Monetary system (issuance and transfer of cash) is a social problem with billions of participants involved.
When I pay you by a paper printed note, paper money, you check the authenticity of the bill you receive from me by examining its signature (put it this way) and we are done. But when there is no famous signature, (cryptocurrency problem domain) the whole society is involved and should confirm my balance and your ownership afterwards. There is just one monetary game playable by 2 participants: physical payment of cash over the counters, other scenarios fall in the most sophisticated and sensitive game played in the world ever: monetary systems.
Are we clear? The whole Bitcoin network is trying to solve a single transaction between 2 participants. It is because the 'thing' that is being transferred is a social phenomenon: part of a balance which is the result of a long history of other transactions. [...]
I'm not sure how the above relates to the Byzantine General's problem.
PoW-based-consus is not about "solving a single transaction between 2 participants". It's about deciding on the "correct" transaction if there are multiple conflicting ones, ie. solving the double-spend problem. Money as a social phenomenon has nothing to do with it.
Double spend is solved by PoW based blockchains like Bitcoin with
transaction ordering i.e. maintaining the ledger which also includes coinbase transactions (issuance of money), hence a whole monetary system with multiple participants.
No P2P transaction is considered valid unless it is stoned in the ledger and it won't get there if it is double-spend (or violates other network rules) . I maintain that only simple hand-to-hand cash transfers fall into the category of 2 participants monetary problem.
To my understanding the Byzantine General's problem only applies to n > 2 participants
Not really.
The N>2 participants may always be considered as (N-1)! pairs. And a single one-to-many transaction could be split to many one-to-one. Thus, the Byzantine General's problem for N>2 can always be reduced to (N-1)! two-participant's solutions, if one ever existed.
What does treating counterparty-pairs like singular market participants have to do with how a pair of market participants negotiate a channelstate between themselves? We're still talking about solving a 1:1 game. The above sounds like breaking down the Byzantine General's problem into a bunch of Byzantine dudes with inner conflict caused by multiple personality disorder.
It is a reductionist approach to monetary systems which is radically different than bitcoin that uses Byzantine Generals problem/PoW based consensus for modeling/managing them. The question would be: Does it deserve to be considered a legitimate approach comparably useful as bitcoin?
Obviously, using a trusted escrow for securing a single 1:1 cash transfer is possible. So one may suggest a escrow based model/solution for monetary systems (instead of Byzantine/consensus) e.g by stacking up some supplementary techniques to eliminate routing challenges, etc.
Actually, we have banks already as an implementation of such a solution in which central banks act as top level escrows for intra-bank clearance procedures.
For LN you have bitcoin and htlc as the escrow system. It could be considered an improvement compared to traditional banking, escrows are replaced by a trustworthy decentralized system and it works somehow (if not now, may be in the future, after it becomes
matured).
But is it really enough to be more secure than banks? Is it what people really need and would take it as an alternative to their banks? I don't think so.
Bitcoin's
primary incentive to approach monetary system by Byzantine problem model and PoW based consensus solution is NOT security considerations. It is decentralization and
resistance axiom.
Folks who have joined bitcoin recently or have lost their faith in it gradually, have no idea about what resistance axiom is and why it is time for setting money free both from debt/inflation and from censorship/surveillance and state control. Trojans like Vitalik Buterin has gone that far to claim it almost impossible to have a system both decentralized and secure and at the same time with acceptable performance. (Check his ridiculous
trilemma shit).
LN won't get mass adopted because security (against compromised banks) is not an urgent priority for people to convince them for transition. And it has roughly, nothing to offer for decentralization and resistance.
On the contrary, routing (you need finding a path to your peer) and liquidity (you need money to deposit/block for every channel) problems leave no space for decentralization. A lot of literature exist out there discussing centralization implication of LN you are welcome to check them.
So, this is it. We have an alternative approach to
p2p electronic cash systems (other than Bitcoin and its Byzantine model) while being a bit more secure than traditional banks (still, less secure than bitcoin) but eventually resembles a similarly centralized hub and spokes topology just like them.
And what's the problem about LN deferring the Byzantine General's problem to the blockchain?
No problem, as long as we are not counting on it as a serious proposal/solution for
scaling bitcoin. It degrades the same bitcoin features that are of vital importance in the specific period of time we live in:
decentralization and censorship/surveillance resistance.