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Anti-philosophical Foundation

Notes On Foundations Of Decision, Game And Probability Theory


The usual method associated with portfolio analysis is to specify an arbitrary “utility function” and connect that function with stocks having an assumed probability level of attaining different values. By this method, one can theoretically create an optimal distribution of stocks in a portfolio. Thus this methodology initially leads to a solution to reasonably concrete problem.

However, subsequent use of this sort of methodology to model the full behavior of a stock market or similar such system has lead to incoherent results. What we have in “non-zero sum game theory”, decision theory or “multi-valued logic” are a class of models that begin with actors possessing arbitrary chosen utility functions mixed somewhat with numeric measures of the likelihood of different phenomenon. The chief characteristic of these is that they don’t form a unique probability model of the situation under consideration. Rather they are intended to be formal equivalents of an informal process. The informal process is the transformation of a verbal sketch of a real world system into a formal model.

On the surface, the inadequate semi-formality of these formulations only goes to show that such processes can’t be made determinate. But really, this also reflects the prejudice of Marxists call “bourgeois ideology”. Here, such ideology seeks to model actors before it creates their circumstances. Moreover, it wishes to model their behavior without the slightest constraint as to what they could be – actors are a-priori from abstracted circumstances. In anycase, it is not surprising that this effort to numerically define actors fails to produce clear, unambiguous models.


Our approach will be different. Rather than going “down from” arbitrary numeric measures of belief and preference, we move “up from” concrete probability models determining all of a given dynamic, including the behavioral aspects of the actors within the model. Thus, these will often be evolutionary models, though they don’t have implication of genetic determinism. Unlike a utility model, an evolutionary model is easy to make deterministic; you begin with an initial distribution of behaviors, rules for interaction and winnowing of behaviors. In a reasonably determined class of models, one will wind-up with a stead-state distribution of behaviors but even a divergent series of distributions tells us something about the model we can specified.  But, in anycase, our model is guaranteed to produce a result, an achievement the usual methodology fails at entirely.

The elements of the model are, then, an initial distribution, a set of interaction rules and a set of behavior rules for the players involved. The point is that individual behavior rules are meaningless without additional interaction rules, rules that determine the actual interpretation of any numeric preference.

This model already gives us an answer to a paradox which often occurs in economics. JM Keynes separated uncertainty from probability mentioning folks would be willing to assign a numeric probability to an event the next day but that “uncertainty” rather than probability must be assigned to a stock market in twenty years time. While this may be a fine approach to informally phrase such a situation, it is not something we want to accept as an unstated aspect of a formal model. Rather, we would prefer to explicitly quantify such phenomenon – what use is a formal model whose boundaries come from “hand waving”.

And our model does allow us to unravel the differences between these aspects. Remember that our model involves a distribution evolving over time from an initial state. This means that a particular element in our ultimate distribution will depend on the distribution as a whole. “Logic” enters such a distribution when each element utilizes adaptive and logical strategies. We can show that such logic is not absolute is the sense that is a single winning approach. Rather, different entire systems specify different logics. Now logic can involve self-questioning and speculation and in some specifiable circumstance, some or all strategies in our ultimate distribution will come from such. But this still doesn’t such rationality can extracted from the system. Among other thing, we can create situations which favor any particular “logic”.

Ok, if we project a stock analyst into such a system, we can see that the analyst’s present insights are part of the total configuration of the stock market. The “probabilities”, likelihoods etc. which he acts on come out of his evolution from the particular stock market system as well as the larger human system. Thus it is plausible whatever logic he uses is sensitive enough to notice when he is “tuned-in” to the process going on.


Emotions And Likelihood

Phenomenon like the stock market are often said to be driven by emotions “in reality”, no matter what the level of objectivity is specified in theory.

However, if we look at a given game as having a historical component which is irreducible to single, dominating logic, we can also start to imagine that emotions might actually play a useful in our process. There is not absolute logic but emotions might serve to determine which logic, as of now, to use. 


In reality, humans don’t have an independent existence. Emotions relate to both our existence or destruction and our level of connection with others.


Humans map different functions onto different body reflexes. Driving a car mobilizing and modifies the reflexes that allow walking and running. Dealing risk often involve projecting those emotional responses which deal with physiological existence. Fear is a strong emotional motivator toward caution and self-preservation. Fear may be a use component for an approach which seeks to continue the existence of an object. Fear may be counter-productive for growth or increasing gain.


Remember now that there is no correct logic but merely correct configurations of logic and situation.


In Our Present Capitalist World


We live in an advanced, capitalist market economy. Ideally, a market is an abstract, quantitative system. Money is a constant reality but it is a tricky question how money translates to utility.


Human visual senses and processing centers are excellent for processing movement in uniform, multidimensional space of infinite extent. Human kinesthetic senses are well adapted to maintaining a physical body of limited extent.


The market creates the potential for such a uniform in a formal space. Prices, qualities and quantities altogether approximate a multidimensional mathematical “manifold” utilized in mathematics and physics. Indeed, even the decorations of a mall imply limitless space despite such space’s non-existence for most people.


A problem in such a situation is how a person reconciles their visual “flight of fancy” within the market’s formal space with their personal, kinesthetic sense of self. One might imagine that a person’s “sense of community” could said to be their normalizing of the situation which they find themselves in.


Utility must a finite measure whereas there is no limit to level of money wealth a person can attain. A personal operating criterion can fail entirely to operate according to a utility function and rather adopt the approach of getting more and more money no matter what. As gambling strategy, this is “playing till you lose” and not a useful approach.


The calibration problem appears as an intractable personal problem at first. But if we apply the same logic as our earlier thinking, we can see that there is always a solution coming out of the evolving dynamic of situation. The thing is that while capitalism does not seem to have a stable calibration point, it hasn’t been around too long. The lack of stable solution here expresses the fundamental instability of the whole dynamic. This world is “spinning, spinning, in a widening gyre”. But moreover, the workable configuration for each person changes as the configuration of everyone changes. Essentially we are all chasing each down the wormhole.