In theory, a market price system should be better than central planning. That's certainly the experience of both the Soviet Union and the People's Republic of China. As a computer programmer, I mostly agree.
Ideally, we want to distribute as much as possible. Centralizing anything creates a single point of failure; although the probability of a single failure is lower than in a distributed system, when a centralized system fails, everything goes down. In contrast, an individual failure is more probable in a distributed system: there are more things to fail, and because we spend less to secure each distributed element, the probability that an individual element fails is higher. However, in a distributed system, the consequences of a single failure are negligible, and the probability that enough distributed elements will fail at once to bring down the rest of the system is lower than the probability of a central failure, however careful we are with the central system. Furthermore, distributed systems generally scale better. Doubling the number of elements in a distributed system is usually cheaper than doubling the power of the central system.
No matter how distributed we get, there is always some need for centralization. The internet, for example, is a massively distributed system. However it requires a number of very centralized systems, notably standards to ensure interoperability, domain name servers, and search engines. The internet would not work without Google or someone like them: it doesn't make sense to distribute web searching. Similarly, a centralized system must still distribute something: it makes no sense, for example, for every Russian to travel to the one centralized grocery store in Moscow to buy food. We cannot just formulate a simplistic distributed good/centralized bad (or vice versa) dichotomy. Centralization and distribution are neither binary nor just a trade-off; they are dialectically related.
But still, in theory, a more-distributed price system is, at a first approximation, clearly more efficient than a more-centralized economic planning system. However, it is at a second approximation that we run into trouble.
The internet works as a distributed system because individual elements don't have much incentive or opportunity to exert more power over the system. Even the internet, however, does present opportunities for over-centralization; the power Google has over searching does afford them both the incentive and the power to control everyone's internet experience. Similarly, the power that trunk carriers have over internet traffic gives them a lot of power to manipulate individuals' experience. Paradoxically, we try to solve these over-centralization problems with another centralized institution, the federal government, with net neutrality and anti-monopoly laws and regulations in general.
A price system, however, by design gives everyone the incentive and opportunity to acquire more money and more power. The fundamental incentive of a price system is to accumulate money. A new firm joins an industry only if it can earn an economic profit; but an existing firm in that industry has a strong incentive to resist entry and maintain its own economic profit. No individual firm wants to be in perfect competition; every firm wants to be a monopoly. A price system tries to establish perfect competition by incentivizing firms to escape perfect competition. This contradiction is fundamental, inherent, and ineluctable to a distributed price system, or, more precisely, a private profit maximizing price system.
Thus, while a central planning system is usually less efficient than a private profit maximizing price system at a first approximation, it might be more efficient at a second approximation, because it eliminates the profit motive to establish and maintain monopolies; in other words, a profit maximizing price system is susceptible to "centralization from within," and worse, these centralized entities are not publicly accountable.
(Note that I say "usually" and "might be" above in the sense that anything can be done badly. Crony capitalism, for example, is a profit maximizing price system done badly, and even Soviet-style bureaucratic centralization might be better. At some point, theory must give way to execution.)
Looking at the problem this way, the real problem is not centralization or distribution, not a "price system" (whatever that is); the real problem is private profit maximization. Communism is, therefore, simply what follows from eliminating private profit maximization (i.e. private ownership of the means of production). Soviet or Maoist centralization is one possible consequence, but not the only consequence.
I've outlined one possible alternative, which I'm not entirely happy with. Here's a brief sketch of another:
First and most importantly, when I talk about government below, I mean a radically democratic government, where all the citizenry are substantively and frequently engaged with public policy and, more importantly, engaged with the actual implementation of public policy. The people may employ a civil service to manage routine and rule-based activities, but the people have and exercise sovereign political power. In other words, I am presuming the radically decentralization and distribution of policy and executive political power.
Second, every person (with democratically decided exceptions) earns the same hourly wage. Within reasonable limits, people can choose to work more or fewer hours, but the hourly wage is constant. Everyone who can work has a social and legal obligation to do so. Under no political or economic system I know about can individuals exercise the actual freedom to work any job they choose, so there are social and economic constraints on what jobs a person can choose between, but no individual can be explicitly forced to take a specific job. Everyone able to work at something socially useful is guaranteed the opportunity to do so, and if there are more people who want a specific job than can be usefully employed at that job, objective and fair procedures determine who gets those jobs. If there are fewer people who want a job than is needed, the people will have to democratically decide how to respond; raising the hourly wage for that job is one possible response.
Third, all firms other than in obvious monopolies (obvious monopolies such as water and electric power distribution or mass transit, with always-declining marginal costs, are directly run by the government, and the workers in those industries are unionized employees of the people) are worker-operated. Firms are not private profit maximizing: they may only pay themselves the standard hourly rate. Once in operation, firms rely on the government for circulating capital, which they must obtain at the beginning of every accounting cycle and pay back at the end. They must price their goods and services appropriately; if they are unable to repay their circulating capital, they automatically (without direct political action) shut down, and the workers must find new jobs (which will always be available); only direct and active political action by the people themselves (never the civil service) can a firm survive illiquidity.
Additionally, firms may not save money from one period to the next. If they run a surplus above wages and circulating capital, they must give it to the government. Indeed, the government can and should require a surplus, usually some fraction of start-up and circulating capital. Failure to deliver a required surplus entails automatic shutdown unless the people actively decide otherwise.
Fourth, all start-up capital (fixed capital, initial circulating capital, and initial wages) are also provided by the government, with some institutional limitations. Each individual may draw on some guaranteed start-up capital; individuals can pool this start-up capital and within reasonable but generous limits (i.e. the business must not be a completely obvious waste of time and resources), start any kind of business they choose. Local and regional governments and the national government — only on active political decisions — can also directly offer start-up capital for businesses deemed socially useful and under-represented. No one, however, can be forced to start up such businesses; individuals cannot be denied guaranteed employment if they do not join the government's preferred businesses.
In this system, firms lack the strong incentive of private profit maximization, but they still have a weak incentive. If the workers operating a firm like their jobs (and if they didn't, because alternatives are available, they would have already left), they want to be as efficient as necessary to stay in business and keep doing the jobs they enjoy.
Let me tell a story.
In the People's Communist Democracy of North America, I want to buy an electric scooter. I search the web, and find out that the only electric scooter available is Acme's, but it's under-powered, low-range, and super-expensive: I'd have to work 40 hours a week and live on 25 hours pay for two years to get one. I think I can make a better electric scooter, and make it cheaper, and I think that would be a fun thing to do.
First, I go to the government's consolidated capital availability website, and see if the government is offering capital for scooter manufacturers. If there is, I'm in: the government will supply the start-up capital. But there's not. Sigh.
So I go to my local council. I sign up for a speaking slot, and when it's my turn, I pitch the idea to the meeting and call for a vote. If a majority votes for it, our delegate goes to city council and asks if the city will provide the capital or ask the delegate to the regional council to pitch the idea there, or bump it up to the national council. However, at any point, the local, regional, or national council might say, "No, that's a stupid idea. Nobody but wants better electric scooters," or, "We've seen a hundred proposals for new scooters, and none of them were viable." This road is blocked. More sighs. But all is not lost.
I can draw on a my guaranteed personal capital. I talk to my friend J, a mechanical engineer, and my other friend Alice, an electrical engineer, and they think an electric scooter is a peachy idea. We advertise for someone who's interested who knows about industrial engineering. (I'm an accountant, financial analyst and market analyst.) We pool our personal capital, and come up with a solid plan to show that we really could make better, faster, and cheaper scooters, and people will buy them.
I now have three options. First, our team has no incentive to keep our plans a secret. We can call Acme scooters, show them our plans, and encourage them to make better, faster, and cheaper scooters. If our plan is good, they have an incentive to build them, and sell one to me. I'm happy — I have my good scooter, and I can work 40 hours and live on 30 hours pay a week to pay for it — and I can move on to a new project. But let's suppose they're dumb and refuse.
I can go back to the council with a real plan and ask again for capital to build a scooter factory. If they refuse, I find 20 or 30 people who want to build scooters and who still have their guaranteed personal capital and start one anyway, and we all have fun building electric scooters. After all that, if I can't find 20 people who want to build scooters, then it's probably a bad idea. The capital I used to build the plan is wasted, but I'm not going to lose my home and I still have a job. If I want to work some extra hours and pay back the capital, I can try something different in a year or two.
By design, no one can get rich being innovative. On the other hand, no one can go broke and be ruined for life for innovating and failing. Democratic innovation!