No. There we go, shortest article ever.
Alright, I’m kidding around. But I’m serious about answering the question. Exploring this answer helps us define the terms and actually opens us up to a new conversation that is more relevant to modern economics than these terms which have largely lost their meaning and intent.
If your attention span is short, I’ll answer it now: It’s likely very rare, but I would surmise that it is possible. You’d have to be very specific about both parts of the term. Let’s start with the Dictionary and expand from there.
Socialism: a political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.
Capitalism: an economic and political system in which a country’s trade and industry are controlled by private owners for profit, rather than by the state.
They do seem exclusive on their face, don’t they? But there’s actually a pretty simple way to make them fit together and it has to do with incentive. In capitalism, the private owners are looking for profit. What if they profited more by sharing their trade tools and product with others? Sounds like a business, sure, but what if they shared ownership of their tools and not just lending the tools out?
This is probably why voluntary socialists and capitalists seem to have so much overlap. Indeed, Adam Smith noticed that lending individual tools out every time when participating in a company was inefficient and wasted money. Even if lent out for free, permission would still need to be gathered from each individual. Can you imagine a McDonald’s where each fryer or grill was individually owned? At any time, the owner could remove privileges and hamstring the entire operation. Capitalists note that it is expedient that profits be paid individually based on work that is often done collectively. It is not against any kind of rule to work alone, but division of labor and human interest suggests that better success is going to come with multiple workers doing various tasks for a single product.
So we’ve seen how a capitalist might fit the definition of a socialist, let’s turn it around now. The owners might choose to share their items and make it theirs. But it is still theirs and not someone else’s; it is still ownership. So no corporate person can close their doors or take their money or their product. Their labor and their fruits do not become exported to anyone else. They might choose to share a label or brand, for commercial reach and consistency purposes, but the actual gains are internalized. This is much closer to a libertarian or voluntary socialist society than the one adopted by essentially every country on earth.
Both are technically compatible in this sense. You can still individually own the fruits of your labor while voluntarily donating the means of labor to a collective. Even so, it’s obvious to see why they clash; this is a very technical case, when the philosophies are expanded, the area of similarity, which is already small, potentially drops off. Most socialists would like wages and profits spread equally instead of by volume or type of labor which then puts it into opposition with capitalism. Most capitalists would want businesses, even the worker friendly ones described above, to compete with other businesses, which is usually against most socialist principles.
The reason I performed this exercise at all, though, is so that we can change the conversation. While there are areas of differentiation, they are clearly not opposites. Even if we use other definitions, like socialists wanting people to be equal and capitalists wanting compensation based on output, they are not mutually exclusive. Many, even most people, believe in equality in opportunity and payment based on difficulty and length of work, which borrows a bit from both economic systems.
Some economic philosophers actually had this debate in the last century, which has been largely lost to history now. It was a matter of praxeology (the study of human activity, though it doubles as a word you can use if you want to sit by yourself on the bus) versus mathematic economy. The mathematics desired for central planners to do what is best for people based on equations that identify maximum output. Praxeologists desired for markets to develop based on what people want and what they are willing to give. Generally speaking, socialists went with mathematics and capitalists went with praxeology, and this is why socialism became associated with centralized authority and capitalism became associated with markets. Neither definition is historically accurate, this is simply how the ideas and conversations evolved until today.
I won’t elaborate because it goes beyond the purview of the article. But the understanding of capitalism and socialism might help explain why you feel like you have a foot in both camps. You probably do and you have more in common with those who oppose your preferred economic model than you think.