Decision Theory
Decision Theory is the science that supports navigating in an uncertain scenario.
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Problem. A system describes attributes with additive and multiplicative values. Two of such systems are independent if and only if the quadratic function of respective values are additive.
Solution. The laws of Pythagoras and Fermat-Wiles are a proof that a2 + b2 = c2 and this is true to only with the quadratic function. This implies that two systems are independent, if and only if such a quadratic energy function is additive. Any interdependence would result in a skewed vectored sum of less or more a2 + b2 <> c2
Moreover, this version of the two theorems implies the Law of the Conservation of Energy as well. Technically this is trivial, but it is rarely addressed, because it spans across Geometry, Statistics, and Physics. (c1)2 + 0 = 0 + (c2)2 when time passes from point one to two. (a1)2 + (b1)2 = (a2)2 + (b2)2 for any arbitrary subsystems.
Time travel, or teleportation does not exist as a result, unless it is something like swapping energy between the two systems meaning being part of an aggregate supervisor system. They are not independent anymore.
This is important because decisions are going to be the cause for a consequence. We have a decision tree and not a decision cyclic graph. Some decisions used to be fabricated as theater in the case of concept trials in Russia of the 1950s.
Our mathematical model of energy can also be applied to the statistical data of average and variance.
Applying the same mathematics to variance looks like the following statement. The quadratic equation is true to systems with correlation coefficient of zero. Assessing the variance or energy of unknown noise helps to make decisions to buy or sell a security or a property, or whether to collect and analyze more data. The square root of accumulated loss is oftentimes the feedback of artificial intelligence, and machine learning training.
Decision theory is closely related to data science as a result. If we experiment with independent systems our goal is to reduce errors and precisely assess correlations. The quadratic function describes how well we are doing assessing the parameter values reducing the quadratic variance of errors. We understand and project correlations making them another independent variable.
The traditional model of Decision Theory is based on choices. Choices can be described with a decision tree. We do this by starting from the present root and adding a node for each option. Other nodes of future decisions follow in additional layers of each subtree. The final utility value of each leaf node is back propagated to each decision with probabilities of events that we do not have impact on. The weighted sum of such values gives an assessment of the potential outcome. Decision makers are supposed to choose the best option. This is usually good enough to optimize cash flows.
Routine decisions
Our argument is that there is a better model. Decisions need to support four different goals for humans. Daily decisions need to be quick and cheap. These are the choices of what to eat, how to drive, how to communicate at work. Such routine decisions can easily be described with a decision tree.
Oftentimes routine decisions are connected to emotions. Emotions are a feedback of our subconscious brain and body through the Parasympathetic Nervous System. Marketing tries to influence such decisions adding labels to colors, logos, or branding.
Risk is low. Routine decisions can be reordered, or corrected easily.
Social decisions
Social decisions are done by managers, salespeople or politicians. They might sacrifice some short term routine goals for the common good of the company or community. They do this knowing that the decision will affect the average member and themselves in the midterm. The thinking that the invisible hand of Adam Smith will improve common product is not new. It assumes that if people and companies do proper accounting of cash flows and insist on positive individual cash flow then the system will provide an optimal outcome.
Problem. Smith's theory can be proven by Kirchoff.
Solution. Indeed. Kirchoff's laws of current and potential can be applied to cash flows and accumulated wealth precisely. Such a system will always be stable. The inflows and outflows of cash at each node is proportional to their own share of consumption and production.
People do not just do routine decisions. They also improve their own future by insisting on sticking to their own benefit, if it is about personal value and money. Such an extra logic should be added to node values in a decision tree.
Our suggestion is to add an extra edge to the root of the decision tree such as "Collect more information." Social decisions oftentimes require more experience.
Harvard Method of money allocation focuses on one division at a time. This assigns the shortest job first to the CEO focusing on the best cost reduction option compared to the management focus required. Parallel tasks oftentimes result in the benefits appearing at once but late missing earnings reports. It also implies that divisions will eventually have a comparable weight of expenses.
Decisions to avoid danger
Negative outcome and occasional losses are not covered by this theory. Computer Science has addressed this in the theories of A* algorithms and Alpha–beta pruning. These assume that occasional fatal outcomes can be applied to decision nodes and that they can be backpropagated respectively. A robot may not test the ground around the trail, when it is at the edge of a cliff. Some edges must be closed in case of a decision tree, even if they have a positive average utility due to their danger. The sign says "Do not gamble here" or "Danger, Keep Out".
Reflexes are typical to react to risky situations. Anxiety tied to places is also a response of the uncertain dangers.
Collecting more information is also important to avoid danger. Trying things in small, simulation, not rushing in may pay off.
Smart decisions
The fourth level of decision-making is intelligence. Intelligence and analytics is required in case of routine, managerial, and life or death situations. Still there is a fourth level that requires time and experience.
The Harvard Method of negotiation is based on the desire to achieve a mutually beneficial result. This applies objective criteria and not positions across multiple parties.
Many religious rules are based on experience. Wise people analyze their memories late in their life and come up with advice for generations that follow. These usually have empirical evidence, but no actual scientific proof at the time of the analysis. Many are connected to a geography, climate and the resulting lifestyle and culture.
Having the ability to address different perspectives also applies to arts, humor, show business, or dating. Arts is oftentimes a projection of subconscious memories, especially unresolved or inconsistent ones.
Life situations may pick different options for a specific goal. These options ignore the decision with the biggest weight in the tree. A common approach of LLMs is to choose random options to do arts. Learning, collection of more information allows better arts and rich experiences.
Confidentiality
Building up a decision tree requires information. Sometimes not all information is available. This is why we deal with probabilities of cash value at each node of the tree. Sometimes we do not want others to influence our decision tree, making the values worse. Secrecy is important in this case.
Privacy is a reflection of our subconscious and Parasympathetic Nervous System. Our body takes care of some decisions in parallel with our conscious thinking process.
Problem. We do not need all information to make the best decisions for all four goals of routine, common good, life or death situations, and intelligent decisions.
Solution. Indeed. We need all information suggested by the microeconomic approach of perfect competition. Pick all the information available about traders on the free market. Choose the right option based on the decision tree by the market logic. Then verify that much of the information was not necessary to pick the right node on the decision tree. Most nodes of options are suboptimal. Other market participants will insist on keeping such information private.
Problem. Information that triggers unwanted feedback is unnecessary to disclose.
Solution. When will you want to make some information confidential? Imagine your decision tree with your optimal choice. If releasing some information changed your decision tree to suggest a worse option, then you would not want to disclose such an information. This implies that data collection could actually be comprehensive as long as it remains private, or any action is delayed.
Many government decisions are kept for historic reasons. Such documents are declassified only after decades to prevent a feedback causing bad decisions.
Tax information is reported monthly, quarterly, or on an annual basis.
Similarly, live geographic satellite data of phones or vehicles may need to be delayed to prevent making traffic worse, or to discourage foreign stalkers.
Historian research usually suggests 50 years. Historians may not publish analysis of current wars influencing decisions. This prevents banning historian's data collection of accurate information.
This article was revised on February 26, 2024.