That would depend on how that local community collectively decides to operate. Most would likely opt for community consensus for something so serious, where an individual cannot forcibly eject someone from the community if there is not community consensus.

The question of majority vs. supermajority is not the question; the question is whether that process is the only means by which the society accepts casting one of their own out.

A state is a centralized hierarchy of power that operates in a top-down structure, where the people at the top of the hierarchy have the ultimate say on what happens to those at the bottom of the hierarchy.

In which case most modern states aren't states at all.

Delegation, in contrast to representation, stresses that the purpose of the delegate is instrumental. The delegate acts like a rubber belt connecting two gears; they are simply a tool for the exchange of force and influence between two greater bodies. They are not the component that creates or directs force, but only act only to guide it. The relationship of the delegate to the organization is like one of a secretary.

Okay, but do you not realize this is how representatives in extant systems have defined themselves since time immemorial?

What makes this incarnation different?

Representation is the opposite. It is a system where the representative who presents the interests of their people is in full power. The delegate is seen simply as a means for directing the ideas of one group to another. It is something that can be fulfilled by anyone The representative is someone who makes the decision of what ideas the group should have altogether.

Again, that's nowhere near how most representatives or representative systems would describe themselves, or, realistically, be described.

It is something that requires political parties, party elections, general elections, campaigning, and an exquisite ability to measure the honesty and integrity of the candidates.

And... you don't find that elections, campaigns, measuring honesty or integrity of candidates, or political tribalism is something anarchist society will have to deal with?

When a society prospers or suffers, blame or praise always go to the organizing force that directed it. Within Delegation, that blame or praise goes to the common people, who must live with their mistakes, or be elevated by their willingness to change.

You do realize that's the exact argument we use today in representative democracies, and most people shrug it off like water off a duck's back, right?

Within Representation, that blame or praise goes to the politician, who is so far removed from the people, that whether they’re guilty or not won’t change the situation the people are in.

And why would the people not scapegoat their delegate for any issue they felt sufficient guilt about? "It wasn't explained clear enough, that wasn't what we meant (and you can't prove it was), we only meant it under very specific conditions, etc"

What is the difference, practically speaking, other than the Representative is now the PEOPLE'S Representative? And yes, that's intentionally invoking the coat-of-paint used by ML societies. Not to equate this anarchist polity proposed with MLs, but to point out that, just as MLs often dress up their structures as though they're new and innovative, oftentimes all they are is fundamentally the old structure with all of its previously flaws and failings - only now those flaws and failings are considered 'politically incorrect' to address.

One system focuses on the people as the guardians of their own welfare; the other focuses on a single person to be the guardians of all.

... that's generally the exact opposite of how representative democracy describes itself, and, again, works.

There is more to it than simply stating that the Delegate can make no decisions and stating that the Representative can make decisions. Both of these systems have developed their own institutions for encouraging either the Authoritarian or Libertarian trends as they see fit. Within Delegation, for example, a delegate can be removed at any time, for any reason and for no reason. Since they are simply the carrier of the group’s demands, it is for the group to decide who is best at any moment for this purpose. Removing a delegate, then, is like reworking the positions of the laborers in the factory – a purely technical matter.

... you do realize that many modern polities have recall elections available for any reason, right?

The Representative does not have this fear, however, of “Recall.” The Representatives of nations, from Germany to Russia to the United States to France to Britain, have always plunged their people into wars, concentration camps, and forced labor – and yet, one could be assured almost, that such miserable conquests never would have started, if these were simple delegates, and not representatives, of the people.

In what fucking way? Other than pointing out that many polities which do have instant recall even for the executive still plunge into wars and genocide, in what way does the 'delegate' stop people from making self-destructive decisions? Fuck, man, the Iraq War, unjust as it was, had, what, 80% approval in the general population when it started? Whose use of recall was going to unscrew that pooch?

The Representative was elected, whereas many delegates some delegates are elected and others are chosen by random ballot. At the start of one of these imperial wars, like the Boer War or any number of the Moroccan Wars, the representative had survived party elections, regional elections, and finally, a national election. Imagine if one of their voters said, “Actually, we don’t like your ideas now, and we want someone else to carry our interests to other nations, because war is not our interest.” The representative could point to a thousand courts that would stand up for them and a million soldiers with bayonets for anyone who would still disagree.

You do realize that most wars are not started in the face of overwhelming popular opposition, right?

... right...?