How to pronounce “quorum” in English

that quorum can vote for the irrefutable statement.

So quorum slices are sets of nodes that include v itself.

and still have a quorum left over with which to make progress.

And a quorum slice is a set of nodes that v believes is important enough that if the whole quorum slice agrees on something, then that thing is true.

And one of your quorum slices is vaguely analogous to in the inter-domain routing setting of two ISPs deciding to peer.

We can say that quorum U is just a set of nodes that contains at least one slice belonging to each one of its members.

And you have quorum-- each node also, to make this even simpler, has only a single quorum slice.

And that quorum slice would include a failed node.

you'll still have quorum intersection.

Or your quorum slices were too small or were poorly chosen.

So any two quorums will intersect in at least one node.

So therefore any two quorums that vote for a value will vote for the same value.

And this guarantees agreement because the quorum size includes a majority of nodes.

or at least have a quorum vote for the same value.

And if you actually have a quorum that votes to commit n, x, then we'll say that it's safe to output the value x.

You actually need there to be a quorum.

So that will convince everybody that a quorum voted for a.

And I'm representing the quorum slices by drawing arrows from a node to all the other nodes in its quorum slice.

then we say that the quorum has ratified the statement.

So ratifying a statement means an entire quorum voting for it.

that it's almost like quorum sensing in bacteria, if anybody knows what that is.

We need to say that any quorums need to share a non-faulty node because a faulty node can just lie and give contradictory votes.

What happens if all your quorums intersect at in the intersection of two quorums because it's entirely of malicious nodes?

And now we're going to pick some quorum sized T where T is greater than N over 2.

So if you have N nodes in your quorum size is T, then the minimum overlap between any two quorums is going to be to 2T minus N. So what

And so if you have N nodes and a quorum size of T, that means you can tolerate up to N minus T failures

f, and the quorum size T to be 2f plus 1.

And you can think of deciding to put somebody in your quorum slice.

believes that three of those nodes constitutes a quorum slice.

And it guarantees safety for well-behaved nodes that enjoy quorum intersection despite the ill-behaved nodes.

And if you reach a point where there's a whole quorum U in which every node has voted for the same statement,

Suppose your system is configured such that you have two quorums that are entirely disjoint.

So you're not going to have two quorums voting for contradictory statements.

They all say, we saw a quorum vote for the value a.

They all say, we saw a quorum vote for a.

So in fact, the smallest quorum that contains v1 is a set of all nodes in the system, v1, v2, v3, v4.

And the view would never be able to hear unanimously from one of its quorums because each of its quorums would include one of its quorum slices.

That's equivalent to saying that the correct nodes have to form a quorum.

And out of that, you can discover quorums and decide when a quorum has actually voted for something.

And great, now all are quorums intersect at v7.

The stalwart three invited me to re-join, and four made a quorum for business purposes.

In order to do anything in the school, we need seven parents for a quorum.

In order to make any changes, we need seven parents for a quorum on our PTA.

In this example up here, you can notice that quorum A here has all voted for the value 9.

Then you'll never be able to output any value because no value will ever actually have a quorum voting for it.

And if for some reason not everybody can see the quorum that voted for 3, f because maybe some nodes failed or something, that's fine.

or one of them is telling the truth so I might as well assume that a quorum has voted for a without actually losing safety.

So each node in the system V is going to pick one or more of what I call quorum slices.

that were chosen by node v. And so now we can define a quorum.