Easy, you simply make the decisions within the confines of the shadow hierarchy that exists within all flat organizations.
Suppose your company has the idea that they want to identify and reward natural leaders and/or those who test limits and push through boundaries.
One way to do it is to tell people your organization is flat, then watch for the people who don't buy that and instead see an opportunity to take charge.
You create a situation with a little bit of an artificial and completely intentional power vacuum, then you watch who takes it upon themselves to step in and fill it. By holding a bit of a vacuum, you encourage these people to show themselves. (And I'm convinced management is actively watching to see who takes that bait.)
I'd say these are the most common responses: (1) never reach awareness that it's happening and continue to take flat at face value, (2) see it as opportunity and take advantage of it, and (3) see it as unnecessary game-playing and dislike it.
Whether 2 or 3 is better is an interesting question. It might separate the practical people from the idealists, or maybe it separates the self-interested from the more community-minded. I can see some of both, personally.
EDIT: I don't necessarily want to be completely dismissive of the idea. There's something to be said for creating situations that allow for people to stretch and try out new roles. That's how people develop. This is informal and stealthy, but it is a way to do that.
In my experience, in the power vacuum there are several types of people:
1. Those who are blind to it
2. Those who want power and have charisma
3. Those who want power and lack charisma
4. Those who do not want the responsibility that comes with the power, but take it to save the team
5. Those who do not want the responsibility and explicitly avoid it
The problem is that those five categorizations are independent of competence, in terms of technical skills but especially in terms of leadership skills. So if you do this sort of social experiment, what you get are people who want power regardless of competence.
Now if that's what you're looking for, then by all means, do it, but I'd bet that you're actually hoping to find the capable ones, not the power seeking ones.
I don't have a good answer for how to set up a self-sustaining organization that consistently surfaces excellent leaders, because I've never seen one, but I'm pretty sure the power vacuum won't do better.
While I'd personally argue that people development is an essential duty of management, they may not see it as important. Also, in some cases, management may just see it as a way to be less rigid.
I'm not in favour of flat systems for exactly this reason. I think they try to solve the problem of bad leadership structurally, by simply pretending to abolish leadership. IMO, it would better be addressed personally - e.g. by investing in leadership training or vetting candidates for leadership roles more thoroughly.
Business schools use a framework of formal power (job title, authority, etc) and informal power (influence and likability).
The most effective organizations are the ones where the formal power structures are very close to informal ones. People know how to make decisions. Flat organizations end up being run by the loudest voices in the room.
Ironically, flat organizations with largely informal power structures are often slower to make decisions because one person can become a huge bottleneck on decision making without realizing it. It can also be culturally corrosive: informal structures encourage Machiavellian behavior and the most Machiavellian people tend to rise to the top — which creates a terrible work environment for everyone else.
There's a nice parallel here to how parliamentary democracy arose. And conversely, there's no point having a chamber full of the people who you wish had power, if they don't have it.
There tend to be problems when founders step back from the top of the formal power structure. Steve Jobs remains the best example I can think of; he wielded immense influence within Apple in the early 80s, but was ultimately a destructive presence once he no longer had formal power because he would go around his bosses to build his pet project (the original Macintosh) and created a corporate culture of distrust and deception. When he left, Apple fell apart culturally and really had no product vision until he rejoined a decade later and resumed the role of founder-CEO.
Reminds me about the stuff I've read about Valve. In theory, and maybe if you have strong healthy de facto leadership it could work. In practice it seems more like an excuse to dodge responsibility, leading to pretty toxic places to work - but maybe there's another side to it.
I would say that the key difference is that in the traditional model I can learn about my potential bosses during the interview process. In the valve model I don't even know who my bosses will be during the interview process. As people like to say, interviews are a two way process.
Update: I read about it and no, they are basically anarcho syndicalist and overall owned by a enligtened/benevolent set of owners.
Align/get yourself in one that works and is healthy for your development and you can thrive. If not, then leave as quickly as you can. Just MHO.
I won't name names, but a company that I worked for was very web-like, which felt good at first because it seems more "fair" or democratic, but it lead to constant confusion, infighting, communication failures, etc., and I discovered that it lead to two forms of employees: hogs that managed to eat more from the trough through clever maneuvering, and "homer simpsons" who figured out they could be lazy and not suffer serious consequences since their title was nebulous and the chain of command was diffuse(an individual with poor performance didn't reflect that badly on a superior).
The team that I worked on functioned mostly as a web, and that actually worked well because we were only 6 people at most, but an entire company functioning as a web is a nightmare.
Congress and President have, as I understand it, a mutual veto - but in the case where both are controlled by the same party, they tend to defer to the party organisation, which in turn defers to the President. Where they don't, you get shutdowns.
The President is generally immune to congress until they do something that gets enough congressional support for impeachment. This has proven extremely hard to do so far. The President also gets significant say over any issue that doesn't strongly unify congress.
Thus, for an issue that is popular in congress and unpopular with the President, but not popular enough in congress to override a veto, the hierarchy does President > Congress (a > b means a is above b). SCOTUS almost never gets involved when it comes to passing laws.
When it comes to an issue that is popular enough congress is willing to override a veto and which is popular enough with voters that congress going against the President on it isn't a threat, then congress > President.
I don't think anyone is claiming there is a simple hierarchy that consistently applies regardless of scenario. Even in a classical monarchy the hierarchy can shift for extreme enough scenarios.
There are likely shadow organizations in the Congress and White House with their own (unpublished) hierarchy, but probably not in the SCOTUS due to its size and the implicit potency inherent in being a Justice.
When your group grows beyond 9 people, that gets harder.
"The Brethren: Inside the Supreme Court" by Woodward and Armstrong looked (amongst other things) at why Nixon's new Chief Justice Warren Burger seemed unable to push the court in a more consistently conservative direction despite more conservative membership. Part of the conclusion was that he just wasn't that great at playing the internal political games required to stay in control.
Incidentally, the main source for that book was eventually revealed as one of the other Justices, Potter Stewart. It's a fascinating read.
That's the 3 branches of government with its checks and balances.
But, other methods might be possible to wield power without hierarchy. An individual with massive wealth can consolidate financial power. They certainly depend on a system that enforces rules and protects financial interests, but can you really call that hierarchy? They might perform significant, world-changing transactions but they do not continue to control the assets once they are traded. It might be a hierarchical distribution in the "trickle-down" sense, but is not hierarchical control nor planning.
Or, if someone obtains some sort of scifi doomsday weapon and uses it to extort others, is that expressing hierarchy?