I have so many objections. First, the basic logical outline I've laid out: "If most users are honest, the system works as intended, with or without X. But if most users are dishonest, X cannot prevent them from abusing the system. Hence X is either redundant or useless in terms of ensuring that the system works as intended." Can you poke a hole in this line of reasoning?

Doesn't matter what X is at this point. I laid out a logical proposition. You cannot refute it by showing that the assumption is "incorrect", because it's given. You can only refute it by showing that the assumption does not entail the conclusion.

It's kind of relevant... IT IS the original question.

Assuming that your assumptions are correct, your conclusion is correct. However, if your assumptions are incorrect, your conclusion need not be correct. I can propose a branch of mathematics where it's given that 2 + 2 = 5, but it won't give any useful results because the premise isn't true, it's contradictory.

@rytan451 If I define "the system" = Bitcoin, X = "All users are eating brownies on Sundays", is the proposition correct?

@rapt The proposition is correct assuming the premises are correct. With this X, the premises are correct, thus the proposition is correct. However, your initial X, the proof-of-work, does not fit the premises: if most users are honest, the system still may not work as intended due to the actions of a few malicious users. I'd challenge you to create a bitcoin-like system with no proof-of-work or proof-of-stake that is nonetheless proof from a minority of malicious users.

@rytan451 "if most users are honest, the system still may not work as intended due to the actions of a few malicious users." Explain why a system with a majority of honest users, without PoW, but with less computationally expensive rules such as "grab the next block from some agreed resource" and "never reverse the blockchain", will fail where Bitcoin will not, assuming the same type of other limitations exist, e.g. vulnerability to Sybil attacks etc.

Assuming negligible PoW cost, there's a way to "buy" things without paying for them. First, purchase the item with Bitcoin. Second, wait for the item to be received. Third, generate a load of blocks on a different branch from your transaction. Therefore, the new load of blocks is the new "valid" transaction history, and therefore your transaction to buy the item is invalidated (though you keep the item). If you argue, "the rest of the users will have made much more blocks; it's impossible to catch up", then that's already a rudimentary PoW system. I'll explain more in an answer.

@rytan451 The majority of honest users enforce the rule "never reverse the blockchain" which I specified. This would nip that attack in the bud. If that was your strongest objection, then my proposition is correct.

The "Never reverse the blockchain" rule would be based on... the timestamp of the block being released? The order the block is received? If the former, then my answer below is valid. If the latter, the order the block is received can differ for each user, thus each user will end up with multiple differing blockchains which can neither converge again.

@rytan451 combine it with the 1st rule I have specified. Most honest users will see the same blocks being added.

"Grab the block from some agreed resource" How will the resource be agreed upon? Using a byzantine fault tolerant consensus algorithm? There are very few algorithms that are byzantine fault tolerant and relatively computationally efficient with the number of agents as Bitcoin has, and one of them is Bitcoin's proof of work. (I say very few because I'm not certain if there's only 2: proof of stake and proof of work)

@rytan451 "How will the resource be agreed upon?" exactly how it's done in Bitcoin etc: by relying (although you may not realize it) on the "honesty" of most users. Seems like you have not read the article I linked to in my original question, nor have you read my other comments related to this page.

@rapt you misunderstand some important points, but you seem more intent on arguing that you are right than stopping to consider this misunderstanding (that several users have pointed out in an attempt to help you).

A system which must decide ’which block is next’ without a central coordinator is non-trivial to design. It is at huge risk of Sybil and DoS attacks, no matter the number of honest participants. PoW is what mitigates this Sybil attack. Without PoW, a single bad actor could destroy the ability of the network to reach consensus, by submitting blocks maliciously