Law of Human Behaviour Dynamics : Decision Making under Uncertainty: Scientific Analysis : Principle of Least Action:Law of Nature

Law of Human Behaviour Dynamics: Decision Making under Uncertainty: Scientific Dynamics: Principle of Least Action: Law of Nature Author : Pankaj Mani New Delhi, India Contact: manipankaj9@gmail.com 10th September 2023 Abstract : In this paper, I try to look at Human Behavior Decision Making Under Uncertainty from the Scientific Dynamics Perspective of how an individual essentially follows the Principle of Least Action which is conceptually equivalent to traveling the Path of Maximum Stability/Utility. But unlike the Conventional Economic Utility Theory by Legendary John von Neumann+ Oskar Morgenstern and the Prospect Theory by Nobel Laureate Daniel Kahneman & Amos Tversky, it looks at scientifically the Governing Law of Human Behaviour. Then one can see how popular economic theories might not be necessarily valid always scientifically as proposed by the learned greats. Blindly following Economic Theories based on Historical Pattern Analysis in the Backward Direction of Time might be misleading in the Real world forward Direction of Time scientifically exposing to Black Swan-type events! I also look at the fact that contrary to the economic social perception that Humans behave irrationally at times, I try to humbly show that” rationality” as the term is relative rather than absolute for all the observers. It might appear “irrational” in social economic behavior terms to an observer or many observers but it essentially follows the Scientific Laws “Rationally”. Hence for the social, economic, and day-to-day Real World Life Decision making under Uncertainty, Individual Human Behavior must be analysed scientifically. In fact, Economic Theories in general must be validated scientifically as some of them could be misleading at times. Introduction : 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 behavior 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 that 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{Relative}\ \mathbit{Utility}\ \mathbit{of}\ \mathbit{Each}\ \mathbit{Path}\ \ \mathbit{U}_\mathbit{i}\ \ \mathbit{for}\ \mathbit{an}\ \mathbit{Individual}\ \mathbit{Human}=\ \mathbit{f}\ (\ \mathbit{Outcome}\ \mathbit{Impact},\ \mathbit{Threshold}\ \mathbit{Inertial}\ \mathbit{Expected}\ \mathbit{Level},\ \mathbit{Risk}\ \mathbit{Involved}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathbit{Probability}\ \mathbit{of}\ \mathbit{Occurrence},\ Causal weights, Randomness Component \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{Net}\ (\ \mathbit{for}\ \mathbit{each}\ \mathbit{individual})=\ \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{Utility}\ \mathbit{Perception}\ \mathbit{by}\ \mathbit{the}\ \mathbit{Individual}.) The Relative Expected Utility U_i is Maximized by an Individual . Will see how this is also effectively the path of Least Action here like in Principle of Least Action in Nature. The Human Behavioral Law coming from the Laws of Nature Every Individual Human in general tries to maximize its Value relatively in its surrounding to attract others in its quantum space-time curvature just like gravitational forces. Essentially this is conceptually Equiavalent to the law that Every Individual Human traces the Path of Least Action as in Physics by Paul Dirac. Yes Human Behavioral Law too follows the Law of Nature. 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. Infact It’s not Physics but essentially coming from the Laws of Nature which applies to both Living and Non-Living Beings in its own ways variably. 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. The Pictures below depict the Principle of Path of Last Action by Paul Dirac. 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 by an Individual = Reference Threshold Inertial Expected Individual 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, Resultant Action Utility \mathbit{U}_{\left(\mathbit{effective}\right)}=\int_{\mathbit{t}\mathbf{1}}^{\mathbit{t}\mathbf{2}}{(\mathbit{U}_(\mathbit{inertia})\ -\ \mathbit{U}_(\mathbit{pat}\mathbit{h}_\mathbit{i}}) \ \ \ \ \ \ \ \ \ \ \mathbit{U}_{\left(\mathbit{resultant}\right)}=\mathbit{min}\left(\mathbit{U}_\mathbit{i}\right)\ \mathbit{for}\ \ \ \mathbit{all}\ \mathbit{the}\ \ \ \mathbit{values}\ \mathbit{of}\ \ \ \ \ \mathbit{i}\ An Individual analyses the Action/Relative Utility over each paths/options relatively and follows the path of least U(effective) means Action , which in other terms maximizes the relative utility over the threshold inertial level to break even. The Path of Maximum Stability/ Least Action. Both are same conceptually, mathematically different. 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) are basically based on this scientific perspectives. Analysing Prospect Theory by Daniel Kahneman Scientifically : How far True ? Prospect Theory : Prospect theory belongs to the behavioral economic subgroup, describing how individuals make a choice between probabilistic alternatives where risk is involved and the probability of different outcomes is unknown. This theory was formulated in 1979 and further developed in 1992 by Amos Tversky and Daniel Kahneman, deeming it more psychologically accurate of how decisions are made when compared to the expected utility theory. Prospect theory challenges the expected utility theory developed by John von Neumann and Oskar Morgenstern in 1944 and constitutes one of the first economic theories built using experimental methods. Prospect theory stems from Loss aversion, where the observation is that agents asymmetrically feel losses greater than that of an equivalent gain. It centralises around the idea that people conclude their utility from "gains" and "losses" relative to a certain reference point. This "reference point" is different for each person and relative to their individual situation. Thus, rather than making decisions like a rational agent (i.e using expected utility theory and choosing the maximum value), decisions are made in relativity not in absolutes Scientific Perspectives of Practical Generic Human Behaviors. Nature doesn’t calculate the least action path using these calculus as we do...they have their own natural tools that automatically calculates the path similarly for human brains. Human Brains automatically calculates the Value, Probability causally for different possible paths using its own Natural, Biological Algorithms. So, Action is minimum consumption of energy path under the given scenarios leading to maximum stability .. Similarly Human also tries to follow the least energy and time short cut path under the given set of causal forces dynamically.* Different Paths Utility attract individual with different energy.. under the given Constraints e.g. Binary or both, the resultant decides the course of action. This is basically the Energy attraction dynamics. Different Possible Outcomes/Paths having different Values are like attractive Energy for an Individual Brain’s Energy. Under the Given Scenarios including the Constraints, the Resultant Energy of Value decides the path taken by Human Brain(Energy). For example, if one has to choose like Binary Option between Paths A & B, then the individual human chooses the path which has highest maximum energy attraction due to possibility of value occurrence ! If no binary and both can occur simultaneously, then individual tries to follow the resultant where it would be proportionate to their energy strengths, in special case of both being equal in strengths, the resultant would be equidistant that means for both equally. So, under the given scenarios and constraints, the resultant energy created by Values of different possible actual causal paths decides the course of action for all. The Conventional Maximum Utility Formula is just one of the many possible scenarios of the Resultant in special cases. As claimed by Prospect theory against maximum utility , I would say that Human Individual Behaviour does trace the path of Maximum Stability/Maximum Utility/Least Action but the formula for that Path is not necessarily always the one explained by Conventional Maximum Utility Theory using the Sum of Product of Probability weightage & Outcome Value. It would ultimately depend on the Resultant Path Scientifically using the Energy Dynamics that different Utility(Values) impact on Individual Human’s Brain Energy. Science : Rationality Vs Irrationality of Human Behavior Dynamics It’s often said that Human don’t behave Rationally but they do behave as per the Laws of Energy and Nature based on causal dynamics of forces. But as it might appear Random at times to an external observer not necessarily as per its set deterministic patterns, it often claims humans tend to behave irrationally . But they behave very much rationally as per the laws of science, though may appear irrational at times due to appearing randomness based on observer’s social understanding !! Explain Patience in terms of Nature Law and Physics Energy Human tries to relate if works or else ignore if the pattern doesn't work for him... It's all energy interactions game as to which path it would travel. Practical Human Behaviour: If the Values are comparable, then Probability weight factors often becomes decisive. To explain, if the two paths/options say A & B having Outcomes of say $120 with probability 40% & $100 with probability 60 %. P.S. Please ignore the exact numerical values randomly put here ..just for demonstration purpose here. In this case, as the outcome values/utility are comparable to some extent, so one would generally prefer the one with more certainty as it would lead to more stability dynamics for energy inside the human brain in general. But as I always state that individual specific behaviour could be different based on the resultant perception relatively for everyone. Another Example : If there is huge difference between Values and Probability might not matter for individual, means in general one individual might go for Higher Value even if with very low probability irrespective of by the Conventional Maximum Utility Theory Calculations, even if lower. Let’s say two examples A has $ 1million with 1 % and $1000 with 99 % and the Individual expectation is $10k as per his individual perception, in that case no matter what the probability weighted sums tell, one might prefer for the 1st option even if the probability is very low and even if the conventional utility calculation by Maximum Utility Theory would be lower. That may not matter. P.S. Please ignore the exact numerical value randomly put here ..just for demonstration purpose here. So, the point is it all depends on case to case to basis and individual preferences and threshold inertial level. There can be N different Scenarios with different combinations of Numerical figures, and the resultant decision might appear irrational to an external but it’s very rational as per the scientific laws of Nature which it essentially follows. Rather than Generalizing, one must look at them scientifically like in physics in forward direction of time . Generalizing and Acting Based on Historical Patterns might be like Misleading Backtesting done in Backward Direction of Time to discover patterns historically and generalize it. So, which one would matter more :Value or Probability would depend if the other one doesn't make much difference practically and also relative to the individual perception. There can’t be fixed rule fit for all. One has to figure out the specific cases individual to individual. It all depends upon which energy attracts the individual more .. Another Feature : Human becomes Passive for Low Probability Extreme Event...on God /Nature .what ever will happen. .would definitely happen...they don't try to hedge that much thinking out of their direct control,so better not be worried and left it unhedged on God's will Human Prefer Certainty as it tends to be more Stable Equilibrium..but only when Value difference between Options not much otherwise if Value difference is huge, they might prefer Uncertainty... Human often prefer Certainty because of trying to become more Stable Energy wise but that would again depends. One might go for uncertainty if that path delivers more Effective Utility as per one’s preference over the time. Humans Behaviour traces the Short Cut (Short here very relative term )as it tends to travel the Path of Least Energy-Time i.e. Action, Maximum Stability under the existence of the Causal Forces and Constraints which include Systematic External forces and Idiosyncratic forces including Emotional, Threshold Inertial Forces Cognitive ,Conscious forces etc.. These are technically different types of forces and form of energy which drives the resultant human behaviours. So, must figure out the causal dynamics like in physics by studying those forces rather than just generalizing based on the empirical patterns which could be misleading at times. It all depends on how the energy attraction dynamics works for each individual case to case Human does essentially follow the Principle of Least Action as in Physics to reach the Stability in the Shortest Possible way as the resultant of emotional, conscious, cognitive and other acting causal forces. Loss Vs Gain Humans often try to avoid Loss generally because Loss might lead to survival panic for them that could unstabilize their individual energy system. Infact, After Gain, they set their Expectation Threshold Inertial Level higher that's why relatively they don't feel too much happier...For example, Before winning $1000 their expectation was say $500, after winning, they set their reference frame threshold inertial expectation level as say $2000 based on relative comparison, so then again virtually the gain of $1000 starts appearing below the threshold reference leading to lesser satisfaction.. Happiness is caused by but after Loss, they set their expectations the same as before that's why they get pained much...In both the cases, the Expectation is the higher possible one...In Loss, the earlier higher one becomes reference so and in gain,future higher are made reference...hence this asymmetry of perceptions in bothe the cases... But it's the Law of Energy to take Higher as the Reference Point of Possible Expectation to look at other Options relatively.... They think relatively in general because they try to be better than others in the neighbour...Value maximization over others... But at the same time many believe in their absolute value and don't try to compare with others... Conclusion : So, all these generic human Behaviours originate from the Science of Energy, Principle of Least Action as in Physics and one shouldn't blindlybelieve in general, many times, many individuals follow the specific ones that could lead to possible Black Swan. Things should be looked at Scientifically as even the General Human Social Economic Behaviours tends to change over the time but that would essentially follow the Geodesic Path as per the Laws of Nature Scientifically driven by Causal Forces and Energy where Randomness being the inherent part of that ! References : Daniel Kahneman : Prospect Theory : Analysis of Decision Under Risk https://www.jstor.org/stable/1914185 Mani, Pankaj, Scientific Investing: Unifying the Extremes : Revisiting the Foundation: Black Swan, Tail Risk,Tail Risk Hedging, Randomness, Uncertainty , Determinism, Causality, Convexity, Causal Factor Investing, Randomized Factor Investing, Flawed Conventional Statistical Tools, Forward Looking Finance in Time (August 17, 2023). Scientific Investing in the Real World: Unifying the Extremes: Randomness Determinism Causality : Black Swan & Tail Risk Hedging by Pankaj Mani, Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4543698 Principle of Least Action Lecture by Richard Feynman https://www.feynmanlectures.caltech.edu/II_19.html