I strongly believe that while it is very effective to structure an organization in a democratic and sociocratic way, a project should be managed completely different. A project should resemble a dictatorship, authoritarian or military hierarchy with a single strong, result-oriented leader who gives explicit orders that are never doubted by subordinates and an explicitly defined hierarchy.
According to Wikipedia at the time of writing, a holacracy exists when "authority and decision-making are distributed" while, on the other hand, autocracy exists when "supreme power is concentrated in the hands of one person".
When I say organization, I mean a team, a startup, a company, that sort of thing. It's something with a brand, an office, a business entity and a bank account. The role of an organization is very similar to the role of a country or a government: to provide security in exchange for freedom. Democracy in a country, as well as in a team, guarantees equality to its members, which is the most important component of security.
A holacracy, also known as a "flat organization", technically refers to the absence of bureaucracy, special privileges, expensive furniture and private parties for top management. In a flat team, the distance between the CEO and a junior programmer is very small. They sit together in the same room, eat in the same cafe, and discuss team strategy like friends. There are no "bosses" on a flat team, only "leaders". They don't give orders, they inspire. They don't punish, they celebrate success and mourn failure together with everybody. Well, that's the idea of a holacracy. And it actually works. I've seen it many times.
However, when we're talking about project management, this very same approach will have catastrophic consequences. A project is something very different than a team. A project is a "temporary endeavor undertaken to create a unique product, service, or result", according to PMBOK. A project is something that starts and ends. The key objective of a project is to end, while an organization's objective is to survive. See the difference? A new mobile app, a conference, a new release, a round of investments—these are examples of projects. They start, and they end. We don't want any of them to live forever; we want them to finish as soon as possible, and obviously with a positive outcome.
Because of this fundamental difference, a project must be managed by an authoritative person who gives orders and has enough guts to ensure those orders are obeyed. That person is called a project manager (PM). And the project will be successful only if its management structure is strictly hierarchical, just like in a military operation. A project cannot be flat, or it will fall apart.
Since a project is a temporary endeavor, it doesn't give security to its participants. And it doesn't take away our freedom. The arrangement is different: A project gives us money and takes our time. The project basically says to all of us, its participants: "Let's get it done and go our own ways". Having this philosophy in mind and understanding the motivation of everybody involved, the PM must use instruments that have nothing to do with what keeps the organization alive.
An organization/team/company/family will stay together for a long time if we value things like tolerance, respect, patience, equality, and appreciation.
To the contrary, a project will finish successfully if we value completely different things: discipline, subordination, awards, punishments, and rules.
To summarize my thoughts, I would say that a successful company combines these two approaches by being a matrix organization that promotes holacracy in the team and autocracy in the projects it is working on.