### Analytical Proof of Bounded Rationality Theory on Unitas SACCO Members in Kenya: Bayesian Approach

#### Abstract

The first of the four fundamental assumptions in

economics and standard finance is that humans are rational

actors, which does not hold good all the time. This anomaly

begot behavioural finance that recognizes instances of irrational

decision making in human beings. Rationality bounds in

financial decision making as espoused in bounded rationality

theory need to be determined to reflect how humans actually

behave rather than how they should behave; to pave way for

modification of classical economics and standard finance

theories. This analytical proof of bounded rationality utilizes

LOT-R parameterized cumulative prospect theory decision

weights function to transform subjective to objective

probabilities. Human intrinsic perceptions and self proclaimed

prospects measured on a 9 point Likert scale are converted into

subjective probabilities. I construct a rationality measuring

instrument on a 0 – 1 scale using the probabilities of making a

rational decision, of observing economic well being increase

after an irrational decision and that of observing economic well

being increase after a rational decision as inputs. Thereafter, I

show that the multiperiod model forms an absolutely converging

sequence in the open interval (0, 1), hence bounded. The

instrument is a Bayesian learning model whereby wealth

movement is the observable dimension variable and the

rationality to be determined is the unobservable dimension

variable. Stochastic discrete time case in a binomial setting is

explored. The concept of entropy from the second law of

thermodynamics in physical chemistry – information theory

version is expected to feature prominently and to guide

recommendations likely to yield global lessons.

economics and standard finance is that humans are rational

actors, which does not hold good all the time. This anomaly

begot behavioural finance that recognizes instances of irrational

decision making in human beings. Rationality bounds in

financial decision making as espoused in bounded rationality

theory need to be determined to reflect how humans actually

behave rather than how they should behave; to pave way for

modification of classical economics and standard finance

theories. This analytical proof of bounded rationality utilizes

LOT-R parameterized cumulative prospect theory decision

weights function to transform subjective to objective

probabilities. Human intrinsic perceptions and self proclaimed

prospects measured on a 9 point Likert scale are converted into

subjective probabilities. I construct a rationality measuring

instrument on a 0 – 1 scale using the probabilities of making a

rational decision, of observing economic well being increase

after an irrational decision and that of observing economic well

being increase after a rational decision as inputs. Thereafter, I

show that the multiperiod model forms an absolutely converging

sequence in the open interval (0, 1), hence bounded. The

instrument is a Bayesian learning model whereby wealth

movement is the observable dimension variable and the

rationality to be determined is the unobservable dimension

variable. Stochastic discrete time case in a binomial setting is

explored. The concept of entropy from the second law of

thermodynamics in physical chemistry – information theory

version is expected to feature prominently and to guide

recommendations likely to yield global lessons.