ok here is the formula.
a = percentage of the total network hash rate controlled by attacker (expressed in decimal notation)
b = # of blocks
n = likelihood of discovering b # of blocks for a % of total network hashrate before anyone else
f(n)=a^(b-1) (im sure this can be simplified but w/e it works)
So back to our 2 blockchains. If the attacker wants to double-spend and has 25% of the total network hashrate, than his chances of discovering 1 block are 25%. 2 blocks in a row is 12.5%.
and after 60 minutes like bitcoin wants you to wait. its 4.3368087e-19.
So the point is that there is an inherent advantage to security resulting from fast blocks. As such the acceptable orphan rate would be a reasonable trade off. It wouldn't come from some effort to approach as close to 0 as you can. Once its too high of course single actors get a bigger advantage since they dont have to wait to start mining ontop of their own block. But the preferable trade off would probably be a higher orphan rate than most people think. You would have to develop some models to get a good idea, but probably 5% is totally reasonable.
These time scales just don't matter. If you want 5 second transactions, you can't get it this way. If you have to wait an hour for effective finality, you can wait a few hours. There is no significant benefit that would offset the disadvantages of an unstable network and pressure toward centralization.
Ok well its completely wrong to say the timescales dont matter. This is a black and white fallacy. There is no on off switch here between hours and seconds. Its a smooth sliding scale all the way across the spectrum between them. At each point on that scale there is a marginal consumer somewhere.
I don't agree. The significant benefit is from real time (up to maybe 30 seconds) and then pretty much everything else is a minor benefit from going faster or slower because it isn't real time. 10 minutes vs. 20 minutes is really not a game changer. This has been discussed pretty widely in the context of Bitcoin recently. You should review some of those discussions (I don't remember exactly where but I saw them on reddit) because they apply almost exactly the same to Monero.
Even a block time of 30 seconds doesn't give you "real time" 1-confirm transactions because it is random. You could have to wait several times the average (and that will happen regularly).
Again i think you are miss characterizing the situation. Again no such black and white line exists where something falls on one half of an imaginary line and everything else on the other. its a perfectly smooth sliding scale from the lower bound (probably something like 30 seconds) to some upper bound (probably something like a day) with an in-finite number of points between any two points. at every point on the scale there lies a group of marginal consumers who appreciate that particular time threashold for their purposes. There are people who benefit a lot from 2 minutes instead of 3 or 3 instead of 4 ect... You cant artifically devide people into two clumps who are fine waiting hours and want it done in 30 seconds.
Though i will admit there is a tendency for people to clump on either end of the spectrum and fewer people to fall in between and that is a counter argument to be made for why less weight should potentially be applied to my argument, it however is not an argument for why my argument should be discarded entirely. Because plenty of people would still fall in between those two clumps.
Additionally there is no black and white line between acceptable number of orphans and not. its a sliding scale just like the one before. you can always have more and always have less, you just have to chose. what im arguing for here is simply a line of reasoning that should be factored into how you decide to make that choice. thats all. its not saying we should have any
particular target. i.e. Its not an argument for or against 1 minute block times.
And if you want to look at the 10 minute situation, its not 10 minutes vs 20 minutes in transactional security. that would be a bigger deal than you are giving it credit for i think if it were the case but it isnt. in this admittedly simplified model which assumes 0 orphan rate but i think is still a useful tool for thought, a transaction with 10 blocks in 10 minutes is 512 times more secure than a single block in 10 minutes. And again thats not just at any 10 minutes, we could make similar models for any two time values you wanted, where ever you personally thought they were most useful.