This piece was reprinted by OpEd News with permission or license. It may not be reproduced in any form without permission or license from the source.
The Supposed Paradox of "The Greatest Good for the Greatest Possible Number"In von Neumann's book he refers to "the greatest good for the greatest possible number" as a contradiction, because according to von Neumann you cannot maximize two or more functions at once, that in a social economy, all maxima are desired at once by various players.
That is, there is no concept that it is possible to cooperate and share an optimal outcome, without it coming out of "your" share so to speak, that comes at a cost of having less instead of more. This is a very basic understanding of economy, and again does not account for how cooperation and creative potential can work to transform the "goods" of an outcome.
For instance, country A is militarily stronger than country B, which is rich in many raw resources. Country A is also stronger politically than country B in that, there are no other countries that will likely intervene against country A's actions if it chooses to invade country B. What course of action will yield the greatest return to country A?
Well, there is a very obvious answer to that question; however, contrary to popular thought it will not yield the greatest optimal outcome. The greatest optimal outcome is rather to cooperate.
It is in both country A and country B's best interest to share knowledge, even if country A has much more knowledge, such that country B develops the capability to refine its raw resources. By doing so, country B will yield a greater return in trade over the long-term to country A, and country A does not have to worry about a future retaliation from country B. By developing a more advanced economy the wealth of trade is increased for both countries. By cooperation, the optimal outcome is transformed and offers a greater return.
This is exactly the model that is being used by China presently in their philosophy of "win-win cooperation," and it has proven itself most effective despite all attempts to villainize it as something nefarious. Rather than fight over resources, there is a cooperation to share technology, increase resource yield and share a greater boon than originally existed.
John von Neumann goes on to state in his book, that the more players in the model, the easier it is to predict the outcome, since the use of statistics and probability are increasingly better indicators of behaviour and performance. As he states:
"When the number of participants becomes really great, some hope emerges that the influence of every particular participant will become negligible and that the above difficulties may recede and a more conventional theory become possible. These are, of course, the classical conditions of 'free competition'."
He goes on to use the example of our solar system, with its nine major bodies, as being much harder to model than 10^25 freely moving gas particles, as per gas theory, simply due to the sheer number of objects you are dealing with.
This is truly a remarkably absurd statement, where von Neumann is asserting that if the solar system had more major bodies orbiting within it, it would thus be easier to model based off of probability.
Every planet in our solar system is a different size and weight, with a different number of moons. Every planet revolves around the sun in imperfect elliptical orbits that change slowly overtime, the planets travel along these orbits in a non-uniform way that is observable through planetary retrograde motions. The fact is that our solar system is not some perfectly closed system that is uniform and consistent in its actions, there are cyclical changes but there are also non-cyclical changes that are occurring. This is due to our solar system orbiting around a galactic center of the Milky Way which is itself moving in yet-to-be discovered ways within a larger cluster of galaxies.
Therefore, you cannot use any theory of probability because the system is in a state of ongoing non-linear change. The more bodies you add to such a system the more complex it becomes, not the more negligible.
For example, there exists no straightforward formula to identify all prime numbers, though there are an infinite number of prime numbers. Prime numbers are a reflection of a non-linear process of change.
Such an oversimplification of nature shows the audacity behind the assumptions that make up such formulations like game theory. You are nothing more than a virtual avatar in their synthetic world with programmed limits to what you can and cannot do in the game they have created for you.
Game theory does not represent the motivations behind human nature, but rather imposes such limitations since, as they acknowledge themselves, it is easier to predict and control your chosen selfish behaviours which are encouraged and rewarded with "incentives."
(Note: You can view every article as one long page if you sign up as an Advocate Member, or higher).
2
2
1
