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Please begin with an informative title:

Let's start by defining two systems of human organization:

1) Cooperative - positions are assigned through absolute demonstration of skill and tie breakers usually involving seniority. Rewards are based on "fair value" - anyone working as hard as they can at whatever position they are in deserves as much reward as anyone else regardless of ability or type of position.

2) Competitive - positions are assigned through relative demonstations of skill. Rewards are based on auction of services to highest bidder.

If a society completely organizes cooperative then the usual deficiencies associated with the "left" result. New technology introduction will be difficult as there is no driver for disruption. Zealotry in the pursuit of equality can result in humans rights issues. Without a class of super rich balancing the power of the state, dictatorship is a constant threat.

If a society completely organizes competitive then it will suffer maladies of the "right". Tragedy of the commons issues in research, the environment, culture and education will be difficult to avoid. Zealotry in the pursuit of inequality can result in humans rights issues. Unregulated winner take all competitions may result in monopolies and an all powerful royalty.

So then come the hybrid systems:

3) Run 1) and 2) for different societal functions in parallel. For instance run science, education, military, culture and regulation using system 1) and other functions using system 2). Problem here is that the wealthy winners from the 2) side will eventually corrupt and dominate the 1) side.

4) Swing like a pendulum between 1) and 2); shifting each time the usual faults of each system emerge. Problem here is that the pendulum may swing wider and wider and the faults get bigger and bigger until there is a melt down.

So the question of how big is the middle comes down to are we a society of 1) and 2) believers that are fighting it out? Or are we mostly 3) or 4) believers that are having difficulty stabilizing those systems? Or is there an unheard of system of organization that would be more agreeable and stable?

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Okay if you have made it past such an abstract introduction then I feel free to take some liberties in addressing you informally. First off I am kind of pissed that the introduction was necessary. It seems to me that most books, blogs and media shows start in the middle of a pie fight whose origins are never explained. I am middle aged and just now beginning to come to terms with what political debate is about. If one is cognisant enough to Google "economics cooperation competition" then the top hit includes this paper:

There is thus a bewildering variety of evidence. Some pieces of evidence suggest that many people are driven by fairness considerations, other pieces indicate that virtually all people behave as if completely selfish, and still other types of evidence suggest that cooperation motives are crucial. In this paper we ask whether this conflicting evidence can be explained by a single simple model. Our answer to this question is affirmative if one is willing to assume that, in addition to purely self-interested people, there are a fraction of people who are also motivated by fairness considerations. No other deviations from the standard approach are necessary to account for the evidence. In particular, we do not relax the rationality assumption.
All this is a long winded way of saying that we might be living in a world that is mixed between followers of 1) and followers of 2). Mathematically the resulting crap fest is made possible by assuming a small number of their definition of cooperative type
First, in addition to purely selfish subjects, there are subjects who dislike inequitable outcomes. They experience inequity if they are worse off in material terms than the other players in the experiment, and they also feel inequity if they are better off. Second, however, we assume that, in general, subjects suffer more from inequity that is to their material disadvantage than from inequity that is to their material advantage
Well I haven't done the math but I'm pretty certain that we can reach the same outcome with a few assholes surrounded by a sea of "subjects who dislike inequitable outcomes".

Moving down the list of search return hits we come to another Nobel prize that has absolutely nothing to do with Alfred Nobel winner proclaiming the rewards of globalization

Protectionism is seductive, but countries that succumb to its allure will soon have their economic hearts broken. Conversely, countries that commit to competitive borders will ensure a brighter economic future...
In this view most everyone but a minority sage elite are in camp 1) but the bad economic outcomes of limiting competition make approach 2) the medicine that must be swallowed.

Next up Jean-Charles and Jean mention that oligopoly like credit card vendors can achieve cooperation also. I think that is just clouding the issue though. For the most part industries that are built competitively from the ground up cannot regulate or cooperate effectively. That was shown recently by the story of the processed food executive who went around begging for self-regulation of sugar, salt and fat - not happening.

Unfortunately our next hit, from the Russell Sage Foundation, also includes institutions as a unit of interaction

Institutions help individuals with fundamental problems of exchange, collective choice, and collective action. If nothing were ever chosen by vote, there would be no problem of cyclical instability. If there were no social dilemmas, we would have less need to deal with problems of communication, cooperation, and coordination. If information were freely available, specialization and delegation would not produce agency costs. If there were no nonsimultaneous exchange, ex post opportunism would not be a concern. However, all these problems exist, and institutions ubiquitously deal with the trade-offs they create, providing opportunities for beneficial transactions that would not take place in the absence of the institutions.
This line of thought, coming from this source, kind of points the way to a fifth hybrid system:

5) The ultra-wealthy winners resulting from unregulated pursuit of 2) create foundations that organize around 1).

That's nice but its not going to stop 2) from creating global warming or making the education system a competition driven test taking skill less zombie. Yes there will be foundations running around picking up the pieces but that's not the same.

Our next search result takes us into the world of parecon. Many of you have been in that world before from watching Star Trek Next Generation crew members on the Enterprise

The proposed electronic "credits" awarded to workers based on their perceived level of effort and sacrifice would simply be deducted from the workers account when used to make a purchase, disappearing rather than transferring the credit to the vendor. People would be able to borrow credits if approved by an appropriate board, but no interest would be charged.
If the dying rich people of 5) really want to make a difference then they should set up a foundation that creates an experiment with a different economic system. The Enterprise could be made a reality for a few right now. But the standard hypocrisy is that competition is good for absolutely everything except economic systems, where it is understood that one size fits all, forever. That leaves most of us citizens of the Emerald City trying to discuss colors other than green.

Which brings us to a different definition of the middle. Maybe being part of the middle isn't about 1 - 5 so much as wondering, even ever so briefly, if there is anything beyond those numbers. If so perhaps the middle is much larger than conventionally believed and the cold war, now fought against ourselves, can finally come to a close.

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