· Belief systems
· Minimizing cognitive dissonance
· Local and global minima
· Changes in our belief systems
Belief systems can be modelled as several individual beliefs linked by consistency constraints. To design a simple model, we use the following two premises:
(i) Beliefs as simple dual values: either true or false.
(ii) Consistency constraints are either positive or negative.
If a consistency constraint is positive, both interconnected beliefs must have the same truth value.
If a consistency constraint is negative, both interconnected beliefs must have the opposite truth value.
Minimizing cognitive dissonance
We could model that an individual seeks to minimize the cognitive dissonance <https://en.wikipedia.org/wiki/Cognitive_dissonance> of its belief system by minimizing the number of inconsistencies.
For example, assuming that the consistency constraints are fixed, one could experience the following change in belief system, illustrated below.
Local and global minima
Minimizing cognitive dissonance may be a very hard problem to solve if you have a system with numerous beliefs.
In order to think about the problem, the concepts of global and local minima are useful. They are illustrated below:
Changes in our belief systems
There might be different states in which our beliefs are in such way that cognitive dissonance is minimized relative to other states.
And there will be only one state in which the cognitive dissonance is minimized among all the different beliefs configurations.
Therefore, we may be in a local minimum in terms of cognitive dissonance, but if we reconsider our beliefs, we may find other local minimum.