(Hah! You thought this was going to be an entry on Buddhism, dintcha.)
Something that observers of politics quickly realize is that the Left-Right model of politics is far too simplistic to be useful. (Well, except for those that take up a Cause and join the Crusade against the Other Side, as such a simplistic, bipolar view makes it easier to force-fit everything into terms of "Good vs. Evil" — typically with a redifinition of what constitutes Right and Left to more conveniently fit into that person's ideals of Good and Evil. "Nazis were Leftists" and "The Soviet Union was state capitalism" crowds, I'm glaring at you.) There have been many attempts to construct multi-axis methods of categorizing the political spectrum, most of them two-dimensional.
Since the dust-up over what defines socialism, I've been meditating off and on about the internal divisions within socialism. Recently, I came to the conclusion that there are three axes that define the different branches of socialism.
The first is Moderate-Revolutionary — an axis that can be applied to any political philosophy — with those that advocate establishment of cooperatives embedded within an otherwise capitalist nation or working within an existing democratic or republican system to implement reforms being contrasted with those that advocate violent overthrow of the existing system and erection of a socialist system from scratch.
The second is Cooperative-State, contrasting worker-owned cooperatives with state ownership/stewardship.
The third and final is Market-Planned, contrasting unplanned economies that rely on market forces with those where direct control of the economy is practiced.
I want to address that last axis, as the notion of a market economy seems contrary to socialism as understood by most. Keep in mind that the definition of socialism is communal ownership of the economic mechanism. Consider, if you will, the scenario of wholly employee-owned cooperatives interacting within a market economy. There's no moneyed class of investors who derive economic benefit purely from owning pieces of each company, so this scenario is definitely not capitalism. Yet, the cooperatives are free to associate with whomever and however their worker-owners want, and competition between coops would likely be just as fierce as between capitalist corporations.
Certainly this scenario isn't a Free Market — at least not in its purest sense — as the lack of capitalist-style, investor-owned corporations seems unlikely without some sort of ban on such entities. A situation where everybody has decided on their own to participate in coops and corporations have withered away organically is certainly possible, but it's so highly unlikely as to be safely disregarded as a Utopian socialist's wet dream. But, then, what about a situation where only a handful of corporations still exist and the vast majority of economic participants are coops?
Where exactly do we draw that line between capitalist and socialist economies? Using purist definitions of either is unworkable. The United States is clearly a capitalist economy, yet cooperatives are allowed, and do exist — credit unions being the most visible example, especially in recent months. It seems far more reasonable to use more inclusive definitions: if most economic activity is by privately-owned entities, then the economy is a capitalist one, if communally-owned entities perform the bulk of economic activity, then the economy is a socialist one.
So, a market economy and socialism are not mutually exclusive as is commonly thought, after all.
The second axis is perhaps less contentious. State ownership is the default state that most think of when they hear the word socialism, but cooperatives are understood to exist and few would fight their inclusion under the socialist umbrella.
The first axis is the least contentious of all: either a particular socialist advocates reform of the existing system, either by using an existing governmental framework to establish state-owned corporations or by purely economic means by getting a group together to pool their resources and start a cooperative, or the socialist advocates blowing the whole thing up and starting over from scratch.
The Revolutionary, State ownership, Planned economy octant is perhaps the most well-known subset of socialism — to the glee of capitalism's apologists — thanks to the communist revolutions of the Twentieth Century begun with the Soviet Union.
Its Moderate counterpart has fewer examples — Salvador Allende's Chile being the only one I can think of off the top of my head — largely due to it being easier to undermine by external organizations (the Catholic Church and Nixon's United States in the case of Chile). However, Chile does show that it is possible to pursue a path to socialism, even the type of socialism most distasteful to capitalists, through democratic means. (So I won't bore you by defining the rest of the octants individually, just understand that each of the following quadrants would have its revolutionary and its moderate advocates.)
The two Cooperative ownership, Planned octants would be defined by locally-owned coops operating within a centrally-planned economy, the coops managing day-to-day decisions while working towards the goals set by the central committee.
The State ownership, Market economy quadrant may seem a bit nonsensical at first glance. The state owns everything, but leaves it up to market forces to manage the economy. This can be achieved by establishing multiple, competing, state-owned corporations in each market. Each would receive some basic subsidy, with profits (yes, that's right: profits in a socialist system) either being distributed amongst employees or being used to finance public works.
The final quadrant, the Cooperative ownership, Market economy — especially its Moderate octant — is the most similar to capitalism as far as its impact on the day-to-day lives of consumers and employees, which is probably why capitalism's apologists ignore it while shouting loudly and pointing fingers at the Revolutionary, State ownership, Planned economy octant. Investor-owned corporations are simply replaced by employee-owned cooperatives with investors and employees becoming one and the same.
A final thought: if socialism alone warrants three axes defining eight octants, what good is the broader Left-Right spectrum for anything other than wanking?