This is one of those posts where I talk about things which I understand more or less intuitively, in terms of things on which I have an educated view. To be more specific, I have no formal background in politics or economics, although I understand agents as well as your average computer scientist and systems at least as well as your average systems engineer.
So, what is socialism? While I won't attempt to give a proper definition here, I can very well state that it must somehow relate to social welfare or social utility. In other words, we cannot speak of socialism unless we try to abstract society as a singular entity. In even more words, the idea of socialism bases itself upon the fact that a society is more than the sum of its parts, i.e. more than just a group of individuals, and that the well-being of the whole must be quantified one way or another.
Of course, well-being is, generally speaking, a rather vague term, but it can be quantified using economics, which deals with resources; and resources can be reduced to money for the sake of simplicity. So if we were more naïve, we would say that social welfare can be represented as the sum of money owned by "the society", which is false, as some pigs are by definition more equal than others, and besides, there's that entity called "the state" which in the socialist view is more equal than individuals. Let alone the fact that "the state" is made up by individuals.
The sudden insertion of the "state" variable in this model is not coincidental: some might say that socialism is founded on the belief that, at least in some cases, the state as a ruling body can make better decisions than the individuals it governs, which of course, may or may not be true, depending on the decisions to be made, or on the individuals governed, or finally, on the state itself, e.g. the way in which it is organized.
So let's assume for now that the state can indeed make some proper decisions, such as for example those pertaining to individual property, safety, freedom of expression and so on. Also, let's assume that citizens are in some respects completely incompetent: for example most of them don't own weapons and can't establish education curricula individually. Finally, let's assume that the subset of citizens actively running the state are interested in maximizing social utility.
As you might have already noticed, there are problems regarding a. the limitations of the model itself and b. the application of the model in real life scenarios, that is, its validity.
Regarding its limitations, it's clear that we can't, for example, rigorously specify the set of decisions makeable by the state. A small or empty set would lead to something close to anarchism. A large set would lead to communism. Besides, there are still unsolved ethical problems such as drugs, genetically modified food or prostitution, which are considered horrendous in an Orthodox Christian society, while being perfectly fine from the point of view of atheists and/or rationalists. This is where the "quality" of individuals, i.e. of having certain values, certain education, certain income etc., clashes with the power of the state and this is how civil wars are started and so on and so forth.
Besides all that, there is a hard limitation on the quantity of individuals a socialist state can manage. I'm no complexity theorist1, so I won't go into the mathematics, but I can use common sense as a basis when saying that this applies to each and every centralized system in nature. It's actually pretty simple: the overhead of (centrally) making decisions grows with the population; as that happens, the state grows and thus becomes an unmaintainable bureaucratic machine, leading to dysfunctions not dissimilar in nature to cancer. This problem is usually solved by changing the structure of the state to a multiple-level hierarchy, e.g. by adding so-called regions or smaller states, which brings about changes in the set of decisions made centrally. But again, there is no general rule as to what is the optimal implementation, let alone the best.
Regarding the validity of the model, well, we have plenty of historical examples of socialist states that made really bad decisions. The classical example is that of attempting to raise budget income by increasing fiscality instead of reducing it, which may work on the short term, but is incredibly stupid on the long term, for various reasons in which I won't go here. Of course, the masses will easily yield to propaganda such as that involving raising the minimum salary, but they seldom think of how this will affect prices in six months or so, which is why people shouldn't be allowed to practice any profession involving thinking until they've studied basic mathematics2 and economics. Unless, of course, they live in North Korea, where being poor is the norm anyway. Besides, it's naïve to assume that most statemen will choose the good of the state over their own. Sure, it might happen, but then again, it often does not, and that's when the phenomenon known as corruption arises.
There exists however an issue which underlies all of the aforementioned, and that is, as Arrow's paradox suggests, that there is in fact no general social welfare function. The concept itself is flawed, as societies themselves are built upon the common interests of their individuals. Trying to quantify exactly that would lead to a partial, and therefore unusable function3. Trying to quantify more than that would increase the gap between various groups of interest4, with the risk of alienation or even dissolution.
Take from that what you will.
Socialism doesn't necessary require the state or any other monopolistic social entity. See libertarian socialism for example.
Right. Socialism requires at least two individuals, one of whom is more interested in the other's goat than the latter would care to approve of.
Libertarian socialism is a transitory state, just like early Marxism and the more recent "liberalism": just as soon as them "libertarians" manage to grab the reins of power, the situation is to devolve into the same old story with a different set of actors.
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