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Mathematical models in cognitive decision-making

Can we quantify choices?

The simple answer to this question is yes because even if you do not know it, we rank different choices in our heads all the time. Whether it's deciding what to have for breakfast, choosing a route to work, or evaluating job offers, our minds are constantly engaged in the intricate process of decision-making.


In this article, we cover some of the mathematical techniques we use to make these decisions.


Bayesian statistics


Bayesian statistics, named after Thomas Bayes, is a branch of statistics that employs probability theory to quantify and update our beliefs or degrees of certainty about events or hypotheses. At its core is Bayes' Theorem, which is a fundamental principle in Bayesian inference. Bayes' Theorem provides a framework for updating our initial beliefs (prior probabilities) with new evidence (likelihood) to arrive at revised beliefs (posterior probabilities).


One of the main reasons for the theorem’s popularity is the validity of what it was proposing. At its essence, Bayes' Theorem acknowledges that our beliefs and understanding of the world are not fixed but can and should change as we learn more information. Hence, the likeliness of events changes as new information surfaces which makes perfect sense now but was incredibly revolutionary when the theorem was first introduced.


This technique is undeniably used as core cognitive decision-making process helping us make choices based on the likelihood of events.


Game theory and utility theory


Game theory and utility theory serve as essential mathematical tools in our exploration of cognitive decision-making.


Game theory reveals the strategic thinking behind decisions and their consequences, shedding light on complex interactions that influence our choices in various contexts, such as economics and social behaviour.


The study of Game theory includes evaluating and optimising payoff matrices which are the framework to model the payoff from the combination of different decisions. An example is shown below where Alice is the row choices and Bob are the column choices. Alice and Bob’s payoffs are dependent on each other’s actions so decision making becomes difficult which is one of the reasons studying game theory is so interesting.


Utility theory, which has ties to Game theory, quantifies how individuals assess the desirability of options. The more you desire an outcome, the higher amount of utility you assign to it. The theory plays a pivotal role in understanding decision preferences and trade-offs. By analysing utility functions, we gain insights into how individuals optimize their choices to maximize satisfaction, aligning our understanding of human decision-making with mathematical precision.


Other mathematical frameworks and applications


In addition to Bayesian statistics, game theory, and utility theory, several other mathematical frameworks enrich our understanding of cognitive decision-making. These include:

-        Markov Decision Processes (MDPs): Essential for sequential decision-making and reinforcement learning, used in robotics, artificial intelligence, and operations research.

 

-        Prospect Theory: Crucial for understanding how individuals make decisions involving risk and uncertainty, particularly in fields like economics and behavioural psychology.

 

-        Decision Trees: Widely used for visualizing complex decision-making processes and often applied in data analysis and operations research.

 

-        Neural Networks: Critical for modelling complex cognitive decision-making processes, particularly in machine learning and deep learning applications.


I would like to thank you for reading. Be sure to check out other mathematics articles on the site!



Written by Temi Abbass

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