Quote from: Forp on September 13, 2012, 09:26:00 PM

In my interpretation of affairs it is important to understand that Bitcoin does not reach consensus, does not stabilize (in a common sense interpretation of the word, as in "eventually reaches consensus") and does not solve the Byzantine Generals problem.

You're right, it's important to understand the distinction: Bitcoin clearly does not solve Byzantine Generals, but hopefully it solves a related weaker problem instead. Is the weaker problem useful? I disagree with your point about the common sense interpretation - I think Bitcoin users have the correct intuition about how the system behaves.

Here's the crux of the distinction. If Bitcoin were a deterministic Byzantine Generals solution, then it would provide a claim like the following: "If you wait 6 blocks before making an irreversible action (e.g. handing over a bar of gold to a stranger), then you're 100% guaranteed not to get double-spent."

This is not one the services that Bitcoin offers to its users. Instead, as you say,

Quote from: Forp on September 13, 2012, 09:26:00 PM

Bitcoin is a highly probabilistic, random algorithm which "only" guarantees a certain probability distribution over time - which, admittedly, after a number of blocks is so centered, that we can treat the outcome as having reached consensus for practically all reasonable expectations.

The generally accepted language for randomized consensus algorithms is that they "eventually converge with probability 1," mostly for the reason that this is a mathematically friendly statement work with. (See for instance Stumbling over Consensus Research: Misunderstandings and Issues) But this isn't necessarily what users want. Certainly the 100% deterministic version would be more user friendly, but it's not possible on an anonymous network. My opinion is that Bitcoin is the perfect balance - strong enough to satisfy demand, just weak enough to be viable. Here's a way of closing the gap between what we have and what we might want:

(Fork Insurance) Imagine there is a market for Bitcoin insurance. A pawn shop that wants to accept Bitcoin payments would probably want to purchase a fork insurance policy. The insurance policy would offer the 100% deterministic option to its customers: if the merchant dutifully waits for 6 blocks before letting the customer walk out with a gold bar, then the merchant is insured for up to $1000.

If you use Bitcoin directly, you're responsible for your own risk assessment and management. What's excellent about Bitcoin is you can do this anonymously yet benefit from the worldwide amortization of mining work. If you are incapable or unwilling to make your own risk assessment, then you can hire someone to make this sort of decision for you. Note this is an individual decision - there's no such thing as an official Bitcoin insurer. Also note that payment processors like BitPay already provide this interface to their customers. They put money in your account right away. Double-spends are their problem. So is evaluating the health of the network.

What's the price of Bitcoin insurance? If you were going to insure a Bitcoin exchange, how would you calculate that risk? And would you put more effort into auditing the exchange's php scripts for silly vulnerabilities or would you focus on shoring up against the dreaded 51% doomsday attack? Are there any Bitcoin actuaries who have started on this sort of modeling? I have no idea what the legal and regulatory environment is for this kind of insurance - is it more or less intimidating than money transmitting?