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A quorum in traditional systems is a minimum number of members in an assembly necessary to conduct the business of that group. In Nano / block lattice, this is the minimum number of nodes that need to cast a vote a positive vote on a transaction, in order for the network to accept that transaction as valid.

In order for a transaction to be accepted and finalised, it needs a minimum of 50% vote quorum from the network (I.e. 50% of the nodes in the network need to agree on the transactions' validity.

I hope that answers the question? I not, feel free to let me know.

ah ok, I think I got it.

Is the positive vote just means that the transaction is valid, meaning it is signed with the proper digital signatures?

I think I'm confused because of there is also representatives, which also vote. But they vote on different things?

Correct, if the vote is positive (50% quorum from the network) means the transaction is valid and accepted.

The representatives kick in when there is no quorum from the network, they vote in case of disputes on transactions, which according to the Nano team is about 1% of the time.

Each round of voting takes approximately 15 seconds, and the maximum rounds of voting is set to 4 (1 minute) at which time the chain takes on transaction and accepts it as true while rejecting the other (only in case of disputes).