Path of Least Action : Human Behavioral Scientific Dynamics Under Uncertainty : Deeper Scientific Analysis behind Maximum Utility Theory, Daniel Kahneman Prospect Theory

Equation of Human Behaviour dynamics under Uncertainty Daniel Kahneman's theory is Prospect Theory, for which he won the Nobel Prize in Economic Sciences in 2002. The theory focuses on how humans make decisions when facing risk, particularly financial risk. The theory states that individuals don't maximize utility but react to possible or perceived changes in gains or losses, which are short-term and emotional. The approach of Expected Utility Theory which was shown by Kahneman to be not valid for human behaviour based on empirical pieces of evidence. I try to show the entire episode from a scientific perspective what is possibly true or not. I have already explained in my other paper that the way the Conventional Statistical Theory of Expectation(mentioned above) as the Summation of All the Probability-weighted Outcomes might not be valid always in different scenarios, especially Human Behavioural Dynamics in the Real World. In fact, Human Behavior does follow the Path of Maximum Utility or Least Action(Energy-Time) as in Principles of Least Action in Nature but the Conventional Statistical Formula might not be the correct approach to calculate that. In fact, rather than this Human Brains follow the path of the least action/maximum stability under the given scenarios driven by the causal forces(that include randomness too) In this paper, I try to provide a scientific approach to human behavioral dynamics and how these actually occur in the realm of causal dynamics of forces like in physics. I must repeat as earlier in my other papers as well- Causal doesn’t mean the absence of Randomness and it doesn’t mean Completely Predictable & Deterministic! Human Behavior does follow the Principle of Least Action as in Nature for inanimate objects in physics in its own ways. Like Human tends to follow the minimum action, energy path, relatively short-cut under the influence of causal forces, which is also geodesic in its own space-time curvature. So, If we look at the steps of how Human behavior works scientifically. It analyses the various paths/options it has in the given scenarios, naturally analyses the utility of each path relatively and selects the path which exceeds its threshold inertial level of utility. It’s like the Laws of Nature as in Physics though parameters are often variable unlike fixed. Now the \mathbit{Utility}\ \mathbit{of}\ \mathbit{Each}\ \mathbit{Path}\ \ \mathbit{U}_\mathbit{i}\ =\ \mathbit{f}\ (\mathbit{Relative}\ \mathbit{Value},\ \mathbit{Threshold}\ \mathbit{Inertial}\ \mathbit{Expected}\ \mathbit{Level},\ \mathbit{Risk}\ \mathbit{Involved}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathbit{Probability}\ \mathbit{of}\ \mathbit{Occurrence},\ Causal weights \mathbit{Time}\ \mathbit{Horizon} \ \mathbit{e}.\mathbit{g}.\ \mathbit{Short}-\mathbit{term}\ \mathbit{Long}-\mathbit{term},\ \mathbit{etc}.\ \mathbit{Individual}\ \mathbit{Behavioral}\ \mathbit{Traits}\ \mathbit{like}\ \mathbit{Emotional}\ \mathbit{Energy}\ \mathbit{Forces},\ \mathbit{Patience}, \ \mathbit{Cognitive}\ \mathbit{Understanding}, \ \mathbit{Individual}\ \mathbit{Perspective}\ \mathbit{of}\ \mathbit{Systemic}\ \mathbit{Market}\ \mathbit{Forces}\ \mathbit{etc}.) So basically \mathbit{U}_\mathbit{i}\ =\ \mathbit{f}\ (\mathbit{Relative}\ \mathbit{Systematic}\ \mathbit{Utility}\ \mathbit{Perceived}\ \mathbit{by}\ \mathbit{Individual}\ \mathbit{of}\ \mathbit{the}\ \mathbit{Path}\ +\ \mathbit{Idiosyncratic}\ \mathbit{Relative}\ \mathbit{Perception}\ \mathbit{by}\ \mathbit{the}\ \mathbit{Individual}.) For example, an individual human naturally calculates the utility of each path /option based on the relative perception of value to self, self-preference of time period involved, personal threshold inertial level of expectation, probability of occurrence, impact involved, risk involved, emotional forces, cognitive forces and then finally traces the path which gives the maximum utility under the given causal set of forces or space-time behavioral curvature, which is also essentially the path of least action(involving energy and time). This is the scientific reason that an individual tries to trace the least possible short-cut under the influence of resultant causal forces which includes the systematic forces, and idiosyncratic natural emotional as well as cognitive understanding forces. Taking a look into the Physics from where it has appeared originally. Action S = \int_{\mathbit{t}_\mathbf{1}}^{\mathbit{t}_\mathbf{2}}\left(\mathbit{KE}-\mathbit{PE}\right)\mathbit{dt} Remember that the PE and KE are both functions of time. For each different possible path you get a different number for this action. Our mathematical problem is to find out for what curve that number is the least. Now to find out in Context of Human Behaviour how to Calculate The Action/ Utility /Value function/ Most Stability that neds to be minimized or maximized. Action/Energy/Stability= f(Relative, Value, Risk, Causal Weight, Probability, Time Period Preference, Idiosyncratic behaviours, etc..) Note: Every Human Behaviour follows the Law of Nature, Energy like Physics(if not exactly). So all these general behaviours put by Kahneman has Energy Causes, that could be different for different individuals idiosyncratically relatively in decision making, not necessarily the same absolute for all. Like higher-order analysis (model-independent approach )rather than trying to find out the absolute value of the function f ( ) and its output, trying to find out which path gives the maximum stability relative to other paths or least action. No need to find the absolute function f( ) of each path rather make it relative making it model independent. Relative Action = Reference Utility – Effective Utility to be minimized over the other paths Relatively Reference Utility is Inertia Level and the Expected Utility needs to break that inertia relatively. So, Relative Action Utility = \mathbit{U}_{\left(\mathbit{relative}\right)}=\int_{\mathbit{t}\mathbf{1}}^{\mathbit{t}\mathbf{2}}{(\mathbit{U}_(\mathbit{inertia})\ -\ \mathbit{U}_(\mathbit{pat}\mathbit{h}_\mathbit{i}}) An Individual analyses the Action/Relative Utility over each paths/options relatively and follows the path that maximizes the relative utility over the threshold inertial level to break even. The Path of Maximum Stability/ Least Action. Human traces the path that takes the least action(energy-time)/maximum stability under the given scenarios of causal forces Further, as mentioned in my other paper, let me also explain regarding Value in Real World as the Input of Utility to an individual human to decide under uncertainty ,which is essentially the path of least action, most stability. So, How is Value Determined in Real World by a Human Individual. Value is Relative Concept for the Observer not the Absolute for all. It keeps on Changing over the time for different Observers/Individual. Value is NOT static figure based on certain ratios etc. It’s a Dynamic figure which keeps on changing over the time. Value is fundamentally a form of energy that attracts the human individual towards it as every individual tries to maximize the Self Value in general. The Value depends on multiple perspective relatively for an Observer based on systematic and individual idiosyncratic perspectives if it maximizes the overall utility over the time. It includes first and higher order derivatives (not just first order absolute ones) dynamics of various factors including risks involved, quality, momentum, cheapness, pricing, timing, emotional, randomness factors leading to the combined perspectives of Value. This Value combined with the Causal Probability Weights, Occurrence all these lead to Effective Utility of the Path/Option for an Observer/Individual/Relatively. If this Expected Utility exceeds the Threshold Inertial Level of the Utility for an Observer/Individual Human under the given set of conditions, it follows that path of maximum utility which is essentially the path of least action, most stability, maximum likelihood causally. Practically a Human Brain Calculates these Figures of Value, Probability, Utility ,Risk ,Gain all over the different paths Relatively and chooses the Path of Maximum Stability /Utility or the Least Action to decide his behavioural decision making under Uncertainty. Literally all the generic Human collective Behaviour(which may not be the same for everyone or might not be correct always if not as per the scientific laws of Nature) are basically based on this scientific perspectives.