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Regarding the fact that in Proof-of-Stake, a stakeholder will be elected randomly as the next validator in each epoch (or each round), logically, in each round there is only a single validator, and so a single proposed block. With these conditions, is there still the possibility of occurring a fork in each round? 

Edit: According to the answer by @Murch , we can say "author of the new block" rather than "validator". Nevertheless, if in each round, only a single author is elected to write the next block (as a winner), whether this block will be validated by the rest of network or not, in this round, only a single block has been created and so no fork occurs. Is n't it?

Concerning a part of @Murc's answer: "If there is actually just a single participant that can author the next block, there would obviously be no possibility of a fork, but that would come at the cost of the blockchain grinding to a halt when the sole author does not issue a block."

But, we have a similar situation in Bitcoin, when a single miner is the only winner of PoW (in most of the case) to be the single author of the next block. This block then will be broadcast to all the miners. If PoW's answer is correct, the block is accepted.

Related question: Proof-of-Stake: How to prevent someone from being always selected as an author of block?

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I think this question has a faulty premise. What usually gets elected in POS systems is the author of the next block. The author of the next block is not the only validator of the blockchain. Every single full node validates the entire chain, so an invalid block will be rejected by all other participants.

Whether or not there is a possibility of a fork depends on the nature of the authorship election. If there is actually just a single participant that can author the next block, there would obviously be no possibility of a fork, but that would come at the cost of the blockchain grinding to a halt when the sole author does not issue a block. Systems I have investigated had some form of backoff strategy to allow multiple authors with different priority to issue blocks, or made it just magnitudes easier for the elected author to find a block.

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  • I added an "Edit" to the question. I'd like to know your opinion. Thanks.
    – Questioner
    Sep 17, 2020 at 16:04
  • So, do you in each round, multiple authors will be elected? Thank you if you could confirm.
    – Questioner
    Sep 17, 2020 at 16:15
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    That edit is just doubling down on the tautology of your question: under the premise that there is only a single author creating a single next block, there is no fork. Obviously true but also completely uninteresting as that's not a workable system (except as a permissioned blockchain with a single central author) because it would suffer liveness issues immediately and would be trivially DOSable.
    – Murch
    Sep 17, 2020 at 16:15
  • Concerning a part of your answer: "If there is actually just a single participant that can author the next block, there would obviously be no possibility of a fork, but that would come at the cost of the blockchain grinding to a halt when the sole author does not issue a block." We have a similar situation in Bitcoin, when a single miner is the only winner of PoW (in most of the case) to be the single author of the next block. This block then will be broadcast to all the miners. If PoW's answer is correct, the block is accepted.
    – Questioner
    Sep 17, 2020 at 21:28
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    That is a false equivalency. In Bitcoin all miners are eligible to find the next block and it is the discovery of the block that determines the author. The way you phrase it, you make it sound as if the author is determined first and then they craft the block which is not the case.
    – Murch
    Sep 17, 2020 at 22:15

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