formal model of bipolar choice
based on a general definition of the self-reflexive system and one assumption
which we called the Axiom of the Second Choice. We show further that such a
deduction of the model reveals its unexpected connection to the relations between
an internal variable of the self-reflexive system, a partial derivative of the entropy
of the environmental influence, and a partial derivative of the entropy of choice
made by the system. This connection allows us to expand the two-alternative
model of bipolar choice to the case of an arbitrary number of alternatives.