How does Nxt agree on a chain when "active accounts" can be easily faked?

Question

From what I understand, in Nxt, blocks are mined (or forged) using a system based on Proof-of-Stake where block creation works similarly to a lottery: people have tickets, and the more tickets you have, the greater the chances of winning and therefore forging a block. Tickets in Nxt are just coins you own in the system.

What I don't understand is that for each block creation, the winner is found from a pool of "active accounts" which so happens to be people that are online at that moment. Based on specific things (like how many coins one has), the winner is then found. My concern is that someone can forge a new block without caring about the "active accounts", he sort of pretends that nobody else is online. So he'll mine it for sure, as he's the only one, and then he'll broadcast it. He keeps doing this for the next blocks and so on.

What's stopping other peers from accepting his chain?

Answer 1

Linking to the discussion on the NXT forum https://nxtforum.org/general-discussion/academic-questions-regarding-pos-and-nxt

Answer 2

As you know from your previous question, a node is entitled to forge a block and submit it to the network when

hit < BaseTarget * EffectiveBalance * TimeSinceLastBlock

where new hit and BaseTarget values are computed from the last block, the hit value being effectively random and the BaseTarget being adjusted to maintain a steady blockchain growth rate of about one new block per minute.

All nodes running the NRS (Nxt Reference Software) use the same formulas to compute these values, and therefore if all of those nodes are on the same fork of the blockchain they will all agree on what the values are. Any new block received from another node is checked to make sure that the rule above was followed. If not, the block is rejected.

It is possible for the blockchain to fork, even when all nodes follow the rules, due to several nodes becoming eligible to forge at about the same time combined with network delays. Or, a subset of nodes could become isolated from the main network for a time.

Once a fork occurs, the competing blockchains will have different tails and all the blocks that make up the tails will have different hit and BaseTarget values. All nodes running NRS will chose the blockchain with the greatest cummulative difficulty, where

cumulativeDifficulty = cumulativeDifficultyOfPreviousBlock + (2^64 / BaseTarget)

cumulativeDifficulty grows with each new block, moreso when BaseTarget is small (more difficult to get a hit).

If a subset of nodes is isolated for a time, those nodes will continue to forge; but because they have a smaller combined balance, initially forging takes longer. BaseTarget will adjust larger to shorten the time between blocks, and thus cumulativeDifficulty will not grow as fast.

When this subset of nodes reconnects with the main network, its fork of the blockchain is considered by the main network (if less than 1440 blocks have been forged during the isolation). But because the main network has a greater combined balance, it will have a greater cumulativeDifficulty and therefore reject the competing blockchain. Likewise, the subset of nodes will consider the main fork and accept it unless more than 1440 blocks have been added on their fork, in which case a blockchain rollback or a fresh blockchain download is required.

This is how consensus is achieved on the network: it is governed by the nodes that have the greatest combined balance.