Your solution to the gold sharing problem doesn’t work that well, because that solution allows any pirate to give an ultimatum to any other pirate of the form “Write X less than you actually had, because I am going to write X more. If you don’t do that, you’ll lose it all.” And that’s the Ultimatum game.
Correct. The solution to that is to prevent any communication beforehand. In principle, someone could still try this strategy acausally, but that’s the sort of thing which everyone else can prevent by simply not simulating any other pirates.
The tricky part in real life is there not being perfect memory.
(However, instead of throwing the chest overboard you could attempt to catch one major defector, and toss them overboard, and distribute the remaining gold (even if the sum before didn’t quite work, but you couldn’t catch the remaining defectors):
If everyone is honest:
then coins_1 + coins_2 + … + coins_n = coins_chest.
If there’s only one major defector, then not only is coins_1 + … + coins_n > coins_chest, but
coins_1 + … + coins_n—coins_major-defector ⇐ coins_chest. (More generally, any sum of entirely honest (and entirely accurate) entries will be less than the number of coins in the chest.))
2)
If you split people up into groups ahead of time, you could keep track of the amount that a group has (more cheaply than keeping track of everyone).
I’m going to stop this train of though here before recreating bitcoin. (If everyone keeps track of a random partition involving everyone else, then will that probably be enough to figure everything else out afterwards?)
Might work against fraud detection though.
(Simpler to just remember what one other person’s amount is though.)
3)
Enough people who have more (and this is common knowledge) agree to an equal distribution. (For example ‘We were all going to use this gold to get drunk anyway. So why don’t we just spend this chest of gold on drinks?’)
4)
Not sure it has an effect but:
Multiple rounds. First round, not everyone is honest, half the gold in the chest is dumped out. Restart.
(Can be combined with method 2.)
Also, if the amounts submitted add ups o a multiple of the amount in the chest, then it can be split based on the proportion.
5)
Pick a random order to go in. Once the amount in the chest is exceeded, it is divided among those people (minus the person who went over). If someone cheats by a lot, they will probably not get it.
6)
Throw out the person who said the most, if the sum is too great.
Your solution to the gold sharing problem doesn’t work that well, because that solution allows any pirate to give an ultimatum to any other pirate of the form “Write X less than you actually had, because I am going to write X more. If you don’t do that, you’ll lose it all.” And that’s the Ultimatum game.
Correct. The solution to that is to prevent any communication beforehand. In principle, someone could still try this strategy acausally, but that’s the sort of thing which everyone else can prevent by simply not simulating any other pirates.
1)
The tricky part in real life is there not being perfect memory.
(However, instead of throwing the chest overboard you could attempt to catch one major defector, and toss them overboard, and distribute the remaining gold (even if the sum before didn’t quite work, but you couldn’t catch the remaining defectors):
If everyone is honest:
then coins_1 + coins_2 + … + coins_n = coins_chest.
If there’s only one major defector, then not only is coins_1 + … + coins_n > coins_chest, but
coins_1 + … + coins_n—coins_major-defector ⇐ coins_chest. (More generally, any sum of entirely honest (and entirely accurate) entries will be less than the number of coins in the chest.))
2)
If you split people up into groups ahead of time, you could keep track of the amount that a group has (more cheaply than keeping track of everyone).
I’m going to stop this train of though here before recreating bitcoin. (If everyone keeps track of a random partition involving everyone else, then will that probably be enough to figure everything else out afterwards?)
Might work against fraud detection though.
(Simpler to just remember what one other person’s amount is though.)
3)
Enough people who have more (and this is common knowledge) agree to an equal distribution. (For example ‘We were all going to use this gold to get drunk anyway. So why don’t we just spend this chest of gold on drinks?’)
4)
Not sure it has an effect but:
Multiple rounds. First round, not everyone is honest, half the gold in the chest is dumped out. Restart.
(Can be combined with method 2.)
Also, if the amounts submitted add ups o a multiple of the amount in the chest, then it can be split based on the proportion.
5)
Pick a random order to go in. Once the amount in the chest is exceeded, it is divided among those people (minus the person who went over). If someone cheats by a lot, they will probably not get it.
6)
Throw out the person who said the most, if the sum is too great.